# Cooperative Localization for Autonomous Underwater Vehicles - a
comprehensive review

Milind Fernandes, Soumya Ranjan Sahoo, and Mangal Kothari M. Fernandes and S.
R. Sahoo are with the Department of Electrical Engineering, Indian Institute
of Technology Kanpur, Kanpur 208016, India (e-mail<EMAIL_ADDRESS>srsahoo@iitk.ac.in).M. Kothari is with the Department of Aerospace
Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
(e-mail: mangal@iitk.ac.in).

###### Abstract

Cooperative localization is an important technique in environments devoid of
GPS-based localization, more so in underwater scenarios, where none of the
terrestrial localization techniques based on radio frequency or optics are
suitable due to severe attenuation. Given the large swaths of oceans and seas
where autonomous underwater vehicles (AUVs) operate, traditional acoustic
positioning systems fall short on many counts. Cooperative localization (CL),
which involves sharing mutual information amongst the vehicles, has thus
emerged as a viable option in the past decade. This paper assimilates the
research carried out in AUV cooperative localization and presents a
qualitative overview. The cooperative localization approaches are categorized
by their cooperation and localization strategies, while the algorithms
employed are reviewed on the various challenges posed by the underwater
acoustic channel and environment. Furthermore, existing problems and future
scope in the domain of underwater cooperative localization are discussed.

###### Index Terms:

Cooperative localization, AUV, Underwater, ASV, CNA.

##  I Introduction

It has been said that we know more about the surface of the moon than the
ocean floor. A large swath of our oceans remains unexplored and unmapped,
owing mainly to its massive size and the cost of operation for any survey
activity. A modern solution to this age-old problem is unmanned underwater
vehicles or UUV’s instead of human-crewed ships. While the UUV’s generally
consist of remotely operated vehicles (ROV) and autonomous underwater vehicles
(AUV), it’s the latter that is best suited for long-duration and long-range
survey missions in the oceans. An AUV is capable of autonomously carrying out
pre-planned surveys, opportunistic seeking missions, and target tracking
without human intervention and control. However, even though the AUV’s have
increased our capabilities to survey the ocean depths, they do have a few
shortcomings. First, an AUV needs a support vehicle in the form of a human-
crewed ship for deployment and recovery, which is costly [1]. Second, since
the AUV works underwater, localization is a huge challenge.

In a terrestrial setting, the localization problem is solved mainly by relying
on GPS. But for underwater environments, no such large-scale system exists.
This is because electromagnetic signals attenuate very rapidly in water and do
not propagate useful distances [2], [3]. In the absence of localization
references such as GPS, it is common for an autonomous vehicle to rely on its
onboard sensors for dead reckoning. But despite the advances in accuracy and
resolutions of sensors such as accelerometers, gyroscopes, compass, etc., the
dead reckoning approach still suffers significant drift from true location,
especially in large distance surveys [4], [5]. Thus, the location of the AUV
becomes increasingly uncertain. The cost of these high-accuracy sensors
renders them prohibitively expensive in missions utilizing large teams of
AUVs. A Doppler velocity log (DVL), which provides velocity measurements, can
be used to bound the growth rate of location error to some extent, as was
shown in [6]. However, the ocean floor needs to be constantly in the range of
DVL for it to be useful. This is not possible if the vehicle operates far
above the ocean floor in the Pelagic zone. This necessitates external
reference systems to minimize or bound the uncertainty in the position within
a specified range.

One of the simplest solutions is for the AUV itself to periodically surface
for a GPS fix. But this is not a very elegant solution because significant
energy and mission time is wasted for surfacing and then heading back down.
Traditionally underwater localization has relied on acoustic localization
systems such as the long baseline (LBL), GPS intelligent buoys (GIB), and
ship/surface vehicle-based short or ultra-short baseline systems (SBL/USBL)
[7], [8]. Other methods, such as those based on Simultaneous Localization and
Mapping (SLAM), geophysical features obtained using camera or SONAR imagery,
magnetic field maps, and bathymetric maps, have elicited interest in the
recent past. The reader can find an excellent review of AUV navigation
technologies and techniques in [9], [10].

The traditional localization systems, such as LBL and GIB, suffer from
installation/deployment and maintenance/recovery issues, whereas SBL and USBL
suffer from lower precision and operating range with bearing measurements
further affected by the surface vehicles’ roll and pitch. Even with LBL, the
operating range is limited to a few square kms. Underwater SLAM, on the other
hand, suffers from a limited set of available underwater features, whereas
optical solutions need clear waters and fail in turbid environments. They also
have high computational requirements and a high monetary cost that escalates
with the number of AUVs for a given mission. Another option that has gained
significant attention in recent times is the range-only single beacon-based
localization due to its inherent simplicity and cost-effectiveness [11]. The
beacon could be either static or moving. While a moving beacon falls in the
realm of cooperative localization (CL), as will be seen in the sequel, the
static beacon-based localization requires the AUV to perform fast turning or
encircling maneuvers for the system to be observable. While this is acceptable
in target tracking (where the beacon is the target), if the AUV has a specific
mission trajectory, this method cannot be used.

All the above issues have contributed to the increasing interest in
cooperative localization-based approaches, especially in AUV teams working
together. At the very least, CL requires a set of sensors that will, by
necessity, be present on each of the vehicles, such as the Inertial Navigation
System (INS), acoustic modem, and DVL. Some CL approaches can even accommodate
vehicles with lower accuracy sensors. The CL-based approach’s primary
requirement is the mutual information exchange between vehicles, using which
each vehicle can improve its respective localization accuracy.

With the growing interest in this area, the literature on underwater CL has
reached a critical mass. However, to the best of the authors’ knowledge, no
publication has yet classified and categorized this trove of information.
Thus, this paper aims to review and classify the existing literature in this
domain qualitatively. With this in mind, the contributions of this paper are
as follows:

  * •

We present an exhaustive review of underwater cooperative localization
literature for AUVs up to date.

  * •

We classify the CL approaches and bring forth their salient features.

  * •

We identify and discuss the open problems in underwater cooperative
localization.

The paper is organized as follows. Section II gives the requisite background
that underlines the operational performance of underwater cooperative
localization strategies. Section III discusses the different categories of
cooperative localization strategies and provides a detailed comparison of
various performance parameters. In section IV, a discussion on the current
shortcomings and future directions is presented. Section V concludes the
paper.

##  II BACKGROUND

In this section, we put forth some of the considerations relevant to the
underwater environment and cooperative localization algorithms. These include
the underwater acoustic channel, state estimation techniques, measurements for
state estimators, among others. This section also introduces some of the
criteria used to compare the current state-of-the-art cooperative localization
strategies for AUVs.

###  II-A Underwater acoustic channel

A water body as a communication channel is quite challenging, especially
considering the severe attenuation of electromagnetic signals, be it radio
frequencies or light. This has led to widespread adoption and advancements in
acoustic communication technologies for underwater use. Still, the underwater
acoustic channel has a fair share of issues that need to be dealt with and
kept in mind while developing algorithms that use acoustically transmitted
information, as highlighted below.

TABLE I: COMMON STATE ESTIMATORS IN UNDERWATER CL Sr. No. | State Estimator | Belief | Model | Advantages | Disadvantages | Remarks
---|---|---|---|---|---|---
1 |  Kalman Filter (KF) |  Gaussian (Mean and Variance) |  Linear |  Fast, Optimal |  Not applicable for Non-Linear models |  -
2 |  Extended Kalman Filter (EKF) |  Gaussian (Mean and Variance) |  Linearized NL (1st order Taylor Series approx.) |  Fast, NL models |  Linearization errors, Requires matrix inversion |  Unsatisfactory performance with outliers
3 |  Unscented Kalman Filter (UKF) |  Gaussian (Mean and Variance) |  Non-Linear (Sigma points) |  Lower NL errors |  Higher computational cost |  Refines only current state
4 |  Extended Information Filter (EIF) |  Gaussian (Information matrix and vector) |  Linearized NL (1st order Taylor Series approx.) |  Fast measurement update |  Slow prediction step |  Canonical Gaussian representation, Dual of EKF
5 |  Particle Filter (PF) |  Non-Parametric (Particles with weights) |  Linear or NL |  Applicable to non-Gaussian distributions |  Computationally expensive |  Can handle outliers
6 |  Maximum A Priori (MAP) |  Gaussian |  Linear or NL |  Better estimates, Estimates computed for all time steps |  Computationally expensive |  Requires storing past states.

  1. 1.

Speed of propagation: The water temperature in seas and oceans is not a
constant function of depth; instead, it varies with it. The warm waters are
near the surface, while the cold waters are near the floor. Similarly, a
column of water may consist of strata of different salinity at any location
and time, thus, different densities. The density of the water is also a
function of the depth. These spatiotemporal gradients of temperature,
salinity, and depth affect the speed of propagation of acoustic signals [12],
[13]. This is especially severe in communications that involve large
distances. While in practice, it is common to assume a constant speed of sound
(1500 m/s) underwater, it does not represent the actual speed of sound at the
instant of time and space, and thus, will be a source of error in methods that
rely on range computations for localization. However, some approaches can
estimate the sound speed profile of the acoustic channel during a mission and
compensate for any such effects [14], [15], [16], [17].

  2. 2.

Latency: This is the direct consequence of acoustic signals’ speed being much
less than RF signals’ speed. It leads to time delays between signal
transmission and reception. The transmitter or receiver might have moved in
that time, which causes an offset between the estimated and the actual
positions. This has led to the development of delayed-state-based estimators
[18], [19], [20].

  3. 3.

Propagation Path: The density changes also cause the acoustic signals to
travel along a curved path instead of straight lines [16]. This introduces
errors in range measurements, as the actual traveled distance is greater than
the exact Euclidean distance between any two points. Unlike the sound speed
profile, this effect is difficult to characterize and compensate for large
distances. In most cases, the path is assumed to be a straight line.

  4. 4.

Multipath effects: These effects are predominantly encountered in shallow
waters, wherein the acoustic signals bounce off the seafloor or surface
boundary and arrive at the receiver with a delay. These can also be
experienced in deep water missions near the seafloor. Multipath signals give
rise to measurement outliers or inaccurate range measurements and cause
significant errors in state estimators’ output. Outlier mitigation is one of
the critical considerations in the performance evaluation of localization
algorithms. Some approaches are given in [21].

  5. 5.

Bandwidth: The acoustic channel is inherently narrow-band since it operates in
the audible/ultrasonic frequency bands. This limits the number of bits one can
transmit per second. Although recent advancements have achieved up to 64 kbps
of throughput [22] over short distances of 300 m, it is a fraction of what is
achievable in terrestrial networks. This calls for CL techniques that are
robust against the limited channel capacity.

  6. 6.

Measurement noise: For mathematical and computational convenience, it is often
the practice to assume any noise source in acoustic communications and
uncertainty in measurement as being Gaussian distributed. However, as evident
from many practical experiments, the distributions are more often than not
heavy-tailed, especially in scenarios where multipath is evident [23]. This
leads to apparent errors in the location estimates generated by the estimation
algorithms.

  7. 7.

Lost transmissions/Packet Loss: Due to the harsh underwater environment,
underwater acoustic channels are far less reliable than terrestrial RF
channels and suffer from intermittent lost transmissions/ packets up to 20-50%
of the total [24]. This severely affects the convergence rate of estimation
algorithms and can even render them unstable.

As can be seen from above, the underwater acoustic channel has many challenges
in terms of communication accuracy and reliability and is an active area of
research. A comprehensive survey of communication challenges, solutions, and
open problems can be found in [25].

###  II-B State Estimation Techniques

As evident from the previous section, it is difficult to get complete location
information in the harsh and dynamic underwater environment. It necessitates
estimation techniques that can predict the vehicle’s current location with a
high degree of confidence by incorporating all the noisy and outlier-affected
measurements from the internal and external sensors of an AUV. State
estimators can be classified into three categories: a) Stochastic, b) SLAM
based, and c) Deterministic [7]. Stochastic, Bayes filter-based estimators
have found wide use due to their simplicity and computational efficiencies. A
brief comparison of the various estimators is in Table I.

While there have been many SLAM-based approaches for state estimation for
which the reader is referred to [9], [26], [27], the domain of underwater
cooperative SLAM is still unexplored except for a few works [28], [29], [30].
Similar is the case with deterministic state estimators that require exact
plant and measurement models, which are difficult to model in an uncertain
underwater environment.

###  II-C Measurement inputs for the state estimators

Figure 1: General system architecture for CL based pose estimation

The common state estimation algorithms in Table I have two stages, predict and
update. The prediction stage uses the past state and beliefs to predict the
next state. The measurement stage corrects this prediction using information
from internal and external sensors. The AUVs general sensor fusion
architecture to estimate the position of a vehicle in a cooperative scenario
is shown in Fig. 1. An AUV will have a bare minimum sensor suite consisting of
the Attitude Heading Reference system (AHRS) and pressure (depth) sensor. The
AHRS consists of a gyroscope and compass/magnetometer and provides the state
estimators with angular accelerations, velocity, orientation, and heading
inputs. Additionally, an Inertial Measurement Unit (IMU) combines an AHRS with
accelerometers, providing additional 3D acceleration information which can be
integrated for linear velocity and position estimates. The Inertial Navigation
System (INS) uses data from AHRS, accelerometers, depth sensors, and DVL/ADCP
(Acoustic Doppler current profiler) (if present) to estimate the vehicle’s
pose, also known as the dead reckoned estimate. The more expensive sensors,
such as DVL, SONAR (Side-scan/Multibeam), gravity (Gravity map-based
localization), etc., may or may not be present. The availability of cheap and
accurate pressure-based depth sensors has rendered the three-dimensional
underwater localization problem to two dimensions. This simplifies analysis
and subsequent computations. However, over time the position estimate becomes
more and more uncertain due to inherent drift in the sensors.

Fusing INS information with other sensor data, such as from GPS, range,
bearing, etc., either eliminates the uncertainty in position or bounds the
error within a desired range. While GPS is available only on the sea surface,
bearing-based methods either rely on visual information or USBL. Visual
information is subject to the water’s turbidity and is inherently limited to
short distances [31]. As mentioned previously, these methods are unsuitable
for long-distance cooperative localization. This leaves the range-based
methods, which explains its wide popularity in underwater localization. Range
information can be acquired through different means. If all the vehicles are
synchronized in time, time of flight (ToF) can be used to measure the distance
between any two vehicles. This method, also known as one-way travel time
(OWTT) ranging, has the benefit that it requires only one acoustic
transmission per range measurement and is scalable with the number of
vehicles. However, it requires high accuracy and stable clocks that are
temperature, bias, and drift compensated, such as chip-scale atomic clocks. If
synchronization is not possible, two-way travel time (TWTT) or Time difference
of arrival (TDOA) can be used [32], [33]. In TWTT, the first vehicle sends a
request ping, to which the second vehicle replies with a finite delay. If the
delay is fixed and known, the distance between the two vehicles is a function
of the total time from transmission to reception at the first vehicle. Since
this method requires two acoustic transmissions for each range measurement, it
is not scalable to large teams. In the TDOA method, the transmission from one
vehicle is received by two or more vehicles. By knowing the arrival times at
each of the receiving vehicles and their respective locations, the location or
range of the transmitting vehicle can be estimated by exchanging data between
the receiving vehicles, as it is a function of the difference in the arrival
times at the receiving vehicles. However, this method requires more acoustic
transmissions and is thus also not scalable. For the above reasons, OWTT has
emerged as the preferred method for range measurements in underwater
environments.

|  |  |
---|---|---|---
(a) Surface Vehicle-AUV |  |  | (b) Server-Client
|  |  |
(c) Mesh |  |  | (d) Surfacing
Figure 2: Overview of most common underwater cooperative localization
approaches

###  II-D Scalability

The CL approach’s scalability is inherently tied to how ranging is performed
and how the data is exchanged between the vehicles involved due to the narrow
bandwidth of the acoustic channel. Consequently, multiple simultaneous
communications cannot exist. Thus, two of the most popular schemes to share
data from one to many are a) broadcasting and b) Time-division multiple access
(TDMA). The first approach is scalable to any number of receiving vehicles,
whereas the latter is not. In a large team, the total time for updating the
location information for one vehicle increases linearly, thus leading to
considerable delays and can affect the convergence of the estimators. Other
approaches, such as data exchange with neighbors-only, have also been reported
[34], which need fewer transmissions but need a scheduling algorithm. There
are also recent approaches of using orthogonal frequency division multiple
access (OFDMA) for simultaneous communications between vehicles, as reported
in [35]. Another aspect that affects scalability is the size of the
communication packets. The smaller the packets, the more reliable the
communication with shorter communication intervals; thus, more vehicles can
communicate in any given duration. But, this contravenes the requirement that
for CL, the vehicles must exchange their states with each other, which is a
lot of information. Thus, there have been attempts to efficiently manage the
bandwidth in CL scenarios, as will be seen later.

###  II-E Other Considerations

Ocean currents can have a detrimental effect on cooperative localization and,
in general, localization of any AUV. Ocean currents tend to exacerbate the
drift in the position estimate of the vehicles. They are dynamic, thus, cannot
be accurately accounted for apriori and need to be estimated in situ for
accurate localization results. To some extent, ocean general circulation
models (OGCM) can be preloaded in the AUV prior to a mission, if available
[36] and can be used to compensate for ocean currents for tasks or missions
involving large areas.

##  III UNDERWATER COOPERATIVE LOCALIZATION

The term cooperative implies that the vehicles involved in localization share
some information about their respective locations/state with each other [37].
The location information shared could be absolute or could be relative. While
absolute location information present with any one of the vehicles in the team
can essentially drive down the error to a minimal value, even relative
position exchange between teams can prevent the error from unbounded growth
[38].

Some of the common AUV cooperative localization approaches are shown in Fig.
2. In (a), surface vehicles are employed to aid the underwater vehicle by
transmitting its absolute position information through acoustic channels. The
surface vehicles could be single or multiple, autonomous or manned, and
localized with the help of GPS signals. In (b), a ”server/leader” underwater
vehicle, which has very high accuracy and expensive sensors for its own
localization, aids in the localization of several other ”client/follower”
AUVs. The client AUVs generally have low-accuracy inertial sensors or an
incomplete sensor suite, along with other mission-specific payloads. Approach
(c) does away with the aid vehicle altogether and instead relies on inter-
vehicle communications to bound their localization error growth. In this type
of approach, only the error growth rate can be lowered. This issue can be
resolved in (d) type, wherein a team member can surface for GPS fix and then
dive back to share the positional information with other team members.

The taxonomy of underwater CL methods is shown in Fig. 3, and a brief
comparison between the various categories is given in Table II. In the
following sections, we describe each of these approaches in detail and put
forth the research contributions in those areas.
Remark 1: Although cooperation for localization could also be with static
sensors on the ocean floor or surface, as in the case with GiB, LBL, or UWSN,
we restrict ourselves to the review of cases where cooperation is between
moving vehicles underwater with or without help from those at the surface.
This is for the reasons mentioned in the prior sections and because the
dynamics of the moving beacons pose interesting and challenging problems. For
UWSN based localization techniques the reader is referred to [39], [32], [33].

Figure 3: Classification of underwater cooperative localization approaches

###  III-A With a dedicated support vehicle

In this approach, dedicated support vehicles are used as navigation aids (NA).
These support vehicles can also act as communication gateways between the AUVs
and ground or ship-based mission control stations. This configuration of the
support vehicles is often termed a communication and navigation aid (CNA).
CNAs have the advantage of being able to facilitate mission parameter changes
and telemetry relays on the fly. Other benefits of using a dedicated NA
include longer mission durations and possibly a facility for docking and
recharging. The NA can either be on the surface of the water body or near the
other AUVs underwater.

While having a NA for localization results in excellent accuracy, they also
pose certain challenges. The primary one being the path planning of the aiding
vehicles. This has led to investigations into the observability of the
localization problem with NA and optimal path planning strategies. This is
more prominent in surface-based navigation aids since aid underwater generally
has the same mission plan as the AUVs. In the following sections, we discuss
these approaches and the related research.

####  III-A1 Navigational Aid on the surface

Having the CNA on the surface has the advantages of being in constant
reception of absolute GPS location data and communication network. However,
this approach does have its challenges, such as more complex mission planning,
longer distances for acoustic communication with AUVs resulting in acoustic
channel issues such as packet loss, higher noise, latency, etc., and
mitigation of other surface traffic. Furthermore, their performance is
dependent on the surface sea states. Some of the earliest results in CL using
surface vehicles were with crewed ships and boats, which were non-autonomous.
The conducive results from these experiments were then extended to autonomous
surface vehicles.

TABLE II: A BRIEF COMPARISON OF UW CL CATEGORIES Class | Subclass | Positive Aspects | Negative Aspects
---|---|---|---
With a dedicated support vehicle |  On surface |  Lower localization error, No time/energy wasted in surfacing |  Requires additional vehicle at the surface, Ship operations cost, Mission Planning
Underwater |  Stealth, Does not require surface traffic mitigation, Relatively simpler mission planning |  Requires additional vehicles, Localization error reduction not as good as with vehicle on the surface
Without a dedicated support vehicle |  Surfacing |  Does not require additional support vehicle, simpler mission planning |  Time/energy wasted in resurfacing, relatively lower localization error reduction
Non-surfacing |  No time energy wasted in surfacing and no additional vehicle required |  without absolute location information, error can grow unbounded.

##### Crewed Ship as localization aid

In this section, we review cooperative localization using non-autonomous
surface vehicles as a navigational aid. These are mainly crewed ships and
boats used for the deployment and retrieval of the AUVs. In one of the
earliest and simplest approaches, Matos and Cruz [40] used two boats as moving
beacons to localize a single AUV in a river. The AUV runs an EKF estimator,
fusing distance information from the two beacons on the boats and its dead
reckoning (DR) data. Both the boats move along a path perpendicular to the AUV
path, which is a bank-to-bank, back-and-forth motion along the river. In [41],
a single ship was used instead, utilizing a least-squares (LS) based approach.
The position is estimated from range information and the known trajectory
through a least-squares estimator, and the resulting data is fused with dead
reckoning data in a Kalman Filter. The algorithm’s accuracy suffered in cases
of poor trilateration geometry. It also required prior knowledge of sound
speed profile (SSP), refraction index, and depth errors, the former two being
challenging to acquire. McPhail and Pebody [42] tackled the problem of
position drift during the dive of a deep diving AUV by utilizing range
information from a surface ship. The AUV, post-diving, is made to move in a
circular orbit about the ship while its true position is estimated using a
least mean square (LMS) algorithm. The paper also discusses mitigation of the
problems mentioned in [41], such as the measurement of SSP, depth error,
refraction, sensor errors, etc., and others, such as the effects of tides and
atmospheric pressure changes. For the same problem, in [43], a strong tracking
algorithm in which the prediction is carried out using unscented transform is
proposed. The observability with successive measurements was proved using Lie
algebra. The proposed algorithm showed marginal improvements over generic UKF.
Folk et al. [44] evaluated relative and absolute localization of AUV to a
naval ship to measure the latter’s magnetic signatures. In the absolute case,
the AUV used EKF for estimating its and the ship’s states, while in the
relative case, only its own states were estimated. Eustice et al. used a ship
as a navigation aid for single or multiple AUVs in [45]. The AUVs localized
using OWTT of the acoustic signal from the ship and its sensors through a
decentralized Least Squares (LS)-maximum likelihood estimator (MLE). The
proposed approach was shown to perform comparably to an LBL system. The ship,
however, was free-drifting without any specific or optimal path. In [18], OWTT
information from a ship was used to localize a deepwater AUV but in post-
processing. The authors used a delayed state centralized EKF (DS-CEKF) to
process the ship, AUV sensor, and range data. The delayed states compensated
for the movement of AUV between acoustic transmission by ship and its
reception by AUV. Centralized post-processing led to the incorporation of the
cross-correlations between the ship and AUV states resulting in the lowest
estimation errors compared to distributed estimation. Hence CEKF is often
referred to as the gold standard of estimation with other estimators compared
against it for performance evaluation. The ship’s motion was confined to a
diamond-shaped path to improve observability. The initial position uncertainty
was tackled by initializing the EKF with an MLE estimate, as improper EKF
initialization leads to its instability. The same authors in [46] proposed a
decentralized extended information filter (DEIF) for localization of multiple
AUVs using a single moving beacon, which is not only scalable but also suited
for the low bandwidth, low capacity acoustic channel. The beacon and AUVs
maintain separate filters. The beacon broadcasts only the changes in its state
and uncertainty, since the last broadcast, to the AUVs asynchronously. The AUV
filter reconstructs the beacon state using the information in the acoustic
messages. The beacon/AUV, process, and observation models are considered to be
linear. The proposed approach is evaluated against CEKF, Egocentric EKF,
Interleaved Update (IU) [47], and DR for two cooperating scenarios: a) Ship as
a beacon b) AUV (resurfacing for GPS) as a beacon. Results show that DEIF
performs similarly to CEKF, although its performance is subject to packet
loss. A pre-planned path is chosen for the beacon since the mission is known.
Allota et al. [48] presented a strategy based on geometrically calculating
individual locations through inter-AUV and AUV-Ship range information, which
is then utilized in the Kalman filter measurement step. The proposed scheme is
evaluated using 3 AUVs and one ship, although it can be scaled while ensuring
at least one AUV has a DVL sensor. The AUV, which has a DVL sensor, is denoted
as the server, and the tetrahedral geometry-based algorithm is run only on it
in a centralized manner with state inputs from other vehicles. The calculated
locations are then communicated to other AUVs. The server AUV uses a non-
linear complimentary filter, while all other AUVs use KF for position and
velocity estimates. Intervehicle communication, excluding server, has no
information exchange and is only used to calculate the range. The scheme has
no limitations on the relative distances or paths, although it requires more
than four vehicles to work. Harris and Whitcomb [49] proposed range and range
rate estimation based on cooperative localization of AUVs, without DVL or
ADCP, with the help of surface ship. A delayed state centralized EKF was used
for estimation. It was shown through simulations that including the range rate
information didn’t improve the localization error. Only in the case of poor
range measurements marginal improvement was observed with range rate. The
above approach was extended in [50] to use a dynamic model of the vehicle
instead of a kinematic model. Compared to AUVs estimating with a kinematic
model without DVL, the proposed method gives results comparable to AUVs with
DVL and kinematic model. The surface ship was navigating along a circular
trajectory about the work area of the AUV. This approach, however, is heavily
dependent on accurate modeling of the AUV. In [51], an AUV was localized using
a surface ship and a static beacon. The approach relies on utilizing
information exchange within the existing ad-hoc network among AUVs, surface
vehicles, and beacon nodes for localization. AUVs are assumed to be operating
in deep water without the bottom lock and rely on IMU, relative velocity, and
range/bearing information for positioning. The ship localizes the AUV using a
high-precision acoustic positioning (HiPAP) system. Each AUV runs two EKF
algorithms, one for its localization and the other to estimate neighboring
nodes’ positions. Outliers are rejected using the Mahalanobis distance metric,
while delays are taken care of using a back-and-forth approach wherein
measurements are used in previous estimates and then propagated forward. The
approach requires that the AUVs be equipped with very high-accuracy INS and a
USBL modem. This not only increases cost, but USBL also limits the size of the
team.

An overview of all the above approaches using crewed vessels as CNA is given
in Table III. While the results using a ship or boat as a CNA show performance
that is almost on par with traditional localization approaches such as LBL,
operating a ship or a boat is prohibitively expensive. This is true,
especially for long-duration missions, due to the crew’s expenses, operations,
and maintenance of the vessel [52], [53]. Furthermore, they are non-autonomous
and thus need the mission path of the AUV known a priori and can only move in
paths that are simple shapes made up of straight lines or circles.

TABLE III: Overview of Crewed ship (non-autonomous) underwater CL

Reference |  Propagation Path  |  Packet Loss |  Packet Latency |  Measurement Outliers |  Bandwidth |  Estimator |  Scalable? |  Ocean Currents |  Results (Sim/Exp) |  Ranging Method |  Velocity Sensing |  Uncertainty111 |  Channel Sharing |  No. of aid vehicles |  No. of aided vehicles |  Remarks
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
[40] |  |  |  |  |  |  EKF |  N |  |  S |  T |  TE |  |  RR/F |  2 |  1 |  Two boats moves along predefined path.
[41] |  |  |  |  |  |  NL-LS/ KF |  N |  |  EPP |  T |  D/A |  Using LBL |  RR |  1 |  1 |  Only straight motion of AUV, validation in post processing
[42] |  |  |  |  |  |  LMS |  N |  |  EPP |  T |  A |  |  RR/F |  1 |  1 |  Deep diving AUV, Error contributions from changes in Sound Speed profile and sensor errors considered
[43] |  |  |  |  |  |  ST-UKF |  N |  |  S |  - |  N |  |  - |  1 |  1 |  Strong tracking UKF. Localization of deep diving AUV while diving. Rician noise distribution.
[44] |  |  |  |  |  |  EKF/ CEKF |  N |  |  EPP |  O |  - |  |  B |  1 |  1 |  Relative and Global localization with respect to ship, Result on post processed data
[45] |  |  |  |  |  |  LS-MLE |  Y |  |  E |  O |  D |  |  B |  1 |  1 |  Ship was either anchored or freely drifting. Decentralized estimator.
[18] |  |  |  |  |  |  DS-CEKF |  Y |  |  EPP |  O |  D |  MLE |  T |  1 |  1 |  Ship moved in a Diamond shaped pattern, Centralized Delayed state EKF considers correlation terms, but only works in post processing
[46] |  |  |  |  |  |  DEIF |  Y |  |  E |  O |  D |  |  T |  1 |  1 |  Non optimal path for ASV, DEIF sensitive to packet loss.
[48] |  |  |  |  |  |  KF |  N |  |  S |  O |  D |  |  T |  1 + 1 AUV |  3 |  Geometry based approach (Trilateration), Scaling is difficult since all vehicles transmit, Ship is assumed stationary
[50] |  |  |  |  |  |  DS-CEKF |  Y |  |  E |  O |  - |  |  T |  1 |  1 |  Used dynamic AUV model, Delayed state centralised EKF.
[51] |  |  |  |  |  |  EKF |  Y |  |  E |  T |  D |  |  T |  2* |  1 |  *Includes 1 static beacon. All assets require USBL. 2 EKF’s run on AUVs.

  * •

Considered  Not considered. Scalability: Y-Yes, N-No. Results: E -
Experimental, S - Simulation, EPP - Post processed experimental data. Ranging
Method: O - OWTT, T - TWTT. Velocity Sensing: D - DVL, A - ADCP, TE - Thrust
estimation from motor speed, R - Required but not specified, N - No. Channel
Sharing: T - TDMA, B - Broadcast, RR - Request/Reply, F - FDMA

  * 1

Uncertainty in the initial location of the AUV.

##### ASV as localization aid

The costs associated with crewed ships naturally led to research on surface
vehicles that are uncrewed, autonomous, and can reliably perform for long
durations at sea. The reader can find a review of uncrewed surface vehicles in
[54]. While the ASV did away with some of the costs associated with the
workforce, maintenance, etc., of a large boat or ship, it introduces new
challenges in the form of its control, coordination, and mission planning.
This has led to new research directions, such as optimal path planning,
formation control, and observability analysis in the context of CL. In the
following subsections, we look at the current state of the art in CL of AUVs
with the help of autonomous surface vehicles.

Single ASV and Range information only: In this approach, the AUVs localize
using range information calculated from the ASV’s acoustic transmissions and
the data therein. In the simplest of these cases, a single ASV is used as a
localization aid for a single AUV. To find its X and Y coordinates with
respect to a pre-defined frame of reference (since depth is known), the AUV
requires at least two distance measurements from two different ASV locations
if its current location is known with some uncertainty. For a mobile AUV
carrying out its mission, this imposes constraints on the ASV motions and
trajectories. Fallon et al.[55] used the current and past range measurements,
current and past locations of the ASV, and distance traveled by ASV in-between
measurements for estimating position with an EKF. For range measurement
updates, the position and covariance of ASV are incorporated, but the cross-
correlation is neglected, which can lead to overconfidence in estimates. As
EKF fails to converge when the initial uncertainty in the location is large,
in [56], methods for estimating the initial location of AUV and the ocean
currents are discussed. Post diving, when the uncertainty is the largest, the
AUV uses a vision system and stored image database to calculate its location
offset. While it is stationary on the floor, an ASV or ship with towed beacon
is used to estimate the initial position and sound speed profile. In [57], an
ASV with USBL was used to localize an AUV without DVL or IMU. The AUV was
assumed to have only attitude information and an acoustic model. The range
information was fused with speed estimation using thruster motor current
measurements in an EKF with state augmented to include unknown current
velocities.

Since EKF linearizes the system, its estimate is less accurate. To mitigate
this, Gao et al. [58] combined an iterative divided difference filter (I-DDF)
algorithm with Huber M-estimator for localizing an underwater vehicle. The
advantage of the DDF filter is that it does not linearize the system, and
compared to UKF, its covariance matrix estimate is more accurate. The slow
convergence of DDF in systems with weak observability and large initial error
is mitigated through iteration. The Huber-based M estimator is employed to
take care of outliers in range measurements. The proposed Huber-M-based DDF
(HIDDF) algorithm is shown to perform better than EKF, DDF, and IDDF alone,
albeit with a higher computational burden. In [59], a factor graph (FG) based
approach is proposed to estimate AUVs location and current velocity in the
absence of bottom lock/DVL using range from a surface vehicle and neighboring
AUVs. A factor graph is a graphical representation of the joint probability
density functions of all the unknown positions of vehicles given the
measurements from sensors. To solve the nonlinear estimation problem, a
Maximum-A-Priori (MAP) algorithm is used, and to maintain the observability of
the whole system, a formation-switching strategy is employed. The effects of
packet loss and clock drift were also evaluated in field trials. The factor
graphs, however, have high memory requirements and can get complex with
increasing team size. In [60], an EKF and MAP based Moving horizon estimation
algorithm (MHE) is proposed wherein the EKF is used to generate high-frequency
estimates using depth and IMU data, while MHE is used to fuse the low-
frequency range information along with its history to generate consistent
estimates that do not suffer from linearization errors. To keep the
computational costs in check, MHE is implemented as a moving window version of
MAP.

The particle filter is another popular filter for state estimation. In [61],
[62], the performance of PF against EKF is compared. Simulations show similar
performance of PF and EKF due to the assumption that the measurement errors
are Gaussian distributed. In [63] the performance of EKF against PF and
nonlinear least squares (NLS) estimators is compared. The NLS estimator
outperformed both EKF and PF, especially in the case of post-processed data.
In [64], [65], a comparison between DR, distributed EKF, and loosely coupled
PF for estimating vehicle states using OWTT ranges and dynamic vehicle model
is presented. The distributed EKF on every vehicle is augmented with other
vehicles’ states. The sum of covariance is used in the augmented covariance
matrix to reduce errors due to overconfidence. In the loosely coupled PF case,
the PF was only used for the measurement update, while the prediction stage
used the output of EKF. A KF-based velocity (due to ocean currents) and
synchronization bias estimator were used to correct errors due to ocean
currents and clock offset. Experimental results show that the PF performed
marginally better than EKF. Including bias and ranges from multiple sources
(AUVs other than on the surface) improved the estimates even further. While
newer techniques, such as MHE, PF, IDDF, etc., are reported, as seen from the
above discussion, EKF is widely popular due to its simplicity and
effectiveness in most cases.

Another interesting challenge with ASV-based cooperative localization,
especially single ASV, is the path planning of ASV to minimize the positional
error of the aided AUVs. In [55], the ASV is made to follow a simple pre-
planned zig-zag path which can be easily parameterized and implemented, but it
is not optimal and unsuitable for more than one AUV. Extension of this work
was presented in [63], where it was also shown that using nonlinear
estimation, the system can be observable under less stringent conditions,
unlike in the case of a linearized version of the system, which causes EKF to
diverge. The ASV paths were generated using AUV position estimates and
uncertainty to maintain the observability of the system. Two such paths, zig-
zag and circular orbit about AUV, were evaluated. In [52], the ASV, from its
knowledge of the AUVs mission, uses a simple heuristic algorithm based on the
minimization of the integral of squared inter-vehicle distance to plan its
positions for acoustic transmissions. The approach, however, is not scalable,
as each iteration of the algorithm requires three transmissions. In [56, 61,
62], to find the optimal waypoint for the next acoustic transmission, the ASV
calculates the error uncertainty ellipse using the state information
transmitted by AUV. The waypoint is then selected such that the error ellipse
is minimized, which is along the direction of the major axis. The above
results were extended in [66] for ASV aiding multiple underwater AUVs by
incorporating inter-vehicle range measurements. Two cases were considered.
One, where the ASV helped minimize the positional error of the AUV with the
worst error, and second, where the ASV helped minimize the positional error of
the whole group. For a similar scenario, Chitre [67] proposed dynamic
programming (DP) based approach to generate ASV paths. It minimizes the
localization error ellipse for the AUV’s along the major axis, which is
orthogonal to the range measurement vector. The Bellman equation for the
optimal solution of DP is solved using an approximation of value function,
i.e., planning over a finite horizon. The approach provides a globally optimal
trajectory for ASV from the knowledge of AUV paths. This is similar to the
work in [68], [69], [70] for localization of AUVs using a single static
beacon. In [71], authors tackle the path planning problem using the Markov
decision process (MDP) framework. An MDP policy maps a state to action. In
this case, the probability of choosing the bearing angle of ASV given its
current state, AUV path, and relative range and angle. The ASV is further made
to adaptively ”learn” to position itself through Cross-Entropy (C-E) method
over a segment of the AUVs path. A smoothing filter is applied to prevent the
C-E method from converging to a local minimum. The ASV path was computed using
three different strategies: a) proximity to the AUV with a larger error, b)
along the centroid of the AUVs formation, and c) based on the sum of errors
squared of all AUVs. The third approach was concluded to be simpler and
produced better results. Computationally, this approach is only efficient once
the learning is done offline and has a linear increase in complexity with the
number of AUVs. A comparison of DP and MDP methods is given in [72]. In [73],
a genetic algorithm (GA) based policy search approach that is computationally
more efficient than the MDP-CE approach is proposed. The state space is
divided using Voronoi tessellations to reduce the number of representative
states compared to MDP. A variable-length GA is used to select the appropriate
state-action pair. Seto et al. [74, 75] proposed an optimal path planner in 3D
for ASV aiding multiple AUVs performing mine sweeping tasks using an approach
similar to [56]. The path planner involves a look ahead strategy that also
incorporates distance penalty, which helps to bound the error and reduces the
computational effort. In [75], two cases are considered, a) the ASV knows AUV
paths a priori, and b) it estimates the AUV paths in real-time using the next
three waypoints communicated by the AUV. In the latter case, the cost of
heading decisions at L future times steps is calculated, and the path is
chosen such that the AUV position errors are minimized. The latter case is
useful in tasks where the AUV may have to change its path in between the
mission. In [76], the condition number of observability gramian and empirical
observability gramian of the linearized discrete system are used to optimize
the trajectory of ASV. In the former, the condition number is minimized by
minimizing the difference between the trajectory inertia matrix’s eigenvalues.
For single ASV localizing multiple AUVs, the condition number-based approach
is shown to be better than the empirical gramian based while being less
computationally taxing. Walls and Eustice [77] proposed an information
maximization-based approach, similar to the maximization of the determinant of
Fisher information matrix (FIM), to compute optimal trajectories for an ASV
localizing multiple AUVs. Only those ASV trajectories are selected, which can
be parameterized by diamond and/or zig-zag patterns instead of searching over
the full space of trajectories. This is in contrast to [72], where the
approach was based on a future segment of AUV paths at any time ’t’. The
performance was evaluated against the approaches in [72] and [52]. It was
shown that the proposed approach could attain higher information gain than
others. A problem with such easily parameterizable trajectories is that if the
pattern is large, the measurements appear to be from a straight line segment,
while if the pattern is small, the difference between successive measurements
may not be much for a vehicle that is far away. Sousa et al. [78] presented
two FIM-based approaches for finding the optimal path, wherein the ASV
calculates its next location with or without using the estimated AUV position.
The calculation involves selecting the one point having the maximum
determinant of FIM within an estimated set of all reachable points from the
current location until the next communication. The effect of AUV depth and the
horizontal range is evaluated on localization performance, with the
localization error increasing with depth and decreasing with radius. In [79],
an extremum seeking (ES) based approach is proposed. In ES, the optimal input
for an unknown input-output map is found using online gradient estimation. The
proposed approach is vehicle model agnostic, subsumes constant disturbances
such as gravity, currents, etc., requires minimal acoustic data transmission,
and does not require AUV trajectory apriori. The cost function is formulated
in terms of the estimation filter’s covariance matrix, thus ensuring low
computation complexity. Its optimal value minimizes the maximum eigenvalue of
the covariance matrix. This, in turn, maximizes the minimum eigenvalue of the
observability gramian. However, the system model considered requires the ASV
to move arbitrarily in the horizontal plane, which may not always be the case.
Also, the approach requires to and fro communications between AUV and ASV,
which will introduce delays and will not scale well in the case of multiple
AUVs. An extension to the case of underactuated beacon vehicles moving in a 2D
plane was presented in [80]. In [81], an algorithm that combines priority-
based expansion of a search tree with random sampling-based exploration to
adaptively plan multiple future waypoints is presented. Sampling-based
exploration is chosen to reduce the number of states that need to be
evaluated. At the same time, the expansion of the search tree is done such
that the angle between the distance vector and the major axis of AUV
uncertainty is minimized. The optimal locations are such that they also
correspond to the optimal time for transmission and are calculated by
considering the limitations of the ASV dynamics. The optimal time for
transmission is chosen from a set of TDMA time slots in which the ASV is
allowed to transmit. In the case of multiple AUVs, the sum of total
uncertainties is minimized since optimal locations for all AUVs will not be
the same. However, priorities, if required, could be assigned. Rua et al. [82]
proposed a novel solution to the single beacon, range-based, cooperative
localization of an AUV wherein the beacon is mounted on a rotating arm, which
in turn is mounted on the hull of an ASV or at a static location. However, the
AUV motion is considered to be in trimming trajectories, i.e., only constant
linear and angular velocities. It is shown that the system is observable in
the case of AUV moving with a) constant linear and angular velocity or b)
constant linear velocity under initial condition constraints, while the system
is unobservable when the AUV is not moving. Further optimality analysis to
find the optimal motions of only the beacon, beacon, and vehicle, optimal
fixed rotation rate of beacon, and optimal energy and rotation rate are
carried out in [83].

Another aspect of cooperative localization between vehicles is the
observability analysis of the states of AUVs. Authors have reported analysis
using nonlinear weak observability [84, 60] and nonlinear to linear time-
varying transformations (NL-LTV) [85, 86]. Viegas et al. [85] presented
observability analysis using NL-LTV transformations using state augmentation.
The authors considered two cases under the influence of unknown ocean
currents: a) ASV transmits velocity and position information to AUV, and b)
ASV transmits only position information, and AUV estimates ASV velocity
through some sensors. A Kalman filter was then proposed for the LTV system,
which guarantees global asymptotic stability of error dynamics. In [60],
nonlinear observability analysis in the discrete domain was presented. It was
shown that the AUV with only IMU, depth sensor, and range information is
weakly observable in nonlinear case but is unobservable in linearized case.

There also have been attempts at efficient and optimal use of the acoustic
channel to share information between cooperating vehicles. In [87], Meira et
al. coupled CL algorithm from [47] with a logic-based communication approach
that transmits location information from ASV to AUV depending on a threshold
instead of a pre-determined periodic transmission. This threshold is based on
the difference between ASV’s position estimate and GPS data. While the authors
analytically proved the position error’s boundedness under certain assumptions
on formation, velocity, and currents, the experimental implementation had no
such assumptions. It was demonstrated that the approach gives only marginally
worse performance than periodic transmission but with almost 62.5% fewer
transmissions. It was assumed that the AUV runs an ASV model parallel to its
own to estimate better filter parameters. In [88], the effects of adaptive
time-of-launch (TOL) of localization packets within the TDMA time slot were
studied. By choosing the TOL based on a criterion, it is shown that the
localization error can be reduced compared to a static TOL. EKF and NLS
trilateration-based estimators were compared in the case of static
single/three beacons, a follower ASV and a lawn mowing ASV, wherein the EKF
performed better than the NLS-based method.

Table IV gives an overview of all the above approaches using a single ASV and
only range information for localization.

TABLE IV: Overview of Single ASV range only CL

Reference |  Propagation Path |  Packet Loss |  Packet Latency |  Measurement Outliers |  Bandwidth |  Estimator |  Scalable? |  Ocean Currents |  Results (Sim/Exp) |  ASV knows Mission Plan? |  Ranging Method |  Velocity Sensing |  Obs. Analysis \ Metric |  Model |  Uncertainty |  Channel Sharing |  No. of aid vehicles |  No. of aided vehicles |  Remarks
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
[52] |  |  |  |  |  |  EKF |  N |  |  E |  Y |  T |  D |  |  - |  - |  RR |  1 |  1 |  Communication intensive approach
[55] |  |  |  |  |  |  EKF |  N |  |  E |  N |  O |  |  NL |  C |  |  RR |  1 |  1 |  Predefined Zig-Zag path for ASV, Long communication times
[56] |  |  |  |  |  |  EKF |  N |  |  S |  N |  O |  D |  |  D |  # |  B |  1 |  1 |  #Initial position estimation using vision and towed beacon. Optimal path for ASV.
[57] |  |  |  |  |  |  EKF |  N |  |  E |  N |  - |  TE |  |  C |  |  - |  1 |  2 |  ASV has USBL. No DVL/IMU on AUV.
[58] |  |  |  |  |  |  HIDDF |  Y |  |  E |  N |  O/T |  D |  |  D |  |  - |  1 |  1 |  Iterative DDF estimator for Nonlinear model. Huber M estimator for outliers. Requires high computations.
[59] |  |  |  |  |  |  FG /MAP |  Y |  |  E |  N |  O |  A |  NL |  D |  |  T |  1 |  4 |  Mid water column with only relative velocity estimate. High memory requirements.
[60] |  |  |  |  |  |  MHE-EKF |  N |  |  S |  N |  - |  N |  NL |  D |  |  - |  1 |  1 |  Nonlinear observability analysis. Static beacon used in simulations.
[61], [62] |  |  |  |  |  |  EKF/ PF |  N |  |  S |  N |  O |  D |  |  D |  |  B |  1 |  1 |  Single ASV-AUV, PF derived trajectory is not smooth. Experimental results in [62]
[63] |  |  |  |  |  |  NLS/ EKF/PF |  N |  |  E |  N |  O/T |  |  NL |  C |  |  RR |  1 |  2 |  Zig-Zag and Circular path for ASV, Long communication times
[64], [65] |  |  |  |  |  |  EKF /PF |  Y |  |  E |  N |  O |  TE |  |  D |  |  T |  1 |  2 |  Distributed EKF. Considered clock offset effects.
[66] |  |  |  |  |  |  EKF |  Y |  |  S |  N |  O |  D |  |  D |  # |  - |  1 |  3 |  AUV share inter vehicle ranges. Cross correlations in the position estimates ignored.
[67] |  |  |  |  |  |  - |  N |  |  S |  Y |  O |  - |  |  D |  - |  B |  1 |  2 |  ASV path planning using Dynamic Programming approach.
[71] |  |  |  |  |  |  - |  N |  |  S |  Y |  O |  - |  |  D |  - |  B |  1 |  2 |  Heuristic MDP-CE based method, sub-optimal paths, learning can take time.
[72] |  |  |  |  |  |  EKF |  N |  |  S |  Y |  O |  D/ TE |  |  D |  - |  B |  1 |  1 |  Comparison of DP & MDP-CE. ASV estimates AUV position.
[73] |  |  |  |  |  |  - |  Y |  |  S |  Y |  - |  - |  |  D |  - |  B |  1 |  4 |  Genetic algorithm based policy search approach.
[74], [75] |  |  |  |  |  |  EKF |  Y |  |  E |  Y/N |  O |  - |  |  D |  |  T |  1 |  2 |  Limited Scalability. AUV depth is considered variable. Doesn’t need mission plan.
[76] |  |  |  |  |  |  - |  - |  |  S |  N |  - |  - |  COG/ CEG |  C |  |  - |  1 |  3 |  ASV Optimal trajectory using path inertia and Empirical Observability Gramian.
[77] |  |  |  |  |  |  Delayed State IF |  Y |  |  S |  Y |  O |  - |  M |  C |  - |  T |  1 |  2 |  ASV Optimal path in terms of zigzag or diamond shapes. No localization error performance details are provided.
[78] |  |  |  |  |  |  EKF |  N |  |  S |  N |  - |  - |  D |  D |  |  B |  1 |  1 |  AUV is remotely operated. ASV is assumed holonomic.
[79], [80] |  |  |  |  |  |  KF |  N |  |  E |  N |  - |  D |  COG |  C |  |  - |  1 |  1 |  Extremum Seeking based path planning for ASV, Model agnostic approach.
[81] |  |  |  |  |  |  EKF |  N |  |  S |  N |  O |  - |  |  - |  |  T |  1 |  2 |  Adaptive ASV path Planning, Computationally expensive for multiple AUVs.
[82] |  |  |  |  |  |  - |  Y |  |  S |  N |  - |  - |  NLTV |  C |  |  - |  1 |  1 |  Beacon mounted on rotating arm in ASV. Trimming trajectories only.
[86] |  |  |  |  |  |  KF |  - |  |  S |  N |  - |  D |  NLTV |  C |  |  - |  1 |  1 |  NLTV Observability analysis and Observer design presented for single ASV-AUV pair.
[87] |  |  |  |  |  |  IU/ Hybrid KF |  Y |  |  E |  N |  O |  |  |  C |  |  LB∗ |  1 |  1 |  ∗Logic based communication. AUV runs a ASV model in parallel.
[88] |  |  |  |  |  |  EKF/ NLS |  N |  |  S |  N |  O |  - |  - |  - |  |  T |  1 |  1 |  Adaptive time of launch within TDMA slot. No optimal path.

  * •

Considered  Not considered. Results: E - Experimental, S - Simulation, EPP -
Post processed experimental data. Ranging Method: O - OWTT, T - TWTT. Velocity
Sensing: D - DVL, A - ADCP, TE - Thrust estimation from motor speed, N -
No.Obs. Analysis \ Metric: NL - Non linear weak observability, NLTV - Non
linear to linear time varying transformation, COG - Condition number of
observability gramian, CEG - Condition number of empirical observability
gramian, M - Mutual information, D - Determinant of FIM. Model: C -
Continuous, D - Discrete. Channel Sharing: T - TDMA, B - Broadcast, RR -
Request/Reply, F - FDMA.

Single ASV with Range and bearing information:

In this approach, localization between vehicles is carried out with sensors
that provide both range and bearing information, such as USBL, SBL, etc. When
range and bearing information is combined with depth sensor data, localization
of any vehicle in 3D ideally requires only one acoustic transmission if the
clocks are synchronized. In practice, considering a single ASV-AUV case, the
ASV initially sends an interrogation signal to which the AUV replies. Using
the two-way travel time and the calculated bearing, the ASV can localize the
AUV. The estimated position is then communicated back to the AUV. In [89], a
hierarchical cooperative localization scheme between one ASV and two AUVs is
presented. One of the AUVs acted as a guide/server for the other AUVs and was
stationed between the latter and the ASV in the water column. It localized
relative to the ASV and the other AUV using USBL along with absolute position
information from ASV and velocity/depth data from acoustic packets. It used a
linearized system model with KF for state estimation of the ASV and the other
AUV. The other AUV only had an AHRS and estimated its states using speed
estimation and data communicated by the middle AUV. In [90], USBL in inverted
mode (iUSBL) with OWTT is used to localize an AUV using a surface craft. In
iUSBL, the USBL modem is onboard the AUV instead of the ASV. The AUV
interrogates the ASV, which replies with its position data. This data, along
with the calculated range and bearing, is then used for localization. This
provides position information for the AUV independent of INS. Using OWTT
further alleviates the need for back-and-forth communication; thus, multiple
vehicles can be localized simultaneously. In [91], a UKF-based state estimator
is proposed for AUV having access to the range, bearing, and elevation
information relative to ASV, along with its velocity estimate and velocity of
the ASV. Packet latency issues are resolved by back-calculating the estimates
using current measurements. Salavasidis et al. [92] proposed an algorithm that
uses EKF for state estimation of AUV, but is run partially on AUV and ASV,
such that the measurement update part is carried out on the ASV using USBL, to
reduce the computational burden on the AUV. The computed location estimate is
then communicated to the AUV. The approach, however, has a high communication
overhead. In [93], the ASV computes the AUV location through USBL and
communicates back only the error measured with respect to the GPS position
instead of the absolute position. It also tracks the AUV using a virtual
target approach while maintaining a given offset. The communicated error is
used in a KF onboard the AUV along with DR sensors to compute its position. A
maximum-a-posteriori estimation-based approach is presented in [94]. The range
and bearing information are acquired using a USBL on the surface vehicle
stationed at a fixed point. In [95], an artificial potential field (APF) based
controller for ASV is presented to support the localization of multiple
underwater agents, which could be AUVs or human divers. The agents use iUSBL
and exchange location, velocity, and course data with the ASV. As iUSBL works
only when communicating nodes are vertically aligned, the APF is created such
that it has an attraction basin between the agents and repulsive fields
directly above them. In [96], MDP is combined with a reinforcement-based
Q-learning approach. However, Q learning complexity increases exponentially
with the increasing number of AUVs.

The back-and-forth communication involved in this approach limits its
scalability to a few vehicles. The bearing calculations are further dependent
on the roll and pitch moments of the ASV when the USBL is mounted on it. The
limited range of the USBL also imposes constraints on the operating area of
the team. Since USBL systems are very costly, utilizing them on each team
member as iUSBL increases the cost drastically. These are the primary reasons
why range-only localization is more popular, and there are very few works in
CL utilizing USBL.

Table V gives an overview of approaches using a single ASV with range and
bearing-based CL.

TABLE V: Overview of single ASV (range and bearing) and multiple ASV CL

Category |  Reference |  Propagation Path |  Packet Loss |  Packet Latency |  Measurement Outliers |  Bandwidth |  Estimator |  Scalable? |  Ocean Currents |  Results (Sim/Exp) |  ASV knows Mission Plan? |  Ranging Method |  Velocity Sensing |  Obs. Analysis \ Metric |  Model |  Uncertainty |  Channel Sharing |  No. of aid vehicles |  No. of aidded vehicles |  Remarks
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Single ASV – Range and Bearing |  [89] |  |  |  |  |  |  KF |  N |  |  S |  N |  U |  TE |  |  D |  |  T |  1 |  1-1 |  Hierarchical cooperative localization scheme. Uses USBL in middle vehicles.
[90] |  |  |  |  |  |  - |  Y |  |  E |  - |  U |  - |  - |  - |  - |  - |  1 |  1 |  Inverted USBL concept. Scalable but costly in terms of hardware.
[91] |  |  |  |  |  |  UKF |  N |  |  S |  N |  U |  TE |  |  D |  |  B |  1 |  1 |  UKF for estimation and considers packet latency. Rest same as [89].
[92] |  |  |  |  |  |  EKF |  N |  |  S |  N |  U |  A |  |  D |  |  RR |  1 |  1 |  EKF partially run on AUV and ASV. High communication overhead.
[93] |  |  |  |  |  |  KF |  N |  |  E |  N |  U |  A |  |  D |  |  B |  1 |  1 |  Considers packet latency, Thresholding for outliers.
|  [94] |  |  |  |  |  |  MAP |  N |  |  E |  Y |  U |  TE |  |  D |  |  RR |  1 |  1 |  MAP based estimation. ASV is stationary.
|  [95] |  |  |  |  |  |  - |  N |  |  E |  N |  U |  - |  |  - |  |  RR |  1 |  1 |  ASV path planning using Artificial Potential Field. Large acoustic period.
|  [96] |  |  |  |  |  |  - |  N |  |  S |  Y |  U |  - |  |  D |  |  - |  1 |  2 |  ASV path planning using MDP with Q learning based approach.
Multiple ASV |  [97] |  |  |  |  |  |  - |  Y |  |  E |  - |  O/T |  D |  - |  - |  - |  T |  2 |  1 |  No AUV was used in experiments, all 3 Vehicles were kayaks.
[47] |  |  |  |  |  |  IU |  Y# |  |  E |  N |  O |  - |  |  - |  |  RR |  2 |  1 |  #Limited scalability of less than 4 vehicles.
[98] |  |  |  |  |  |  EKF |  Y |  |  E |  N |  T |  - |  - |  D |  |  B |  3 |  1 |  Tracking of diver. Delay between ping reception and reply is ignored.
[99] |  |  |  |  |  |  MHE |  Y |  |  S |  - |  O |  - |  - |  D |  |  T |  4 |  1 |  MLBL based approach.Moving horizon estimator. Uses linear model.
[100] |  |  |  |  |  |  UKF |  N |  |  E |  - |  T |  - |  - |  D |  |  - |  4 |  1 |  Acoustic channel modeling for sound speed profile. Consensus current estimation. Shore based centralized approach. High communication overhead.
|  [101], [102] |  |  |  |  |  |  - |  Y |  |  E |  Y/N |  - |  - |  D |  C |  |  - |  2 |  1 |  Observability analysis. Cooperative Tracking of target with Companion that has its own mission which is known or unknown. Continuous Kinematic Model, Discrete Measurement Model.
|  [14] |  |  |  |  |  |  - |  Y |  |  S |  N |  D |  - |  D |  C |  |  - |  6* |  3 |  3D model, Distance Dependent Noise, Multiple ASV tracking Single/Multiple Targets, no. of ASV$>$AUV. *1 static sensor.
|  [103] |  |  |  |  |  |  EKF |  Y |  |  E |  Y |  O |  - |  |  - |  - |  B |  2 |  1 |  Static beacon used as one of the ASV
|  [104] |  |  |  |  |  |  HTM-EKF |  Y |  |  E |  Y |  T |  D |  |  D |  - |  RR |  2 |  1 |  Outlier mititgation using heavy tailed Gaussian mixture model

  * •

Considered  Not considered. Results: E - Experimental, S - Simulation, EPP -
Post processed experimental data. Ranging Method: O - OWTT, T - TWTT, U -
USBL, D -TDOA. Velocity Sensing: D - DVL, A - ADCP, TE - Thrust estimation
from motor speed. Obs. Analysis \ Metric: NL - Non linear weak observability,
NLTV - Non linear to linear time varying transformation, COG - Condition
number of observability gramian, CEG - Condition number of empirical
observability gramian, M - Mutual information, D - Determinant of FIM. Model:
C - Continuous, D - Discrete. Channel Sharing: T - TDMA, B - Broadcast, RR -
Request/Reply, F - FDMA.

Multiple ASV’s as localization aids:

For a single ASV to aid even a single AUV for localization requires that the
ASV moves to optimal waypoints, as seen previously. The primary advantage of
having multiple ASVs to aid in localization is thus the relaxed requirements
on the motions and trajectories that an ASV has to execute to keep the
localization error of AUVs within bounds [76, 80, 78]. It is also beneficial
when the AUVs’ team size is large and spread over a larger area, as it would
be impossible for a single AUV to satisfactorily aid all the AUVs at the same
time and will necessitate a priority-based approach. It also increases the
probability of acoustic data reception from AUVs, minimizing packet loss
errors. This, however, has additional costs in terms of hardware, mission
planning complexities, and computations required. Although the performance
benefits outweigh the costs, only a few works have addressed this problem.

One of the first works to propose multiple autonomous surface craft as a CNA
is [97]. This is an extension of moving long baseline (MLBL) work done in
[105] by using ASVs instead of boats. MLBL is similar in concept to LBL, but
the beacons are considered to be mobile. Bahr et al. [47] used two ASVs for
cooperative localization of an actual AUV and proposed an Interleaved Update
(IU) algorithm that works in the presence of measurement outliers and can
scale to large team size. At each instant probable position, candidates are
evaluated, and by minimizing a cost function based on Kullback-Leibler
divergence (KLD), the most appropriate one is selected. In [98], a diver/AUV
position estimation technique using multiple ASVs was proposed. The maximum
velocity, acceleration, and turning rate of the diver target are assumed to be
known. The position is deduced using transmit/reply TWTT scheme through a CEKF
algorithm that uses the back-and-forth technique to take care of delays and
vehicles’ motion during measurements. Chen et al. [99], extended the work in
[60], which uses single ASV, to use MHE for localizing a single AUV with
multiple surface vehicles in an MLBL approach similar to [106, 107]. The
proposed approach is compared against a KF, showing marginal improvements. The
same author in [108] investigated the optimal number of ASVs, the range
between AUV-ASV, and the effect of distance-dependent noise factor using a
cost formulation. It was shown that the cost is inversely proportional to the
number of ASVs and directly proportional to the distance-dependent noise
factor. An optimal value of range to minimize the localization error for AUV
is also found.

In [100], a shore-based centralized approach that uses the knowledge of the
ocean current model is presented. The AUVs employ a UKF, with drift, due to
ocean currents modeled as a random walk, used as one of the states. The AUVs’
estimates are processed using a consensus algorithm at a shore-based
centralized server via surface vehicles as communication intermediaries. The
consensus current estimate is then communicated back to the AUVs to improve
their estimation. In [101, 102], a concept of using a companion vehicle to aid
ASV for localization of a target using range information is proposed. The
companion vehicle can be solely used as an aid or could be performing an
independent mission of its own. Furthermore, the companion vehicle’s location
may or may not be known to the ASV, which is measured in the latter case. In
all cases, the companion vehicle shares the information about its range to the
target with the ASV. The ASV optimal trajectories are calculated by maximizing
the determinant of FIM. Except when the companion is also cooperatively
tracking the target, the target is assumed to be stationary. In [14], an
approach for localizing N target AUVs by M cooperating surface AUVs, where
M$>$N, using the TDOA technique in 3D, is presented. The effects of distance-
dependent noise, uncertainty in the target AUV’s initial location, and curved
path in acoustic signal transmission are taken into account. The optimal
formation/locations for the surface AUVs are arrived at by sequentially
evaluating the determinant of FIM at each time step and moving only if it’s
higher than the current value. The optimal formations are evaluated in
simulations against different depths for target AUV, centralized and
decentralized sensor pairings, different numbers of surfaces, and target AUVs.
However, only the cases with static target AUVs are considered. In [103], a
multi-ASV system for localization of multiple AUVs that is scalable in the
number of AUVs was proposed. The AUVs are made to be passive listeners, while
the ASVs transmit their location information using TDMA. The ASV is assumed to
know the AUV path for it to be in its vicinity to aid in localization. The
optimality of the ASV location, although, has not been considered. In [104] a
robust KF is proposed that uses heavy-tailed mixture distribution for outlier
mitigation in the case of two ASVs aiding a single AUV. It is shown using
experimental data that the proposed approach is better than several
contemporary approaches for outlier-affected acoustic communication.

Table V gives an overview of approaches using multiple ASVs.

####  III-A2 Navigational Aid underwater

While the CNAs, on the surface, have the advantages of lower localization
error and communication, they are unsuitable in certain applications,
especially in defense such as espionage, target tracking, etc. Furthermore,
surface craft can be affected by sea states and other surface traffic.
However, the acoustic channel’s challenges, particularly with deep-diving
AUVs, can have a far more detrimental effect on CL performance. An alternative
approach is to have the navigation aid (NA) vehicles close to the AUV team
performing specified tasks. This also benefits from outfitting the survey AUVs
with high-accuracy task-specific sensors and medium or low accuracy (thus low
cost) navigation sensors. The aiding AUVs meanwhile have high accuracy
inertial navigation sensors, which are fewer in number. In case absolute
positioning information is required, the NA AUVs can then resurface for a GPS
fix. While different terminology has been used for this category in
literature, such as leader-follower, mother-daughter, and master-slave, we
will refer to it as the server-client approach. Here the server vehicles are
the ones that have high-accuracy navigational sensors and provide localization
support for the client survey AUVs by sharing their current location
information.

One of the earliest solutions resembling cooperative strategies for
localization was presented in [109], wherein a server-client approach was
used. The client AUVs would localize using USBL with respect to a server AUV,
which in turn would localize itself using LBL. In [110], a similar approach
was proposed, but the client AUVs use only range and location data from the
server through an acoustic modem instead of USBL, along with data from their
DR sensors. Vaganay et al. [105] is the first work to present the MLBL concept
wherein two AUVs perform the role of CNA for other survey AUVs. The time-
synchronized survey AUVs calculate their positions by passively listening to
location update pings from CNA, which flank the former on both sides. Since
the survey AUVs are passive listeners, this approach is highly scalable. In
[111], a centralized delayed state EKF (DSEKF) running on a server was
proposed for fusing information in one server, multiple client configuration,
which takes into account the delay in propagation of acoustic signals. With
one filter instance for every client vehicle, the computational complexity
increases with the number of vehicles. In [112], a distributed approach
combining Dynamic SLAM and cooperative localization of client AUVs is
proposed. The server AUVs are assumed to be localized with very low error and
are used as dynamic landmarks for client AUVs’ SLAM algorithm. In the absence
of server AUVs in proximity, CL with other client AUVs is used to bound the
error. Consistency is preserved by using the client AUV with the least
covariance as the beacon. Both DSLAM and CL are formulated as independent
Bayes filters and solved using EKF. The consistency issue when using server
AUVs is resolved in [113] by formulating a distributed modified EKF (MEKF).
Here, MEKF takes care of the cross-correlations by employing Jacobian
multipliers that the client AUVs use to track the server AUV’s location
changes during each DSLAM correction phase. But since the AUV model is non-
linear, the error performance of MEKF is limited, which is why PF is then
proposed in [114]. It is shown that the PF performs marginally better with
similar or lower computational complexity than MEKF. In [115], an algorithm
based on the origin state method is proposed to estimate the states of
multiple client vehicles using acoustic range measurements and pose-graph
information from multiple server vehicles. It is robust against packet loss
and is bandwidth-efficient. The server communicates incremental pose-graph
information relative to a server state known by the client, termed the origin
state. The server vehicles are assumed to have their absolute position
information, for example, through a surface vehicle. It was shown that the
performance using a DEIF estimator on client vehicles produced consistent
results similar to centralized estimation schemes without any overconfident
estimates. The above results were extended in [116] by constructing the local
state in the form of factor chains using a factor graph framework with
odometry and/or GPS as factors. These factor chains are then approximated
through composition, unlike approximations relative to the origin pose as in
the previous paper, and are shared with the other vehicles. This approach does
not require shifting the origin pose and allows vehicles without odometry to
join the network. While it is similar to [24], it has lower communication
overhead and better performance. Ben et al. [117] used factor graphs for the
case when both range and bearing information are used for client position.
Since cycles may exist within the graph, a clustering method is used to obtain
cycle-free graphs. Zhang et al. [118] presented a triangulation-based approach
to localize a single client AUV using three server AUVs. The server paths were
independent of each other and the client’s mission. This approach fails if the
server tasks are such that it takes them beyond the AUV’s communication range.
In [119], a parallel projection algorithm (PPA) based approach is proposed
wherein the global pose of the vehicle to be localized (rotation matrix and
translation) is estimated through MLE formulation that is convexified and
solved using PPA. The approach is compared against a semi-definite
programming-based approach for the coordinate alignment-based formulation. The
proposed approach is shown to have similar or better performance while having
a faster convergence rate. Zhang et al. [120] extended the MDP-CE approach
proposed in [71] to the server-client configuration, using two server AUVs to
aid multiple client AUVs. However, the approach requires training the CE
algorithm every time the trajectory of the clients is changed. In [121], the
effects of unknown constant current are investigated. Only the server is
equipped with DVL and uses USBL to measure the clients’ range and orientation.
Locations of the server and clients are estimated by the server using a hybrid
UKF-KF estimator, wherein the prediction step uses UKF while the measurement
step uses linear KF. The authors also consider the case where the clients also
communicate among themselves but don’t consider the cross-correlation, thus
giving overconfident results that are worse than no intercommunication. Yan et
al. [122] proposed a cooperative localization approach for server-client UUVs
in polar regions where navigation is difficult as meridians converge faster,
thus leading to calculation overflow and error magnification in conventional
SINS. For this, a polar grid algorithm-based state formulation is used, and a
delayed state Adaptive KF is employed for state estimation of follower UUVs.
In [123] [124], multiple AUVs are used as localization aids for the main AUV
performing a critical task. Centralized processing is carried out on the main
AUV, which estimates its state and the state of the aiding AUVs. The aiding
AUVs take turns to resurface for GPS fix and use EKF to estimate their states
using this data and information received from the main AUV.

In [125], a KF-based solution to the time delay problem in server-client
cooperative localization is presented. The client AUV is localized by server
AUV using USBL. The time delays are taken care of by modifying the update step
of KF in terms of the delayed measurement updates, i.e., time delays are
converted into a bias in the observation equation. Simulations show that the
proposed approach reduces the error in estimates by orders of magnitude. In
[126], an augmented EKF (AEKF) for mitigating time delays in the acoustic
channel was proposed. With the knowledge of the delay, the client AUV’s state
vector was augmented with all the states from the actual transmitted time till
the current time, using which the estimate was then propagated to the current
time. Results presented indicate AEKF can bound the localization error better
than EKF in the presence of time delays at the expense of computational cost.

In [127], cooperative localization of a single client vehicle with multiple
servers using a probability hypothesis density filter is presented. The filter
runs on all server vehicles and estimates the client location using TWTT. The
estimates are communicated back to the client, which uses an information
entropy-based approach to fuse and obtain the best estimate of its position.
However, the proposed method has high communication overhead and is
computationally complex. In [128], an improved TWTT communication scheme for
the server-client CL approach is presented. The server interrogates each
client AUV using TWTT, but instead of re-transmitting measurement updates to
each client AUV, the complete state information is broadcast. Thus requiring
$2N+1$ acoustic transmissions instead of $3N$, where $N$ is the number of
client AUVs. In [129], localization of a single client AUV with two server
AUVs without time synchronization is presented. The range calculated using
TWTT from both server AUVs was used in EKF to estimate the clients’ position.
While the proposed method is not affected by clock drift, it is not scalable.
Qu et al. [130] investigated the optimal formation for multiple AUVs acting as
servers for a single client AUV. The formulation uses FIM and area of
information ellipse. This approach requires clock synchronization among the
vehicles and bearing information. In [131], these shortcomings are mitigated
by relying on RSSI information instead.

Fan et al. [132] proposed a maximum correntropy (MCC) based unscented PF to
mitigate outliers in range measurements wherein it used KLD-based re-sampling.
Compared to PF, CKF, MCC-UKF, UPF, Huber-based UPF, and cubature KF, the
proposed algorithm produced the least average error but is computationally
intensive. In [133], an adaptive extended Kalman filter that estimates the
unknown process and measurement noise covariances using the expectation-
maximization method was presented. For a localization problem involving two
servers and one client, the proposed method is compared against DR, EKF,
Innovation AKF, and Sage-Husa AKF. The proposed algorithm converges the
fastest while having better error performance than other methods except for
EKF, where it is marginally better with higher computational complexity. In
[134], an unscented PF (UPF) based estimator was proposed to take care of the
non-Gaussian nature of noise and depletion of particles in PF. In UPF, UKF was
used to update the state of each particle in the client AUV. While the
proposed algorithm has the lowest error compared to EKF, UKF, and PF, it
requires ten times more computational time. In [135], a Student-t based EKF
(SEKF) for outlier mitigation is presented. The students-T distribution is
used for process and measurement noises instead of the usual Gaussian
distribution. Results indicate that the proposed method has almost $30-40\%$
better error reduction than Threshold EKF and $60-50\%$ better than standard
EKF, albeit with slightly higher computational requirements. In [136], a
maximum correntropy criterion (MCC), adaptive neuro-fuzzy inference system
(ANFIS), and CKF-based approach for mitigation of outliers and acoustic packet
loss is proposed. The packet loss is taken care of by ANFIS, which is a fuzzy
system wherein the fuzzy membership function and rules are trained using the
neural network from a large amount of data instead of being selected
arbitrarily. For the outliers, the MCC is used. State estimation when there is
no packet loss is carried out using a cubature Kalman filter based on the MCC
data. The same is used for training ANFIS. The trained ANFIS model predicts
the location when there is packet loss for more than 3 seconds. The proposed
approach improves error performance by over 60% against only CKF and by over
40% against ANFIS-CKF. While MCC-CKF computational requirements are almost the
same as CKF, ANFIS requires a large amount of training data. This can be an
issue if the packet loss is frequent and not enough data is acquired to train
ANFIS. The MCC kernel bandwidth is chosen heuristically. To mitigate this, an
adaptive version of the algorithm is proposed in [137]. The same authors in
[138] combined adaptive cubature KF to track ranging errors and used ANFIS for
detecting anomalies in ranging data. In [139], a robust Gaussian approximate
smoother based on expectation maximization is presented for outliers
mitigation and sensor faults. A faulty DVL is considered, and any bias in
acoustic modem data is treated as unknown inputs.

As for the path planning of the aiding vehicle, there are very few papers that
investigate the problem. This is because the server’s path is generally the
same as the client’s mission. However, there are few works where this
assumption is not held true. In [140], the server plans its path using a
dynamic programming-based approach from [67]. The server AUV is assumed to
know the survey plan a priori. In [141], an algorithm for optimal positioning
of server AUVs, without prior knowledge of client AUVs paths, is presented.
The server AUV calculates the optimal positions to broadcast position
information that will minimize the combined location uncertainty for all
client AUVs. This is done by dividing the area into grid points that can be
reached by server AUV before the next broadcast and estimating the
minimization of uncertainty by broadcasting from all those grid points. The
point that leads to the minimum error estimates is chosen. While the proposed
approach is distributed and robust against the number of beacons/survey AUVs
at any instant, correlations among the vehicles are ignored. In [142], a
belief space path planner based on a partially observable Markov decision
process (POMDP) model was proposed, which uses a probabilistic acoustic
channel model that accounts for randomness in measurements such as packet
loss. Optimal open-loop control actions or parameterized paths are generated
for the server using EKF, the proposed model, and the known client trajectory.

Table VI gives a summary of the approaches using underwater navigational aid.

TABLE VI: Overview of CL using underwater navigation aid

Reference |  Propagation Path |  Packet Loss |  Packet Latency |  Measurement Outliers |  Bandwidth |  Estimator |  Scalable? |  Ocean Currents |  Results (Sim/Exp) |  LAUV1 knows mission? |  Ranging Method |  Velocity Sensing |  Uncertainty |  Channel Sharing |  No. of aid vehicles |  No. of aided vehicles |  Remarks
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
[105] |  |  |  |  |  |  - |  Y |  |  EPP |  Y |  T |  D |  - |  B |  2 |  1 |  Boats used as AUV to gather data. Approach calls for CNA-AUV to resurface for GPS fix periodically
[111] |  |  |  |  |  |  DSEKF |  Y |  |  S |  Y |  O |  D |  - |  - |  1 |  2 |  Delays in acoustic communication are taken care of using centralised delayed state EKF.
[112], [113], [114] |  |  |  |  |  |  SLAM/ EKF/ PF |  Y |  |  S |  N |  T |  - |  |  - |  3 |  3 |  Leader vehicles are dynamic landmarks for SLAM in background ocean flows. In their absence follower AUVs resort to intra-vehicle state exchange.
[115] |  |  |  |  |  |  DEIF |  Y |  |  E |  A |  O |  D |  - |  T |  1 |  2 |  Pose-graph information based. Easily scalable, bandwidth efficient and robust against packet loss.
[116] |  |  |  |  |  |  Factor Graphs |  Y |  |  E |  A |  O |  D |  - |  T |  1 |  2 |  Factor graphs based approach. Low communication overhead.
[117] |  |  |  |  |  |  Factor Graphs |  N |  |  E |  A |  O |  D |  - |  B |  2 |  1 |  Factor graphs based approach using range and bearing information. SBL type appraoch for bearing.
[118] |  |  |  |  |  |  EKF |  Y |  |  S |  N |  O |  - |  |  T |  3 |  1 |  More number of leaders than followers, Trilateration approach.
[119] |  |  |  |  |  |  MLE |  N |  |  S |  N |  - |  - |  |  - |  1 |  1 |  Uses convexified MLE solved using parallel projection algorithm. Computationally expensive.
[120] |  |  |  |  |  |  EKF |  Y |  |  S |  Y |  O |  D |  - |  B |  2 |  3 |  MDP-CE for leader AUVs optimal path planning. Requires training.
[121] |  |  |  |  |  |  Hybrid UKF |  N |  |  S |  Y |  - |  T |  - |  T |  1 |  2 |  Orientation is measured by leader using USBL. Assumes unknown currents. Does not consider cross correlations.
[122] |  |  |  |  |  |  DS-AEKF |  N |  |  E |  Y |  U |  D |  - |  - |  1 |  1 |  Polar regions. Delayed state adaptive EKF. Requires bearing measurement.
[123], [124] |  |  |  |  |  |  CEKF/ CSLAM EKF |  N |  |  EPP |  Y |  - |  N |  - |  T |  3 |  1 |  Cross correlations ignored. Aiding AUVs need higher endurance.
[125] |  |  |  |  |  |  KF |  Y |  |  S |  - |  U |  D |  |  - |  1 |  1 |  Time delay compensation. Both leader and followers have USBL. Leader is assumed to be stationary.
[126] |  |  |  |  |  |  AEKF |  Y |  |  S |  Y |  O |  - |  - |  B |  1 |  1 |  Augmented EKF for time delayed measurements. Higher computational load at follower AUV.
[127] |  |  |  |  |  |  PHD/IE |  N |  |  S |  N |  T |  - |  |  - |  2 |  1 |  Leaders localize follower vehicle using bearing and range information. Follower AUV strictly only 1.
[128] |  |  |  |  |  |  EKF |  N |  |  EPP |  Y |  T |  D |  - |  RR |  1 |  4 |  Roundtrip ranging. Predefined zigzag path for beacon AUV.
[129] |  |  |  |  |  |  EKF |  N |  |  S |  N |  T |  - |  |  T |  2 |  1 |  Localization in absence of clock synchronization. Needs 2 leaders.
[130] |  |  |  |  |  |  EKF |  Y |  |  S |  Y |  - |  - |  |  T |  5 |  1 |  Different formations of multiple leaders. Requires clock synchronization and bearing measuremnts.
[131] |  |  |  |  |  |  EKF |  Y |  |  S |  Y |  R |  - |  |  T |  5 |  1 |  Different formations of multiple leaders. Ranging using RSSI.
[132] |  |  |  |  |  |  MCC-UPF |  N |  |  EPP |  Y |  T |  D |  - |  B |  2 |  1 |  Maximum correntropy based outlier mitigation. Computationally intensive. Non Gaussian noise.
[133] |  |  |  |  |  |  AEKF |  N |  |  EPP |  Y |  T |  D |  - |  T |  2 |  1 |  Expectation maximization based adaptive EKF.
[134] |  |  |  |  |  |  UPF |  Y |  |  S |  N |  O |  - |  |  T |  2 |  1 |  2 leader AUVs. Non Gaussian noise assumption.
[135] |  |  |  |  |  |  Students T-EKF |  N |  |  EPP |  Y |  - |  D |  - |  B |  1 |  1 |  Students-T based EKF for outlier mitigation. Leader has a zigzag path. High computational requirements.
[136, 138] |  |  |  |  |  |  Cubature KF |  Y |  |  E |  Y |  O |  D |  - |  B |  2 |  1 |  Adaptive neuro-fuzzy inference based packet loss & Maximum correntropy based outlier mitigation.
[140] |  |  |  |  |  |  EKF |  Y |  |  E |  A |  O |  D, TE |  - |  - |  1 |  1 |  Aid AUV knows survey plan a priori and has better sensor suite. Optimal path planning for Aid AUV.
[141] |  |  |  |  |  |  EKF |  Y |  |  S |  N |  - |  - |  |  T |  1/2 |  1/2 |  Optimal path planning. Inter vehicle ranging used in estimation. Ignores correlations in EKF.
[142] |  |  |  |  |  |  EKF |  Y |  |  EPP |  Y |  O |  - |  - |  - |  1 |  1 |  Parameterized paths for the server. Probabilistic channel model.
[143] |  |  |  |  |  |  EKF |  - |  |  S |  - |  - |  D |  |  - |  1 |  2 |  Simple EKF implementation.

  * •

Considered  Not considered. Results: E - Experimental, S - Simulation, EPP -
Post processed experimental data. Ranging Method: O - OWTT, T - TWTT, U -
USBL, D -TDOA, R-RSSI. Velocity Input: D - DVL, A - ADCP, T - Thrust
estimation from motor speed. Channel Sharing: T - TDMA, B - Broadcast, RR -
Request/Reply, F - FDMA. Mission plan: Y- Yes, same as follower, A - Aware,
not same as Follower, N- Not aware. 1Leader AUV.

###  III-B Without a dedicated support vehicle

Although having a dedicated aid vehicle has its merits in better localization
and communications, there are several demerits. In addition to their path
planning, aiding vehicles may not carry any mission-specific sensors and thus
don’t contribute other than in localization. Also, if the aiding vehicle
fails, the whole mission can get compromised. In this section, we look at the
approaches that do away with support vehicles altogether. This can be done
either with one of the vehicles surfacing for GPS or through other sensors,
such as vision, SONAR, gravity, etc., that aid in localization.

####  III-B1 Surfacing approach

In this approach, one of the AUVs in the team resurfaces to get absolute GPS
position information. With this information, the AUV dives back and shares its
absolute position with other team members resulting in a reduction in their
localization error. In all the following works, one of the vehicles surfaces
for a GPS fix. The earliest results in this category are by Maczka et al.
[144], wherein they demonstrate cooperative navigation by sharing inter-
vehicle ranges over acoustic communication channels to complement DR
estimates. To mitigate the inability to transmit the full estimation error
covariance matrix due to insufficient bandwidth, only a scalar function of the
main diagonal elements is shared instead. Acoustic latency is taken care of by
recalculating past estimates using the range measurement and propagating it to
the current time. In [24], a MAP-based scheme is proposed that computes
consistent estimates of the full multi-robot trajectory with a communication
strategy involving constant packet size, adaptive performance with respect to
acoustic channel, and which scales linearly with the number of AUVs. Every AUV
maintains two-factor graphs, multi-AUV, and its own DR. Instead of all the raw
sensor data, only change in position factor and associated covariances from
the DR factor graph, depth, range data, acknowledgment bits, and GPS fix (if
available) are communicated. To maintain consistency, bookkeeping-based
tracking is employed. Backlogging due to communication channel issues is taken
care of by combining multiple data. Liu et al. [145] describes the ’SUAVE’
algorithm for localization among a swarm of AUVs. In it, the AUVs with average
tracking variance above a certain threshold resurface and remain stationary to
act as beacons for other AUVs. The authors propose an iterative multiple model
(IMM) based estimator utilizing a fusion of KF and EKF for linear and angular
motion, respectively. In [146], a decentralized, opportunistic communication-
based CL within a team of AUVs, wherein the members can join or leave at any
time, is proposed. There is no dedicated timeslot for vehicles to communicate.
The localization is performed through trilateration among the team members
through the non-linear least-squares approach using OWTT ranging and data.
Time delay in data packets is compensated by taking into account the vehicle’s
own motion during the time difference between the received timestamp and its
clock. In [147], an approach that uses a measure of each AUV’s confidence of
location (LC) estimate to fuse relative pose information through KF for
reducing localization error is presented. When LC is below a limit for any of
the swarm members, they return to the surface for a GPS fix. The effect of a
rouge AUV with high LC in propagating wrong information is also considered.
Swarm subsections that have low LC are aided by specially deployed AUVs with
high LC to improve their localization, but this was not validated by the
authors in the simulation.

Although this approach does not need any support vehicles, as mentioned
before, resurfacing for absolute position information wastes time and energy.
Also, once the surfacing AUV dives back down, depending upon the depth it has
to dive, its position estimate would have drifted by a significant amount.
Hence the total useful contribution in error reduction from resurfacing will
not be as good as with a surface vehicle.

An overview of all the papers using this approach is given in Table VII.

####  III-B2 Non Surfacing

In this approach, there are no aiding vehicles nor resurfacing for GPS. The
team either relies only on their inter-vehicle range and exchanged data or
SLAM to keep the localization error in check. However, it may be possible that
some of the team members have high accuracy sensors than others, but unlike
the server-client approach, they have their separate mission. In SLAM, the
AUVs rely on other geophysical information such as gravity, magnetic field,
and bathymetry map (using vision, side-scan SONAR, multibeam SONAR, etc.) to
bound their localization error. The advantage of this approach is that it does
not require a support vehicle or surfacing. However, the localization error
growth will be the worst among all the strategies due to the absence of
absolute position information.

##### Alternating Landmark

Matsuda et al. [148, 149] proposed a novel cooperative strategy in which a
group of AUVs alternatively performs the role of static landmarks (beacons)
and survey vehicles. A particle filter (PF) is used for estimating the
horizontal position and yaw of the vehicles from onboard sensors, including
DVL, together with relative range and angle measurements. The vehicles are
assumed to be hover-capable and equipped with accurate but expensive fiber
optic-based gyro sensors. While this approach is able to keep the error growth
in check, the performance is not guaranteed in the presence of ocean currents,
as the group designated to act as a landmark will drift in such a case. In
[150], a communication scheme to reduce the communication overhead in the
previous work is proposed wherein the particles are clustered using K-means
clustering. Only the averages and standard deviations are then shared across
other vehicles leading to lower data transmission. In [151], the requirement
of hover-capable AUVs is mitigated by having the landmark AUVs remain
stationary by landing on the seafloor. The vehicles are divided into two
separate groups of landmark and survey vehicles, with only the landmark
vehicles alternatively remaining stationary. In [30], two methodologies are
considered. In 1st, one of the AUVs acts as a static landmark while the other
two moves; later, the other two are static and estimate the position of 1st
AUV. In the second method, a server-client approach is used, in which one of
the AUVs acts as a moving beacon, and the other two localize with respect to
the server AUV. However, the EKF estimation is carried out in a centralized
manner on one of the robots, including estimating the landmark robot state,
which is then shared with it. This, however, leads to overconfident estimates.

An overview of all the works in this approach is given in Table VII.

TABLE VII: Overview of CL using surfacing and Alternating landmark based
methods

Category |  Reference |  Propagation Path |  Packet Loss |  Packet Latency |  Measurement Outliers |  Bandwidth |  Estimator |  Scalable? |  Ocean Currents |  Results (Sim/Exp) |  Ranging Method |  Velocity Sensing |  Obs. Analysis\ Metric |  Model |  Uncertainty |  Channel Sharing |  Team Size |  Remarks
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Surfacing |  [144] |  |  |  |  |  |  Distributed Egocentric EKF |  Y |  |  E |  O |  R |  - |  D |  GPS |  TB |  2 |  Overconfident estimates as correlations not shared, One of the vehicles resurfaced for GPS.
[24] |  |  |  |  |  |  MAP |  Y |  |  EPP |  O |  D |  - |  D |  GPS |  T |  2 |  Decentralized approach. One or some AUV’s surface intermittently for GPS Fix. Consistent Estimates.
[145] |  |  |  |  |  |  IMM(KF) |  Y |  |  S |  O |  TE |  - |  D |  GPS |  S |  10 |  Assumes AUV can receive 3 messages simultaneously which is difficult in practice.
|  [146] |  |  |  |  |  |  NLS |  Y |  |  S |  O |  - |  - |  - |  - |  - |  5 |  Trilateration based centralized approach. AUV may surface or the team can take support from ASV. Opportunistic Communication.
|  [147] |  |  |  |  |  |  KF |  Y |  |  S |  O |  R |  - |  - |  GPS |  T |  150 |  Large swarms. Effect of wrong information being shared also considered.
Alt. LM |  [148], [149], [151] |  |  |  |  |  |  PF |  Y |  |  E |  U |  D |  - |  D |  LM |  B |  3 |  Alternating Landmark-Moving AUV architecture, Requires relative range and angle measurement. Vehicles requires hovering capability or land on ocean floor.
|  [30] |  |  |  |  |  |  EKF |  N |  |  S |  - |  N |  - |  D |  LM |  B |  3 |  Heterogeneous team, Leader-follower and Static LM approaches. Centralised Estimation.

  * •

Considered  Not considered. Results: E - Experimental, S - Simulation, EPP -
Post processed experimental data. Ranging Method: O - OWTT, T - TWTT, U -
USBL, D -TDOA. Velocity Sensing: D - DVL, A - ADCP, TE - Thrust estimation
from motor speed, R - Required but not specified. Obs. Analysis \ Metric: NL -
Non linear weak observability. Model: C - Continuous, D - Discrete. Channel
Sharing: T - TDMA, B - Broadcast, RR - Request/Reply, TB - TDMA Broadcast, S -
Simultaneous.

##### Parallel

In this approach, the team members share range and position information with
their immediate neighbors or all the team members through broadcast. In the
prior case, we have directed graph-based topology, while in the latter, we
have mesh topology. When absolute position information is not available with
any of the vehicles, only the error growth rate can be reduced with this
method. Eventually, at least one vehicle will have to acquire absolute
positioning information from GPS, ASV, LBL, etc., to bound the error.

In [152], the authors present an interleaved update (IU) algorithm that
ensures consistency of estimates free from overconfidence that could be
induced due to the reception of multiple instances of the same information
from different vehicles. For this, the authors suggest a bookkeeping approach
to properly keep track of measurements to be incorporated, including the
cross-correlations of position estimates between vehicles. Every vehicle has
multiple estimation filters that track the source of each range measurement.
Only those estimates are used which are known to be uncorrelated. The team is
assumed not to have a structure, and any member can join or leave at any time.
The approach can also take care of lost packets. The disadvantage is that the
method cannot be scaled beyond three to four vehicles due to the large
covariance information that needs to be transmitted. Also, the estimates are
quite conservative. In [153], a linear programming and convex optimization-
based solution for multiple AUVs equipped with low-cost sensors is presented.
Each AUV is assumed to have a sensor that can measure range and bearing with
respect to other AUVs. The complexity of this algorithm increases rapidly for
a team size of more than ten. In [154], a probabilistic method to minimize the
localization uncertainty for AUVs working under ice sheets is proposed. The
acoustic packets exchanged between AUVs are used to estimate the ranges
between them, and using Doppler shifts, the velocity of own vehicle is
estimated. Using them and the uncertainties in other vehicles’ locations
transmitted in packets, a probabilistic method minimizes the location
uncertainty. An algorithm to optimize the trade-off between communication
overhead and localization error is also presented. In [155], an approach using
inter-vehicle ranges and range differences that do not need time
synchronization is proposed. Each vehicle interrogates other vehicles
sequentially and calculates the relative range from the reply using TWTT.
Other vehicles not in the current communicating pair eavesdrop on the
broadcasts and use the range information to calculate range differences, which
are then used along with their ranging information to construct Euclidian
Distance Matrices (EDM) for localization. To mitigate noisy and incomplete
data, which will lead to ill-defined EDM, three optimization-based techniques
are proposed and evaluated against a least-squares-based approach and non-
optimized EDM. Results indicated EDM with plain ranges and Lower-Bounded
Epigraph performs the best. In [34], geometric constraints that may exist
within the team are exploited through the projection approach. The paper uses
nonlinear to LTV transformation from [156], which lends to the use of simpler
linear KF for state estimation. The inclusion of the geometric constraints
gives much lower positional errors and covariance than without. It is required
that there exists a cyclic connectivity within the connection graph, which may
not always be true. In [157], decentralized state estimation in formations of
vehicles with time-varying topologies is presented. Each AUV relies on a local
observer using local measurements and limited communications with neighboring
vehicles for its state estimation. Some of the vehicles are assumed to have
access to absolute position information from LBL/USBL system. Sufficient
conditions for global exponential stability of error dynamics are derived
using switching systems theory. The approach is extended to acyclic formations
with fixed topologies In [158]. The performance of KF is shown to be similar
to EKF but with observability and stability guarantees. This is important as
EKF is known to diverge rapidly if the choice of initial conditions is poor.
The same authors addressed the problem of distributed state estimation in a
multi-vehicle fixed formation framework using discrete KF formulation in
[159]. Two algorithms, one-step and finite horizon, are proposed to find the
steady-state discrete-time KF gains with sparsity constraints. The first one,
which calculates current gain based only on current covariance, is
computationally less intensive and simple; its error performance is worse. The
latter has better error performance but has a higher computational load. In
[160], a DEIF-based decentralized cooperative localization strategy that is
well suited for low bandwidth acoustic communication and is robust against
packet loss is proposed. Its performance is compared against distributed Naive
KF and Single KF for different packet loss scenarios. It is shown that the
proposed method provides better estimates compared to the other two and is
robust against packet loss. In [31], an approach using relative concurrent
range and bearing measurements from vision-based sensors is presented. The
localization problem is solved using a variant of convex disk relaxation. A
set of position/bearing reference nodes or anchors are assumed to be deployed
at fixed locations and accessible to vehicles over time. The approach is most
effective when the vehicle trajectories are predominantly linear and suffers
from position /attitude ambiguity when anchors are not accessible. In [36,
161], localization among a team of AUVs in the mid-ocean zone in the presence
of ocean background flows is investigated. The large background flows are
preloaded from ocean general circulation models (OGCMs) and are used in
localization, while the local flows are measured using ACDP/DVL sensor. The
vehicles communicate state information when in range of each other. Cross-
correlation is taken care of with the covariance intersection method. A
marginalized PF/Rao-Blackwellized PF is used for state estimation utilizing an
EKF for position and velocity estimation to reduce the number of particles
otherwise needed considering the large state vector size. In [162], an
approach that uses information entropy-based criteria to evaluate and select
information from neighboring vehicles to update its state is proposed. The
performance was evaluated based on mutual information, relative distance, and
estimated covariance in two cases, leader-follower and parallel architecture.
The simulations indicate that selecting the AUVs closest for updates gave the
best performance. A fuzzy logic-based localization scheme for large swarms is
presented in [163]. The localization is carried out using a trilateration
approach using PSO at each AUV. Some of the AUVs are updated from a boat using
USBL. These AUVs then communicate and localize others in the swarms.

TABLE VIII: Overview of CL using parallel method and CSLAM

Reference |  Propagation Path |  Packet Loss |  Packet Latency |  Measurement Outliers |  Bandwidth |  Estimator |  Scalable? |  Ocean Currents |  Results (Sim/Exp) |  Ranging Method |  Velocity Sensing |  Obs. Analysis\ Metric |  Model |  Channel Sharing |  Team Size |  Remarks
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
[152] |  |  |  |  |  |  IU/ EKF |  Y |  |  S |  O |  - |  - |  D |  TB |  3 |  Bookkeeping for tracking measurement origins ensuring estimate consistency.
[153] |  |  |  |  |  |  LP/ Convex Opt. |  Y |  |  S |  - |  - |  - |  - |  - |  13 |  Complex algorithm, requires bearing measurements along with range.
[154] |  |  |  |  |  |  UKF |  Y |  |  S |  O |  P/A |  - |  - |  T |  12 |  Incorporates Doppler shifts in communication for reducing uncertainty in under ice autonomous navigation.
[155] |  |  |  |  |  |  Euclidean Distance Matrices |  N |  |  E |  T |  - |  - |  - |  RR |  3 |  Ranges and range differences are used to localize. Requires large number of acoustic transmissions. AUV’s eavesdrop on other transmissions. Experiments with towed nodes.
[34] |  |  |  |  |  |  KF |  N |  |  S |  - |  R |  NLTV |  C |  - |  4 |  RPMG based approach. Requires cyclic connections in graph for geometric constraints (for observability).
[157], [158] |  |  |  |  |  |  Luenberger (Decentralised) |  Y |  |  S |  - |  - |  LTI |  C |  - |  6 |  Decentralized Observer. Time varying topologies [157]. Acyclic fixed topologies[158]
[160] |  |  |  |  |  |  DEIF |  Y |  |  EPP |  O |  - |  - |  D |  RB |  3 |  Low bandwidth acoustic communication that is robust against packet loss.
[31] |  |  |  |  |  |  LS |  N |  |  S |  - |  - |  - |  D |  - |  10* |  Hybrid approach. *Requires static beacons. Visual bearing sensors.
[36] |  |  |  |  |  |  RBPF |  Y |  |  S |  O |  A |  - |  D |  - |  4 |  Uses Rao-Backwellized PF. Requires ocean general circulation models. Mid water zone.
[162] |  |  |  |  |  |  EKF |  N |  |  S |  - |  D |  - |  D |  B |  9 |  Requires bearing information. Information entropy based neighbor selection.
[163] |  |  |  |  |  |  EKF/PSO-Fuzzy |  Y |  |  S |  O |  D |  - |  D |  T |  50+ |  Fuzzy logic based. PSO trilateration at each node.
[164] |  |  |  |  |  |  EKF |  Y |  |  S |  - |  N |  DJ |  D |  - |  2 |  AUV’s are assumed to not suddenly turn or accelerate, Only one AUV localizes with respect to other. Uses linearised model.
[165] |  |  |  |  |  |  EKF |  - |  |  EPP |  O |  R |  NL |  C |  - |  2 |  Observability analysis. 3D Model. Experiment using two surface crafts instead of AUV
[166], [167] |  |  |  |  |  |  Ext. Luenberger [166]/ EKF[167] |  - |  |  EPP |  T |  D |  NL |  C |  - |  2 |  Experiment using one AUV and one static beacon. Uses inverse of condition no. for optimality.
[156], [168] |  |  |  |  |  |  - |  - |  |  S |  - |  R |  NLTV |  C |  - |  2 |  3D Model. Observability of relative positioning between 2 AUV’s. Cases where at least one AUV has zero linear speed. Point mass model
[29] |  |  |  |  |  |  DSEKF |  Y |  |  E |  - |  - |  - |  D |  - |  3 |  Heterogeneous server-client. Doesn’t consider bandwidth limits. Experiments on land robots.
[28] |  |  |  |  |  |  FG |  Y |  |  S |  O |  D |  - |  D |  T |  2 |  Uses side scan SONAR imagery. Low communication overhead.
[169] |  |  |  |  |  |  EKF |  N |  |  S |  T |  D |  - |  D |  T |  7* |  *Uses 5 beacons as landmarks. Centralized processing.
[170] |  |  |  |  |  |  PF |  Y |  |  EPP |  O |  TE |  - |  D |  RB |  3 |  Bathymetry based, uses Decentralized Marginalized PF, Requires a priori map.
[171] |  |  |  |  |  |  PF |  Y |  |  EPP |  O |  D |  - |  D |  RB |  3 |  Terrain Relative Navigation based PF with Covariance intersection.

  * •

Considered  Not considered. Results: E - Experimental, S - Simulation, EPP -
Post processed experimental data. Ranging Method: O - OWTT, T - TWTT, U -
USBL, D -TDOA. Velocity Sensing: D - DVL, A - ADCP, TE - Thrust estimation
from motor speed, R - Required but not specified, P-Doppler shift in
communication packets. Obs. Analysis \ Metric: NL - Non linear weak
observability, NLTV - Non linear to linear time varying transformation, DJ -
Determinant of Jacobian. Model: C - Continuous, D - Discrete. Channel Sharing:
T - TDMA, B - Broadcast, RR - Request/Reply, TB - TDMA Broadcast, RB - Round
Robin.

Quite a few works have also investigated the observability conditions in the
parallel approach. In [164], the observability analysis of localization using
DR and range measurements between two AUVs is presented under the assumptions
of no velocity measurements and zero latency of acoustic signals in a 2D
scenario. The local weak observability condition is derived from the
determinant of the Jacobian of two consecutive range measurements, which
requires that the two vehicles should not move parallel to each other at the
same velocity. In other words, the team members should exhibit sufficiently
exciting relative manoeuvrers for the network to be locally weakly observable.
This is extended to 3D space in [165]. The nonlinear model-based weak
observability condition is shown to be less stringent than the conditions
using a linear model. The linear observability condition requires non-null
angular velocity; in contrast, the weak observability condition does not. The
authors use EKF-based observer for state estimation using their own and other
vehicles’ linear and angular velocity, orientation, and depth data. Instead of
the binary rank condition for observability presented in [165], [166, 167]
propose inverse of the condition number of observability matrix as a better
measure of observability. The analysis is carried out in 3D space, and it is
shown that the state’s vertical component does not affect observability if it
can be directly measured. Further, the system is observable as long as the
relative position and velocity vectors are not parallel. In [156],
observability analysis using the state augmentation technique to transform a
nonlinear system into a higher dimensional LTV system is presented for a case
of two AUVs. Linear system observability analysis is used to find the
indistinguishable states of the nonlinear system. This is done for a limited
case of constant angular and linear velocities and a point-mass model to keep
the analysis mathematically tractable. It is shown that the approach leads to
global observability conditions rather than the weak local notion of
observability and that there is a one-to-one correspondence between the
trajectories of the augmented LTV system and the original nonlinear system. In
[168], the above analysis is extended to the case wherein both the AUVs move
with constant nonzero linear velocities and the observing vehicle with
constant nonzero angular velocity. Also, the relative angular velocity, as
seen from observing the vehicle, is assumed constant. The observability
analysis of the augmented state vector belonging to $R^{25}$ is carried out
using Popov - Belevitch - Hautus (PBH) Lemma. However, it is assumed that the
vehicle can turn on the spot, i.e., the angular and linear velocities are
independent. This restricts the analysis of a limited set of underwater
vehicles.

An overview of parallel approaches is given in Table VIII.

##### Cooperative SLAM

In simultaneous localization and mapping (SLAM), an extensive review of which
can be found in [172], the autonomous vehicle is assumed to be equipped with
some sensor with which the vehicle can map its surroundings. The most popular
are LIDAR, ultrasonic distance sensors, monocular or stereo vision systems,
RADARs, and SONARs. In an underwater environment, SONAR-based sensors such as
side scan, multibeam, and echo sounders are much more prevalent than LIDARs
and vision. This is due to the reasons mentioned in section II. However, in
clear waters and narrow structures such as flooded mines/caves, etc., LIDARs
and vision sensors are finding increasing acceptance. With a single vehicle,
though, mapping and subsequent localization can take a large amount of time.
This has led to an interest in the field of cooperative SLAM. Here, each of
the vehicles is outfitted with some mapping sensor, information from which is
shared with others for localization.

Walter et al. [29] presented an approach using a heterogeneous server-client
AUV configuration. The sensor data of environmental observations made by all
the vehicles are fused using a SLAM algorithm in a centralized manner on one
of the leader vehicles. The output is communicated back for the navigation of
other parent and child vehicles. Data association is carried out using a joint
compatibility branch and bound (JCBB) test. In [28], a CSLAM algorithm
utilizing side-scan sonar images and INS is proposed. The proposed algorithm
is robust against packet loss and generates acoustic packets that are small
enough to be transmitted in the underwater acoustic channel. The method
employs factor graph-based SLAM with data reduction using intermediate
(between communications) state marginalization by Schur’s complement and
further consistent sparsification by convex optimization using KLD as the cost
between original and sparsified data. In [169], an acoustic-SLAM approach is
proposed in which a client AUV and static beacons are localized using a server
AUV having USBL. The static beacons’ location, which later acts as landmarks,
is assumed to be initially unknown. The estimation is carried out centrally on
the server AUV using EKF, which then communicates the estimates to child and
beacon nodes. The approach does not scale with the number of client vehicles
due to the TDMA scheme employed and two-way communication. Furthermore, the
necessity of static beacons requires deployment and retrieval. Tan et al.
[170] proposed a bathymetry based multi AUV cooperative localization scheme
wherein the AUVs utilize only a low-cost sensor set of an altimeter, depth
sensor, and an acoustic modem. The collected sensor data is fused in a
decentralized Marginalized PF (DMPF), i.e., the marginalized linear dynamical
states are estimated using KF while the others with PF reduce the
computational and communication load. The other vehicles’ beliefs, along with
the estimated inter-vehicle range, are used to influence the particle
distribution and likelihood computation and are not fused directly in the
filter to prevent the effects of large errors in the beliefs/position on
estimates. The bathymetric map data is used to update the measurement model of
the PF. This approach requires the bathymetry map of the area a priori, and
the proposed DMPF algorithm does not take cross-correlation into account. In
[171], terrain relative navigation with inter-robot measurements is proposed
for multi-robot localization. A particle filter is used along with a
covariance intersection filter. The complexity only grows linearly with the
number of vehicles. However, it is assumed that the terrain map is available
and clocks are synchronized.

The major impediment to this approach is the large amount of data that needs
to be exchanged among the vehicles. Given the bandwidth of the acoustic
channel, this is a very difficult challenge and remains an active area of
research.

###  III-C Other works

Several works have also investigated mixed strategies or combinations of the
approaches discussed in the previous sections. In [173], the authors proposed
a modular measurement distribution framework that is scalable and allows any
cooperating team member to share measurements using TDMA, enabling the whole
team to estimate positions consistently and accurately. The framework is
amenable to any cooperative approach, such as ASV/CNA-based, server-client,
parallel/mesh, or surfacing type, and is independent of any state estimation
scheme. It does not need an entire covariance matrix to be transmitted to
ensure no overconfidence in position estimates and ensures scalability,
although the algorithm is sensitive to packet loss. In [174], the experimental
comparison between 3 estimation algorithms, i.e., simple distributed EKF,
interleaved update, and distributed extended information filter (DEIF) against
a centralized EKF (Post-processed), are reported. In the case of DEIF, the
assumptions made render it useful only in two-node unidirectional topologies.
Different cooperating strategies considered between one ASV and two AUVs are
AUV aiding AUV, ASV aiding two AUV, 3 Node mesh, and ASV aiding AUV, which in
turn is a server for other AUVs. Results indicate that the distributed EKF
produces overconfident estimates when a strong correlation persists, while IU
and DEIF give consistent results. Otherwise, DEKF performs nearly as well as
CEKF. While DEKF and DEIF bounds error, IU does not. DEIF requires the largest
packet size among the three and is the least robust against packet loss.

There have been other approaches as well that combine cooperating vehicles
with one or more static beacons. For example, Mirza et al. [175] presented a
factor graph-based approach using maximum likelihood for CL between multiple
underwater vehicles and beacons in a distributed setup. Real-time and non-
real-time centralized setups were evaluated against real-time distributed
setup for cases wherein a) all states were shared with all neighbors (RTD-A),
b) all states were shared with an immediate neighbor only (RTD-B), and c)
current states shared with an immediate neighbor only (RTD-C), the latter
being the one with the least communication overhead and thus preferred in an
underwater scenario. The RTD-C scheme was evaluated for different no of
beacons and vehicles, indicating more collaborating vehicles and beacons, the
lower the error. When all the vehicles are in intermittent contact with the
beacons, it was reported that collaboration did not provide any improvement in
error, while minimum error for all vehicles is achieved when the beacons are
uniformly distributed. Maximum gain is for those vehicles which are not in
contact with the beacon. However, the proposed approach tends to deteriorate
collaborative localization performance when any one or more vehicles are
consistently not in contact with the beacon in a team of more than two
vehicles. Rego et al. [176] evaluated the performance of estimating the
position and velocity of vehicles under stringent communication bandwidth
constraints. It is assumed that there is a fixed beacon at a known location.
The vehicles either exchange measurements or state estimates. Adaptive
quantization is used to limit the amount of data sent over a communication
link under a zero packet loss assumption. In [177], an algorithm for optimal
placement of multiple heterogeneous beacon vehicles (including static nodes
such as GIB) not capable of rapid motions relative to AUVs is proposed.
Optimum locations are found by minimizing the trace of appropriately defined
CRLB matrix using range-only information. The locations are always estimated
on the perimeter of a circle, and at each step, the dynamic beacons move to
the optimal location. In [178], a hierarchical beacon-server-client
cooperative localization scheme using range information from time delays is
presented. The server AUV localizes with respect to the beacon, while the
client AUV localizes with respect to the server AUV and the single beacon. The
proposed architecture reduces the number of acoustic transmissions required
relative to each AUV localizing with respect to the beacon. However, the
server AUV errors are not discussed; the motions are considered to be stop-
and-go and require the server AUV speed and heading to be different from the
team members. In the coordinate fusion technique, all AUVs have to
communicate, which negates the original proposals’ advantage of lower
communication overhead.

This concludes the review of all the works in the domain of cooperative
localization in the underwater scenario. In the next section, we briefly
discuss the issues and open problems in this area.

##  IV DISCUSSION AND OPEN PROBLEMS

Before we discuss the open challenges in the cooperative localization of
underwater vehicles, we briefly summarize the research presented in the
preceding section.

As noted, the estimation algorithm forms the heart of the localization
problem. While EKF [40, 55] is widely popular, as can be gauged from the
tables, several different estimation techniques have been proposed across all
categories, such as least squares [41], least mean squares [42], UKF [43, 91],
Decentralised LS-MLE [45], Decentralised EIF [46], distributed extended
information filter [174], Delayed State Centralized EKF [18, 111], centralised
EKF [98], Interleaved Update (IU) [47, 47], iterative divided difference
filter [58], Factor graphs: [59, 117, 175], Maximum-A-Priori (MAP) [59, 94],
moving horizon estimation [60, 99], particle filters [61, 63], distibuted EKF
[64], distributed modified EKF [113], origin state method [115], Parallel
projection algorithm+MLE [119], hybrid UKF-KF estimator [121], delayed state
Adaptive KF [122], augmented EKF [126], probability hypothesis density filter
[127], unscented PF [134], Student-t based EKF [135], Linear programming
[153], fuzzy logic [163] and SLAM [28, 169, 170]. Authors have also exploited
geometric properties of the localization problem, such as in [48, 118, 34].
Often the initial location of the vehicle may not be known; for this, a few
methods are suggested in [56], which are useful for initializing EKF-based
estimators.

As for the challenges presented by the acoustic channel, several authors have
presented solutions for low bandwidth, such as by using estimators [46, 160],
logic-based communication [87], adaptive time-of-launch [88], reducing
communication overhead [154] and adaptive quantization [176]. For outlier
mitigation most approaches use Mahalanobis distance metric [51] while others
have proposed different noise distributions such as heavy-tailed mixture
distribution [104], Student-t based EKF [135] or different estimators like
Huber based M estimator [58], maximum correntropy-PF [132], unscented PF [134]
and MCC-ANFIS [136]. Managing delays in communication is carried out either
through back and forth technique [98, 51] or delayed state estimators [18,
125, 126]. Some techniques to estimate sound speed profile and refraction are
mentioned in [42].

For path planning of ASVs and server vehicles the approaches include simple
paths such as diamond [18], zig-zag [55] or circular [63] or online path