# ConservationBots: Autonomous Aerial Robot for Fast Robust Wildlife Tracking
in Complex Terrains

Fei Chen
School of Computer Science
The University of Adelaide
SA 5005, Australia
<EMAIL_ADDRESS>
&Hoa Van Nguyen
Department of Electrical and Computer Engineering
Curtin University
WA 6102, Australia
<EMAIL_ADDRESS>
&David A. Taggart
School of Animal and Veterinary Science
The University of Adelaide
SA 5005, Australia
<EMAIL_ADDRESS>
&Katrina Falkner
School of Computer Science
The University of Adelaide
SA 5005, Australia
<EMAIL_ADDRESS>
&S. Hamid Rezatofighi
Department of Data Science & AI
Monash University
VIC 3800, Australia
<EMAIL_ADDRESS>
&Damith C. Ranasinghe
School of Computer Science
The University of Adelaide
SA 5005, Australia
<EMAIL_ADDRESS>

###### Abstract

Radio tagging and tracking are fundamental to understanding the movements and
habitats of wildlife in their natural environments. Today, the most
widespread, widely applicable technology for gathering data relies on
experienced scientists armed with handheld radio telemetry equipment to locate
low-power radio transmitters attached to wildlife from the ground. Although
aerial robots can transform labor-intensive conservation tasks, the
realization of autonomous systems for tackling task complexities under real-
world conditions remains a challenge. We developed ConservationBots—small
aerial robots for tracking multiple, dynamic, radio-tagged wildlife. The
aerial robot achieves robust localization performance and fast task completion
times—significant for energy-limited aerial systems while avoiding close
encounters with potential, counter-productive disturbances to wildlife. Our
approach overcomes the technical and practical problems posed by combining a
lightweight sensor with new concepts: i) planning to determine both trajectory
and measurement actions guided by an information-theoretic objective, which
allows the robot to strategically select near-instantaneous range-only
measurements to achieve faster localization, and time-consuming sensor
rotation actions to acquire bearing measurements and achieve robust tracking
performance; ii) a bearing detector more robust to noise and iii) a tracking
algorithm formulation robust to missed and false detections experienced in
real-world conditions. We conducted extensive studies: simulations built upon
complex signal propagation over high-resolution elevation data on diverse
geographical terrains; field testing; studies with wombats (Lasiorhinus
latifrons; nocturnal, vulnerable species dwelling in underground warrens) and
tracking comparisons with a highly experienced biologist to validate the
effectiveness of our aerial robot and demonstrate the significant advantages
over the manual method.

Keywords— aerial robotics, autonomous UAV, radio-collared animals, remote
sensing, VHF telemetry, position tracking

##  1 Introduction

Understanding movements, activities, and patterns in animal behaviors are
essential for biodiversity conservation, natural resource management, and
precision agriculture. Today, field scientists employ multiple techniques,
such as vision-based sensors [101, 64, 92, 69], Global Positioning System
(GPS) tags, or Very High Frequency (VHF) tags [67, 82] to study animal
behaviors, movements, and activity. Despite the advances in technology, VHF
radio telemetry or radio-tracking is still the most important tool employed to
study the movement of animals in their natural environments. Because they are
smaller, lightweight, suited for nearly all mammal and bird species, and
operate for longer in comparison to GPS-based counterparts. Consequently,
remain a popular and cost-effective technique for field studies [63, 114].
However, the traditional method of radio-tracking typically requires
researchers to trek long distances in the field, armed with cumbersome radio
receivers with hand-held antennas and battery packs to manually home in on
radio signals emitted from radio-tagged or collared animals. The precious
spatial data acquired through radio-tracking comes at a significant cost to
researchers in terms of manpower, time, and funding. The problem is often
compounded by other challenges, such as low animal recapture rates, equipment
failures, and the inability to track animals that move into inaccessible
terrain or underground burrows.

Developments in low-cost unmanned aerial vehicles (UAVs) with the capacity to
carry payloads, such as radio receivers and antennas [58], is a potential
solution. Because of the advantages offered by the ease of deployment and high
mobility, UAVs have the potential to automate and scale up manual tasks to
significantly reduce the time, labor, and cost of employing traditional
tracking approaches. Early achievements in autonomous systems for wildlife
tracking have demonstrated robotic platforms for the task [105, 107, 66, 90].
The approaches localize VHF radio-tagged animals using either the Receiver
Signal Strength Indicator (RSSI) or Angle of Arrival (AoA) of radio signals
emitted from radio tags where the robot’s trajectory planning algorithm endows
autonomy to improve the localization accuracy—[65, 66] or reduce the tracking
error— [90]. Despite the recent advancements, the realization of an autonomous
UAV capable of dealing with the technical and practical complexities of the
problem remains a challenge. For example:

  * •

RSSI-based approach—capable of rapid measurements and benefiting from a simple
receiver that requires a single directional antenna, only demonstrates
superior performance across mostly flat terrains or when the radio propagation
model is accurately known [90]. But, building and employing an accurate radio
propagation model requires access to terrain information and dealing with
variables that can change dynamically, such as changes in signal attenuation
due to the appearance of trees and the impact of moisture conditions on signal
propagation.

  * •

AoA approach—although more robust in unfamiliar or complex environments,
requires a larger and bulky antenna array and long measurement acquisition
times; 45 seconds per measurement [65].

  * •

Practically, autonomous systems need to operate under limited battery power,
on-board processing, flight times, and payload capabilities of UAVs (ideally,
an aerial robot should fly, track and locate animals and return to base
without needing an intervening battery change away from the base).

  * •

Multiplicity of VHF radio signal propagation in complex terrains complicates
automatic localization algorithms and detection of, often weak signals, of
simplistic wave modulations from VHF radio collars.

  * •

Potential disturbances to animals caused by the operation of the UAV [100, 75,
73], is counterproductive to the task and requires mitigation strategies.

Our work formulates a planning problem for a new hybrid approach to exploit
the simple and fast RSSI measurement acquisitions and selectively exploit the
slower, more robust AoA measurements by providing an aerial robot the autonomy
to plan not only its trajectory to track and locate animals but also its
measurements to track multiple, mobile, radio-tagged wildlife, simultaneously.
The robot we have developed is fast, robust, and scalable to simultaneously
track and localize multiple radio-tagged wildlife while planned trajectories
minimize disturbances to wildlife. We summarize our main contributions below:

Figure 1: A ConservationBot in flight, right after take-off to track and
locate Southern Hairy-nosed wombats. Inset: Southern Hairy-nosed wombat
_Lasiorhinus latifrons_ released into their habitat after being tagged with a
VHF radio collar.

  1. 1.

We propose planning not only trajectories but also the measurement method. The
planning algorithm formulation determines the most informative trajectory and
measurement acquisition actions to reduce the time needed to track and locate
multiple, dynamic, radio-collared wildlife in various terrain conditions. The
planner allows the robot to i) exploit the simplicity and rapidity of RSSI
measurement acquisitions for range-only tracking; and ii) the time-consuming
bearing measurement method when range-only measurement uncertainty is high.
Importantly, to avoid close approaches to wildlife and minimize potential
disturbances, trajectory planning is constrained by a probabilistic void
region.

  2. 2.

Our state estimation algorithm for tracking is robust across variable
environmental and terrain conditions as well as VHF signal propagation
artifacts to localize radio-tagged wildlife in various outdoor environments in
3D settings without detailed terrain information. To achieve this robustness:
i) we integrate an imprecise likelihood function to account for the complex
radio propagation effects such as signal diffraction and vegetation
attenuation, removing the need for a precise RSSI measurement model. This
method expands the versatility of the estimation algorithm to allow RSSI
measurements to be used for tracking when an accurate model of measurements in
a given terrain is difficult to build; ii) we propose a bearing detector based
on the rotation AoA measurement method to generate more robust AoA
measurements under noisy conditions; and iii) compared to prior approaches, we
have explicitly considered practical challenges in tracking radio-tagged
animals such as missed measurements, object birth, and death, poor signal-to-
noise ratio impacting signal detection probabilities and formulated a
Bernoulli Bayesian filter (BF) for the tracking task.

  3. 3.

To examine the performance of our system, we used extensive Monte-Carlo
simulations modeling complex VHF signal propagation over 3D terrains with
different levels of complexity and extensive field experiments. Our field
testing included over $30$ missions and a pilot study with radio-tagged
southern hairy-nosed wombats (Lasiorhinus latifrons), a nocturnal, burrowing
species that uses underground warrens and, therefore, challenging to track
with manual methods as well as an autonomous system versus expert-human-
tracker field trials to demonstrates the efficacy, performance, and
versatility of our system.

##  2 Related Work

The problem of using UAVs to localize radio sources has been studied recently
in the literature. More broadly, existing studies can be categorized based on
the measurement methods employed; those using RSSI-based methods or those
using AoA-based methods. The design of the system and algorithms are primarily
a function of the measurement method employed. Hence it is useful to consider
previous methods from this perspective. We also provide a brief review of
related works in Multi-object tracking methods since our work focuses on
tracking multiple animals.

###  2.1 AoA-based systems

A widely used method for measuring the AoA of RF signal is through the use of
a phased array antenna. While the method can measure AoA with high accuracy
with minimum measurement time, it requires specialized hardware and
sophisticated signal processing algorithm. Therefore, such a sensor payload is
difficult to mount and employ on a UAV platform due to weight, size, and
processing power constraints. Consequently, an alternative approach has
emerged using a directional antenna, which is rotated to determine the
direction of the signal source to detect AoA. [72], an early study,
demonstrated a ground-based robot system that used a rotating directional
antenna to determine the AoA and locate the source of a wireless node. [108]
later developed an RF source-seeking system with a single-wing rotating micro
aerial vehicle. By fitting a directional antenna to its wing and exploiting
the natural rotation of the vehicle, the system can quickly estimate the AoA
of an RF source at each rotation.

Early efforts to demonstrate the rotating AoA-based methods for radio-tagged
animal localization were reported in [105],[65],[113], [66], and [106]. The
studies developed a multi-rotor UAV system with a path-planning algorithm to
direct the UAV to collect AoA measurements. AoA methods are robust against the
multi-path effects of radio propagation but the measurement time required (45
seconds per measurement in [65]) is significantly longer than RSSI-based
approaches with near-instantaneous measurements. The impact of longer
measurement times is more practical—it limits the maximum search area,
increases flight times to complete a task, and reduces the ability to locate
mobile animals. For example, while undertaking a slow rotation can increase
the accuracy of the acquired AoA measurement for static wildlife, it is
counterproductive if objects are mobile.

An alternative, a pseudo-bearing approach [68], sought to address the
limitations of rotational AoA methods by incorporating an additional uni-
directional antenna along with a directional antenna, albeit for operation at
a much higher frequency, 2.4 GHz, than VHF. As a result, the methods can
perform measurement updates more quickly and improve localization time.
However, this approach requires a more complex radio receiver with multiple
antennas; consequently, it increases the weight of sensor payload on a UAV,
especially in VHF signal tracking scenarios necessitating antennas with large
physical dimensions, while trajectory planning with such an approach also
remains to be demonstrated in practice.

###  2.2 RSSI-based systems

In contrast, the RSSI-based systems utilize signal strength to estimate the
distance between the radio transmitter and the receiver. This approach only
requires a simple and lightweight receiver and antenna. The use of RSSI-based
measurements on board a UAV to locate radio-tagged wildlife was demonstrated
by [83], where a fixed-wing UAV equipped with a directional antenna was used
to locate a fixed location radio tag. Then, a system based on a multirotor UAV
with an omnidirectional antenna was presented in [99]. The approach employed a
receiver to capture measurements of the radio signal’s signal-to-noise ratio
and estimated the radio tag’s position offline. [90, 89] demonstrated an RSSI-
based aerial robot with online path planning for RSSI measurements and a
particle filter-based estimation method using a customized, lightweight
directional antenna for localizing multiple mobile objects on relatively flat
terrains. [78] took a similar approach using a small UAV with a dipole antenna
to collect RSSI measurements along a fixed trajectory where the positions of
radio-collared animals were determined offline based on a signal propagation
model.

In contrast to AoA-based methods for the task, an RSSI-based system is more
efficient due to its simpler receiver and faster measurement acquisition
times. However, the key limitation is sensitivity to environmental effects
impacting radio signal propagation, signal diffraction, scattering, and
vegetation attenuation. Because propagation characteristics of the radio
signal need to be accurate but, in practice, can be difficult to model.
Topographical variations, vegetation coverage, or weather can result in
unpredictable attenuation of radio signals and thus limit the scenarios in
which RSSI-based methods can be reliably applied. As a consequence, RSSI-based
methods are mostly used in less complex environments where radio propagation
is easily modeled and predictable.

###  2.3 Multi-object tracking

The primary problem in multi-object tracking is to estimate the state of
multiple objects when the associations between measurements and objects are
unknown. Traditional methods, including joint probabilistic data association
(JPDA) filter [60], multiple hypothesis tracking (MHT) filter [62] explicitly
associate measurements and objects. More recent approaches based on random set
statistics[87] have led to methods such as the probability hypothesis density
(PHD) filter[88], cardinalized PHD (CPHD) filter [86], multiobject multi-
Bernoulli filter [87, 112], generalized labeled multi-Bernoulli (GLMB) filter
[111] and labeled multi-Bernoulli (LMB) filter [95]. However, in our problem,
individual radio-collared wildlife can be uniquely identified by the frequency
of its radio-collar signal. Therefore, we do not need to solve the complex
data association problem. The model for measurements (RSSI or AoA) is non-
linear, therefore a filter suitable for non-linear systems, such as a particle
filter [70] was used in prior robotic systems for the task. In contrast, we
consider a particle implementation of a Bernoulli filter [87] formulation not
only to account for a non-linear system but also to explicitly model practical
signal propagation effects, such as measurement miss detections and false
detections into the formulation. Thus, making the method of estimating the
location of wildlife more robust than the particle filter.

###  2.4 Summary

RSSI-based and AoA-based methods are commonly used for estimating the location
of radio sources. When radio propagation can be accurately modeled, the RSSI-
based methods provide significant advantages over AoA-based approaches, given
their simplistic receiver design and low measurement time. However, in a
complex environment, the AoA approach is a more robust method due to it being
invariant to various environmental variables and the difficulty of building
accurate propagation models for complex terrains to support RSSI-based
methods. We present an approach that combines the advantages of these two
measurement approaches; an aerial robot system that takes advantage of both
methods while minimizing their limitations.

Importantly, existing systems, irrespective of the measurement method, used an
online estimator to determine the location of objects. The estimator, based on
Bayesian estimation theory, requires accurate noise models and sensor
measurement models to determine the probability distribution of objects; these
estimation methods include particle filters [90] [83], grid filters [65][66]
and Kalman filters [81]. Notably, these estimators cannot handle practical
challenges with trackings, such as missed detections and false detections;
explicitly modeling these real-world conditions may lead to better estimation
accuracy.

Figure 2: An overview of the proposed Bayesian-POMDP theoretical framework to
realize an autonomous aerial vehicle for fast, robust tracking of multiple
wildlife in complex terrains. Here, the UAV state is denoted by
$\mathbf{u}_{t}$, and the belief densities of the set of objects (in our case
wildlife) are denoted by $\mathbf{X}_{t}$. Briefly: i) the proposed
compensated AoA measurement detector employs RSSI measurements
$\mathbf{Z}_{\text{R},t}$ during an AoA measurement action
$\mathbf{a}_{t}\in\mathbb{A}_{\text{AoA}}$ to generate an AoA measurement
$\mathbf{Z}_{\text{A},t}$; ii) Bernoulli filters utilize RSSI measurements
$\mathbf{Z}_{\text{R},t}$ along with the imprecise RSSI model and AoA
measurements $\mathbf{Z}_{\text{A},t}$ along with the AoA model at time $t$ to
achieve robust estimations of object states (e.g., the position of each
wildlife); and iii) the new measurement (AoA, RSSI) and trajectory planning
formulation using a POMDP generate control actions $\mathbf{a}_{t}$ while
ensuring the UAV maintains a safe distance from the wildlife of interest by
generating void constrained trajectories.

##  3 Proposed Planning for Tracking and Localization Problem Formulation

We consider the problem of controlling a UAV equipped with a simple sensor
system—a directional antenna and a digital signal processing module—for
autonomously localizing multiple radio-tagged wildlife while maintaining a
safe distance from the wildlife of interest to prevent potential disturbances.
Performing tracking (estimating the positions of individual radio-tagged
wildlife over time) in real-time necessitates an online estimation method. And
performing the task autonomously necessitates a dynamic planning method for
robot navigation. In contrast to previous problem formulations, we consider
incorporating an RSSI measurement model uncertainty to remove the need for
accurate measurement models—difficult to derive in practice due to changing
terrain and environmental conditions—and consider practical signal detection
artifacts such as missed and false detection to formulate a robust method of
estimating the locations of wildlife using a Bernoulli Bayesian filter.
Further, in contrast to previous approaches, we consider dynamically planning
both the trajectory and the signal measurement method using a POMDP (partially
observable Markov decision process) formulation to allow the autonomous
selection of the most informative measurement method: i) simple and fast RSSI
measurements; or ii) slower but more robust AoA measurements.

Figure 2 provides an overview of our proposed planning for tracking and
localization approach built upon a joint Bayesian-POMDP theoretical framework,
which includes: i) an AoA measurement model and an RSSI measurement imprecise
model for increased tracking and localization robustness against the impacts
of varying terrain and environmental conditions; ii) compensated rotation AoA
measurement method to generate AoA measurements with higher accuracy under
noisy conditions; iii) Bernoulli Filter employing both RSSI and AoA
measurements to produce estimated object states (tracks), even under low
measurement detection probabilities, experienced in practical system
deployment settings; iv) measurement and trajectory planning to select both
the best trajectory and measurement method for faster and more robust
localization under different terrain conditions while minimizing disturbances
to the wildlife of interest. In the following sections, we detail our
formulation of real-time planning for tracking and localizing wildlife
described in Figure 2.

###  3.1 State Estimation and Measurement Models

This section presents our online tracking and localizing formulation under the
theoretical framework of a Bernoulli Bayesian filter to formulate a robust
method of estimating the locations of wildlife using the proposed AoA
measurement detection method, the associated measurement model, and the
imprecise RSSI measurement model.

Prior to proceeding further, we introduce the following conventions for
notation consistency: standard letters (_e.g._ $x,~{}X$) for scalar values,
lowercase bold letters (_e.g._ $\mathbf{x}$) for vector values (_e.g._ single-
object states); bold capital letters (_e.g._ $\mathbf{X}$) for set values
(_e.g._ multi-object states); blackboard letters (_e.g._ $\mathbb{X}$) for
state spaces.

####  3.1.1 Radio Signal Model of a VHF Wildlife Collar

It is first useful to understand the nature of the signal source since the
measures of this signal will need to be employed to estimate the location of
each wildlife. Each radio tag employed for studying wildlife emits an on-off-
keying signal at a unique frequency $f$ with an unknown time offset
$\tau\in\mathbb{R}_{0}^{+}$ as illustrated in Figure 3. Now, let’s denote the
state of the UAV (observer) as
$\mathbf{u}=[\mathbf{u}_{l}^{T},\theta^{(u)}]^{T}\in\mathbb{R}^{3}\times[0,2\pi)$,
including its position $\mathbf{u}_{l}=[u_{x},u_{y},u_{z}]^{T}$ and heading
angle $\theta^{(u)}$ and the state of each radio-tagged wildlife as
$\mathbf{x}=[p_{x},p_{y},p_{z}]^{T}\in\mathbb{X}\subseteq\mathbb{R}^{3}$,
where $(\cdot)^{T}$ is the matrix transpose. Then, the noiseless signal
$\chi(t)$ at time $t$ from an object with state $\mathbf{x}$ received by a
directional antenna mounted on a UAV with state $\mathbf{u}$ in the far field
region can be modeled as [91]:

Figure 3: On-off-keying signal with pulse width $D$, period $T$, time offset
$\tau$ and amplitude $\gamma$.

$\chi(t)=\gamma(\mathbf{x},\mathbf{u})\cos[2\pi
ft+\Phi_{t}]\operatorname{rect}(D,T,t-\tau)$ (1)

where

  * •

$\Phi_{t}\in\mathbb{R}$ is the received signal phase at time $t$;

  * •

$\gamma(\mathbf{x},\mathbf{u})=\Gamma(d_{0})G_{r}G_{a}(\zeta(\mathbf{x},\mathbf{u}))(d_{0}/d(\mathbf{x,u}))^{n/2}$
is the received signal amplitude when the distance between object $\mathbf{x}$
and observer $\mathbf{u}$ is $d(\mathbf{x,u})$ and with source signal
amplitude $\Gamma(d_{0})$, which is measured at reference distance $d_{0}$
[93]; $n\in\mathbb{R}^{+}$ is the environment-dependent path-loss exponent;
$G_{r}$ is the receiver gain; $G_{a}(\cdot)$ is antenna gain pattern;
$\zeta(\mathbf{x,u})=\operatorname{arctan2}(\frac{p_{x}-u_{x}}{p_{y}-u_{y}})-\theta^{(u)}$
which convert the azimuth angle from object $\mathbf{x}$ to observer
$\mathbf{u}$ into the local reference frame of the observer with heading
$\theta_{u}$;

  * •

$\operatorname{rect}(D,T,\cdot)$ is a periodic rectangular function with pulse
width $D$ and period $T$, and $T>D$:

$\operatorname{rect}(D,T,t-\tau)=\sum_{i=-\infty}^{\infty}\operatorname{boxcar}(\tau,\tau+D,t+iT)$
(2)

and

$\operatorname{boxcar}(a,b,x)=\begin{cases}1,&a\leq x\leq b\\\
0,&\text{otherwise}\end{cases}$ (3)

####  3.1.2 Bernoulli Filter

To infer the unknown state $\mathbf{x}\in\mathbb{X}$ (3D coordinates of
wildlife) given noisy measurements $z\in\mathbb{Z}$, AoA and RSSI measurements
extracted from the received signals, we consider a Bernoulli filter—also known
as JoTT or joint object detection and tracking filter—[87][109][110]. Recall
each object—radio-collared wildlife—emits a signal at a unique frequency;
hence a unique object’s state $\mathbf{x}$ can be estimated from the
measurement and tracked independently. Thus, we do not need to solve the
complex data association problems typical of a multi-object tracking setting
and can estimate the state of each object using a Bernoulli filter formulation
independently.

The Bernoulli filter is an exact Bayesian filter based on the random finite
set theory (RFS) [87]. Notably, the filter is capable of handling practical
signal detection artifacts such as missed and false detections and dealing
with the reality of animals with VHF radio collars wandering in or out of the
sensor’s detection range in a unified framework.

The Bernoulli RFS $X$ can either have at most one element with probability $r$
distributed over the state space $\mathbb{X}$ according to probability density
function (PDF) $s(\mathbf{x})$ or empty with probability $1-r$:

$\Psi(\mathbf{X})=\begin{cases}1-r,&\text{if }\mathbf{X}=\emptyset\\\ r\cdot
s(\mathbf{x}),&\text{if }\mathbf{X}=\\{\mathbf{x}\\}\\\ 0&\text{if
}|\mathbf{X}|\geq 2\end{cases}$ (4)

where $|\mathbf{X}|$ denotes the cardinality of $\mathbf{X}$.

Given measurement set
$\mathbf{Z}_{t}=\\{z^{(1)}_{t},\ldots,z^{(|\mathbf{Z}_{t}|)}_{t}\\}$ at time
$t$, the posterior distribution $\Psi(\mathbf{X}_{t}|\mathbf{Z}_{1:t})$ from
time $t-1$ to time $t$ can be propagated in two steps, the prediction step and
update step. Notably, Bernoulli RFS (4) is entirely described by its existence
probability $r$ and single object PDF $s(\mathbf{x})$. Therefore, the
prediction and update step of (4) only needs to propagate $r$ and
$q_{\mathbf{x}}$.

The prediction step for the Bernoulli filter is

$\displaystyle\begin{split}r_{t|t-1}&=r_{b}\cdot(1-r_{t-1|t-1})+r_{s}\cdot
r_{t-1|t-1}\\\ q_{t|t-1}(\mathbf{x})&=\frac{r_{b}\cdot(1-r_{t-1|t-1})\cdot
b_{t|t-1}(\mathbf{x})+r_{s}\cdot r_{t-1|t-1}\cdot\int
q_{t|t-1}(\mathbf{x|x^{{}^{\prime}}})\cdot
s_{t-1|t-1}(\mathbf{x^{{}^{\prime}}})d\mathbf{x^{{}^{\prime}}}}{r_{b}\cdot(1-r_{t-1|t-1})+r_{s}r_{t-1|t-1}}\end{split}$
(5)

$r_{b}$ is the probability of object birth and $b_{t|t-1}(\mathbf{x})$ is the
spatial distribution of predicted object birth. These two parameters models
object to enter or leave a search space. In our context, wildlife may
disappear from a search space, such as going underground or appearing suddenly
from burrows, as is the case with the species we investigate in our field
trials. $q_{t|t-1}(\mathbf{x|x^{{}^{\prime}}})$ is the object transitional
density, which describes the object’s dynamic.

The update step for the Bernoulli filter is

$\displaystyle\begin{split}r_{t|t}&=\frac{1-\Delta_{t}}{1-\Delta_{t}\cdot
r_{t|t-1}}\\\
q_{t|t}(\mathbf{x})&=\frac{1-P_{D}(\mathbf{x})+P_{D}(\mathbf{x})\sum_{\mathbf{z}\in\mathbf{Z}_{t}}\frac{L_{t}(\mathbf{z|x})}{\lambda
c(\mathbf{z})}}{1-\Delta_{t}}s_{t|t-1}(\mathbf{x})\end{split}$ (6)

where

$\Delta_{t}=\int
P_{D}(\mathbf{x})s_{t|t-1}(\mathbf{x})d\mathbf{x}-\sum_{\mathbf{z}\in\mathbf{Z}_{t}}\frac{\int
L_{t}(\mathbf{z|x})s_{t|t-1}(\mathbf{x})d\mathbf{x}}{\lambda c(\mathbf{z})}$
(7)

with $L_{t}(\mathbf{z|x})$ being the measurement likelihood function and
$\lambda$ being the expected number of false measurement with PDF
$c(\mathbf{z})$. $P_{D}(\mathbf{x})$ is the probability of detection given
state $\mathbf{x}$.

For more detailed derivation and implementations of the Bernoulli filter, we
refer the reader to [87][98] for further reference.

The filter update step (6) requires the likelihood of measurements
$L_{t}(\mathbf{z|x})$ to obtain the posterior distribution. We derive the
measurement likelihood for two types of measurements; i) RSSI; and ii) AoA.
Recall we consider an imprecise measurement model for RSSI; we describe its
formulation next, followed by our proposed robust AoA detector formulation and
the AoA measurement model for filter updates.

####  3.1.3 Imprecise RSSI measurement model

Given signal with form (1), the primary measurement can be obtained is RSSI
measurement, which is completely characterized by $\gamma(\mathbf{x,u})$ and
defined as its Root-Mean-Square (RMS) power. Suppose the receiver gains
$G_{r}=1$, then an RSSI measurement can be expressed as:

$\displaystyle\begin{split}z_{R}=h_{R}(\mathbf{x,u})&=10\log_{10}\big{(}(\gamma(\mathbf{x},\mathbf{u})/\sqrt{2})^{2}\big{)}\\\
&=\tilde{\Gamma}(d_{0})-10n\log_{10}(d(\mathbf{x,u})/d_{0})+\tilde{G}_{a}(\zeta(\mathbf{x,u}))\end{split}$
(8)

where
$\tilde{\Gamma}(d_{0})=10\log_{10}((\frac{\Gamma(d_{0})}{\sqrt{2}})^{2})$, and
$\tilde{G}_{a}(\zeta(\mathbf{x,u}))=10\log_{10}(G_{a}(\zeta(\mathbf{x,u}))^{2})$.

In a non-urban environment, the received radio signal is usually corrupted by
environmental noise and can be modeled as

$z_{R}=h_{R}(\mathbf{x,u})+\mathit{w}_{R}$ (9)

where $\mathit{w}_{R}\sim\mathcal{N}(\cdot;0,\sigma^{2}_{R})$ is measurement
Gaussian white noise with covariance $\sigma_{R}^{2}$.

(9) yields the RSSI likelihood function:

$\mathcal{L}_{R}(z_{R};\mathbf{x,u})=\mathcal{N}(z_{R};h_{R}(\mathbf{x,u}),\sigma_{R}^{2})$
(10)

where $\mathcal{N}(\cdot;\mu,\sigma^{2})$ is the Gaussian probability density
function with mean $\mu$ and variance $\sigma^{2}$.

The path-loss model in (9) is accurate when the receiver is within direct
line-of-sight to the transmitter and other forms of loss are negligible.
However, in complex terrain conditions, other forms of loss introduced by
multi-path propagation, diffraction, scattering, shadowing, or attenuation due
to vegetation, are not negligible, which makes such a model generally
inadequate. An illustration of vegetation and terrain loss variations over an
example terrain gathered from digital elevation map data from [59] is
presented in Figure. 4. Without detailed terrain and site information (such as
vegetation), it is generally difficult or impractical to construct an accurate
measurement model, especially under complex terrain conditions such as hills,
mountains, and varying vegetation conditions.

Figure 4: (a) An example complex terrain from [59] with a fixed receiver (RX)
marked by a red circle; (b) Simulated environment-dependent signal strength
attenuation resulting only from terrain loss and vegetation loss, without the
attenuation component $(d_{0}/d(\mathbf{x,u}))^{n}$ over distance with a
transmitter placed at each coordinate point on the terrain map. For
transmitter locations without significant blockage from terrain conditions
(locating at $Y<$1000\text{\,}\mathrm{m}$$), the signal attenuation is
significantly less than those blocked by the terrain (most locations when
$Y>$1000\text{\,}\mathrm{m}$$. Notably, terrain loss simulated is formulated
in (33) and vegetation loss is formulated in (32) in Section 4.1.

In order to handle the practical constraints of using RSSI measurements, we
consider incorporating a model uncertainty or imprecision to remove the need
for an accurate measurement model. We introduce an additional error term
$\mu_{S}(\textbf{x, u})$ which can represent any practical propagation
complexities that can cause the RSSI measurements to deviate from the simple
model in (9). Now, we express the RSSI measurement model that incorporates
various measurement model uncertainties:

$z_{R}=h_{R}(\mathbf{x,u})+\mu_{S}(\mathbf{x,u})+\mathit{w}_{R}.$ (11)

The term $\mu_{S}(\mathbf{x,u})$ can be considered as an unknown parameter of
the measurement function, and (11) can be rewritten as:

$h(\mathbf{x,u};\mu)=h_{R}(\mathbf{x,u})+\mu_{S}(\mathbf{x,u})$ (12)

where we refer $\mu\in[\mu_{min},\mu_{max}]$ as the (RSSI) model imprecision,
and $\mu_{min}=\min(\mu_{S}(\mathbf{x,u}))$ and
$\mu_{max}=\max(\mu_{S}(\mathbf{x,u}))$,
$\forall\mathbf{x}\in\mathbb{X},\mathbf{u}\in\mathbb{U}$ are the upper and
lower bounds of the model imprecision respectively. Although it is usually
impractical to know $\mu_{S}(\mathbf{x,u})$ precisely, it is relatively easier
to estimate its upper and lower bounds $\mu_{min}$ and $\mu_{max}$.

Due to the presence of unknown parameter $\mu$,
$h:\mathbb{X}\rightarrow\mathbb{Z}$ from (12) is not a function, since a point
in $\mathbb{X}$ now map to infinitely many points in $\mathbb{Z}$. To find the
likelihood function for the imprecise measurement model in (11), the
measurement set $h(\mathbf{x,u};\mu)+w_{R}$ can be represented by a random
closed set $\mathcal{Z}\subseteq\mathbb{Z}$ [87]. Then the generalized
likelihood function characterized by the imprecise measurement function
$h(\mathbf{x,u};\mu)$, which accounts for the model imprecision $\mu$ is
defined as:

$\tilde{L}_{R}(z;\mathbf{x,u})=Pr(z\in\mathcal{Z})=Pr(z\in
h(\mathbf{x,u};\mu)+\mathit{w}_{R})$ (13)

where $Pr(\cdot)$ denotes the probability of an event. In the following
sections, we will refer to (13) as the imprecise likelihood function since
$\mu$ represents the model imprecision.

When $\mathit{w}_{R}$ is zero mean white Gaussian, (13) can be solved
analytically [96]:

$\tilde{L}_{R}(z;\mathbf{x,u})=\int^{\mu_{max}}_{\mu_{min}}\mathcal{N}(h;z,\sigma_{R}^{2})dh=\mathcal{C}(z;\underline{h},\sigma_{R}^{2})-\mathcal{C}(z;\overline{h},\sigma_{R}^{2})$
(14)

where
$\mathcal{C}(z;\mu,\sigma^{2})=\int_{-\infty}^{z}\mathcal{N}(\zeta;\mu,\sigma^{2})d\zeta$
is the Gaussian cumulative distribution function (CDF),
$\underline{h}=\underset{\mu}{\min}(h(\mathbf{x,u};\mu))$ and
$\overline{h}=\underset{\mu}{\max}(h(\mathbf{x,u};\mu))$.

We can understand the consequence of using an imprecise likelihood as having
the effect of broadening the posterior PDF and imparting a higher variance
compared to using the precise likelihood where the model imprecision $\mu$ is
known [96]. The imprecise likelihood enables us to expand the application
scenarios of RSSI measurements for object tracking and localization by simply
providing upper and lower bounds of model imprecision $\mu$.

In addition to the RSSI measurement, we also consider obtaining 2-D (azimuth)
angle of arrival measurements possible by planning a gyration motion by the
drone as these are robust to variations in RSSI measurements impacted by
complex terrain conditions. However, AoA measurements are still detected from
the RSSI measurement receiver, and we propose a robust detection method and
describe the AoA measurement model in the following section.

####  3.1.4 Compensated AoA detector and measurement model

Since the UAV system we consider is highly maneuverable and is only equipped
with a lightweight payload of a directional antenna and a simple receiver to
provide RSSI measurements, we adopted the antenna rotation approach. The
planning algorithm considers a measurement action involving the rotation of
the antenna-equipped UAV to obtain the AoA of a radio signal. However, a
problem arises under weak signals from distant radio tags. We describe the
problem and our proposed compensation method to build a robust AoA detector
and the associated measurement model below.

Correlation coefficient based detector. The UAV performs one full rotation and
uses the correlation between the collected RSSI measurements and the antenna
gain pattern to determine the AoA. More specifically, after collecting $k$
detected RSSI measurements
$\mathbf{z}_{R,t_{1}:t_{k}}=[z_{R,t_{1}},\dots,z_{R,t_{k}}]^{T}$ with
associated detected object state
$\mathbf{x}_{t_{1}:t_{k}}=[\mathbf{x}_{t_{1}},\ldots,\mathbf{x}_{t_{k}}]$ and
UAV state
$\mathbf{u}_{t_{1}:t_{k}}=[\mathbf{u}_{t_{1}},\ldots,\mathbf{u}_{t_{k}}]$ at
time $[t_{1},\dots,t_{k}]^{T}$, the rotation AoA measurement is then given by:

$z_{A_{1}}=h_{A1}(\mathbf{x}_{t_{1}:t_{k}},\mathbf{u}_{t_{1}:t_{k}})=\underset{\alpha}{\operatorname{argmax}}~{}\rho(\mathbf{z}_{R,t_{1}:t_{k}},\tilde{G}_{a}(\bm{\theta}_{t_{1}:t_{k}}^{(u)}+\alpha))$
(15)

where Pearson correlation coefficient
$\rho(\mathbf{x},\mathbf{y})\triangleq\operatorname{cov}(\mathbf{x},\mathbf{y})/(\sigma_{\mathbf{x}}\sigma_{\mathbf{y}})$,
and
$\bm{\theta}_{t_{1}:t_{k}}^{(u)}=[\theta^{(u)}_{t_{1}},\ldots,\theta^{(u)}_{t_{k}}]^{T}$
are UAV headings extracted from UAV states $\mathbf{u}_{t_{1}:t_{k}}$ (Recall
that $\mathbf{u}=[\mathbf{u}_{l},\theta^{(u)}]^{T}$).

While the correlation coefficient approach is sufficient when the receiver can
detect the majority of radio pulses, its performance deteriorates as the
strength of the detected signal reduces. This can significantly impact the
ability to localize distant objects or objects equipped with radio tags
configured with low transmit power. Figure 5 illustrates a scenario from field
testing the AoA measurement method where the receiver is only able to detect a
fraction of the radio pulses emitted by the radio tag during a full rotation
action when the distance between the UAV and the radio source is increased.
The measurement sequence for distance objects correlates more strongly to the
back lobe of antenna gain than the front (main) lobe under a low number of
detections; consequently, the correlation coefficient approach leads to an AoA
measurement with approximately $None$ error in these instances.

Figure 5: Illustrations of the correlation coefficient based AoA detector
performance with RSSI measurements collected at different distances in field
tests. (a) For a close object, the majority of the signal emitted can be
detected, and a correct AoA can be detected from the distinct peak in the
correlation coefficient plot; (b) For a distant object, not all signals
emitted are detected. In this scenario, measurements correlate more strongly
to the back lobe of antenna gain than the (main) front lobe. Consequently, an
incorrect AoA is detected; we can observe an approximately $None$ error.

Cross correlation-based detector. In a scenario where the signal strength is
weak, we can observe the receiver to be more likely to detect the signals when
the main lobe (front) of the antenna is directed at the signal source.
Therefore, instead of using the Pearson correlation coefficient, cross-
correlation can be used to prioritize matching the strongest RSSI measurement
to the front (main) lobe of the antenna:

$z_{A_{2}}=h_{A2}(\mathbf{x}_{t_{1}:t_{k}},\mathbf{u}_{t_{1}:t_{k}})=\underset{\alpha}{\operatorname{argmax}}~{}\langle\mathbf{z}_{R,t_{1}:t_{k}},\tilde{G}_{a}(\bm{\theta}_{t_{1}:t_{k}}^{(u)}+\alpha)\rangle$
(16)

where $\langle\cdot\rangle$ is the dot product, i.e. $\langle a,b\rangle=\int
a(x)b(x)dx$.

While (16) can be used individually to generate AoA measurements with fewer
outliers, from our observation in practice, when the radio tag’s signal
strength is strong, the cross-correlation method (16) produces AoA
measurements with higher variance than the correlation coefficient-based AoA
detector. Hence, the sole use of a cross-correlation-based detector is
detrimental to localizing radio tags approaching the UAV receiver. To overcome
this issue, we introduce an approach to correct outlier AoA measurements.

Compensated AoA detector. Based on the observations we discussed, we propose
taking advantage of both AoA detection approaches to construct a more robust
detector. We propose employing the cross-correlation (16) method alongside the
correlation coefficient method (15) to mitigate the AoA measurement ambiguity
resulting from a correlation coefficient detector.

We propose exploiting the deviation between both AoA detectors to correct the
correlation coefficient AoA detector measurements. When an outlier AoA
measurement is produced by the correlation coefficient AoA detector, the
cross-correlation AoA detector’s measurement will be significantly different.
Notably, the correlation coefficient AoA detector can generate AoA measurement
with $None$ error. Now, the compensated AoA measurement based on a decision
threshold, $z_{A_{Th}}$, can be expressed as:

$z_{A}=\begin{cases}z_{A_{1}}&\text{if}~{}|z_{A_{1}}-z_{A_{2}}|<z_{A_{Th}}\\\
z_{A_{1}}-\pi~{}$\text{\,}\mathrm{rad}$&\text{otherwise}\\\ \end{cases}$ (17)

While we present the formulation of the method here, further discussion of
experimental results from field tests to demonstrate the effectiveness of the
proposed approach is presented in Section 6.3.

AoA measurement model. The distribution of $z_{A}$ is complex but can be
approximated by a Gaussian distribution in practice [66, 106] while assuming
the object remains stationary during the rotation. Then:

$z_{A}\approx h_{A}(\mathbf{x}_{t_{k}},\mathbf{u}_{t_{k}})+\mathit{w}_{A}$
(18)

where$\mathit{w}_{A}\sim\mathcal{N}(\cdot;0,\sigma_{A}^{2})$ is a zero mean
Gaussian noise with variance $\sigma_{A}^{2}$ and

$h_{A}(\mathbf{x},\mathbf{u})=\operatorname{arctan2}(\frac{u_{x}-p_{x}}{u_{y}-p_{y}})$
(19)

Then the AoA likelihood is:

$L_{A}(z_{A};\mathbf{x,u})=\mathcal{N}(z_{A};h_{A}(\mathbf{x,u}),\sigma_{A}^{2}).$
(20)

###  3.2 Joint Measurement and Trajectory Planning Method

In our proposed approach, the UAV not only needs to determine the trajectory
action to navigate in the search environment but the measurement method to
reduce the position uncertainty of wildlife to achieve a robust and rapid
method of tracking and locating wildlife. The problem of automatically
determining the best action can be formulated and solved efficiently under a
POMDP framework.

Formally, a POMDP is defined by tuple
$(\mathbb{X},\mathbb{A},\mathbb{Z},\phi,\mathcal{R},\mathcal{L})$.
$\mathbb{X},\mathbb{A},\mathbb{Z}$ are state space, action space, and
observation space respectively. $q(\mathbf{x^{\prime}|x},\mathbf{a})$ is the
state transition function given action $a$ and current state $\mathbf{x}$,
$\mathcal{R}$ is the reward function which characterizes the objective of the
planner, and $\mathcal{L}(\mathbf{Z|x},\mathbf{a})$ is the observation
likelihood function, where
$\mathbf{Z}\in\mathbb{Z},\mathbf{x}\in\mathbb{X},a\in\mathbb{A}$. Considering
the resource limitations and the need for an online planner for the tracking
task, we consider a computationally tractable POMDP formulation. Consequently,
we employ a myopic planning strategy where the goal is to determine an optimal
control action using a discrete action space at each planning iteration. Under
a myopic planning strategy, the computational complexity is reduced by
selecting one control action at a single planning iteration as opposed to
considering multiple control actions in the future at multiple planning
iterations. The optimal control action for a myopic planner
$\mathbf{a}^{*}_{t}$ is defined by maximizing the expected reward function
$\mathcal{R}_{t+H}(\cdot)$ over the action space:

$\mathbf{a}^{*}_{t}=\underset{\mathbf{a}\in\mathbb{A}}{\operatorname{argmax}}~{}\mathbb{E}\left[\mathcal{R}_{t+H}(\mathbf{a})\right]$
(21)

The following subsections describe essential elements of our POMDP-based
planner and considerations that enable real-time planning decisions in the
context of a UAV with limited onboard computing resources.

####  3.2.1 Information-based rewards

In a POMDP framework, the reward function can be categorized as i) task-based
rewards [71]; ii) and information-based rewards [84]. A task-based reward is
only applicable when the objective can be explicitly formulated. For object
localization scenarios, the information-based reward is preferable to a task-
based reward since the primary objective is reducing the position uncertainty
of objects of interest, and information-based rewards prioritize gathering
information; hence, has a strong relationship with the objective of improving
the localization accuracy of objects [76, 61]. Importantly, in our problem
formulation, information-based rewards provide a means to evaluate the quality
of measurement type to aid the planner in deciding between taking RSSI or AoA
measurements. Consequently, we considered three information-based reward
formulations since a theoretical basis for determining the most effective
formulation for our planning for tracking problems does not exist.

Given the predicted belief density of an object
$\mathbf{\Psi}_{t+H|t}=\Psi_{t+H}(\cdot|\mathbf{Z}_{1:t})$ and the future
updated posterior belief density
$\mathbf{\Psi}_{t+H|t+H}=\Psi_{t+H}(\cdot|\mathbf{Z}_{1:t},\mathbf{Z}_{t+1:t+H}(\mathbf{a}))$
at time $t+H$, where $\mathbf{Z}_{t+1:t+H}(\mathbf{a})$ is the hypothesized
measurement set if action $\mathbf{a}$ was executed, The three information-
based rewards we considered are defined:

  1. 1.

Rényi Divergence [94] [97]

$\mathcal{R}_{t+H}^{(\text{R\'{e}nyi})}(\mathbf{a})=\frac{1}{\alpha-1}\log\int\mathbf{\Psi}_{t+H|t}^{\alpha}\cdot\mathbf{\Psi}_{t+H|t+H}^{1-\alpha}\delta\mathbf{X},$
(22)

where $\alpha\geq 0$ parameter determines the effect of the tails of two
distributions on the rewards.

  2. 2.

Shannon Entropy [102]

$\mathcal{R}_{t+H}^{(\text{Shannon})}(\mathbf{a})=\mathcal{H}(\mathbf{\Psi}_{t+H|t})-\mathcal{H}(\mathbf{\Psi}_{t+H|t+H}),$
(23)

where
$\mathcal{H}(\Psi(\mathbf{X}))=-\int\Psi(\mathbf{X})\log{\Psi(\mathbf{X})}\delta\mathbf{X}$.

  3. 3.

Cauchy-Schwarz Divergence [74]

$\mathcal{R}_{t+H}^{(\text{CS})}(\mathbf{a})=-\log\left[\frac{\langle\mathbf{\Psi}_{t+H|t},\mathbf{\Psi}_{t+H|t+H}\rangle}{\langle\mathbf{\Psi}_{t+H|t},\mathbf{\Psi}_{t+H|t}\rangle\langle\mathbf{\Psi}_{t+H|t+H},\mathbf{\Psi}_{t+H|t+H}\rangle}\right],$
(24)

####  3.2.2 Measurement and trajectory planning control actions

One of the major strengths of employing the quad-copter UAV is the high
maneuverability offered for traversing in a 3D space. Consequently, we have
significant flexibility in designing the control action space. In our task,
the available control actions should allow the UAV to explore the search area
and collect RSSI or AoA measurements. To measure RSSI, the UAV does not
require any special maneuvers, thus allowing for a change in heading to change
the navigation path is sufficient. But, to measure AoA, a full rotation action
must be executed by the UAV. Therefore, our action space for the planner can
be decomposed into two sub-spaces, illustrated in Figure. 6, and described
below:

$\mathbb{A}=\mathbb{A}_{\text{RSSI}}\cup\mathbb{A}_{\text{AoA}}$ (25)

Recall that we consider a discrete action space to reduce the computational
demands on the planner. Then, for the RSSI action space
$\mathbb{A}_{\text{RSSI}}$ we define $n_{\xi}$ discrete headings, with each
heading $\xi$ uniformly distributed across $None$ to $None$ (with reference to
the geographical north), at a fixed altitude for $T_{P}$ seconds.

For the AoA action space $\mathbb{A}_{\text{AoA}}$, we augment the RSSI
actions to include a full rotation action. Therefore, the AoA actions include
two modes: i) traveling along $n_{\xi}$ discrete, uniformly distributed
headings at a fixed altitude for $T_{R1}$ seconds followed by: ii) a full
rotation maneuver with duration $T_{R2}$ seconds.

Figure 6: Illustration of an RSSI action in which the UAV travels along
heading $\xi$ and an AoA action in which the UAV travels along heading $\xi$
followed by performing a full rotation maneuver.

The action space we define intentionally limits the UAV to a constant
altitude, with two benefits: i) it extends the flight time of the UAV as
changing flight altitude consumes a substantial amount of energy; ii) it
simplifies the planning procedure. Further, allowing a change in altitude
necessitates an obstacle avoidance component to ensure the safe operation of
the UAV, which increases computation demands. By limiting the control action
to only allow a UAV to travel on a 2D plain, we are able to ensure the UAV
will not collide with obstacles as long as its initial altitude is higher than
the tallest obstacle in the search area.

Notably, when evaluating the best control action between an RSSI action and an
AoA action, their reward
$\mathcal{R}_{t+T_{P}}(\mathbf{a}\in\mathbb{A}_{\text{RSSI}})$,
$\mathcal{R}_{t+T_{R1}+T_{R2}}(\mathbf{a}\in\mathbb{A}_{\text{AoA}})$ cannot
be directly compared unless both rewards are evaluated at the same horizon,
i.e., $t+T_{P}=t+T_{R1}+T_{R2}$. Therefore, we constraint the action space
such that $T_{p}=T_{R1}+T_{R2}$ so that RSSI actions and AoA actions take the
same amount of time to execute. Notably, when the UAV performs an AoA action,
the receiver is still capable of measuring RSSI during the first traversal
phase of the action. Hence, to avoid loss of useful information, the UAV also
uses these RSSI measurements in addition to the AoA measurement generated at
the end of executing the action to update the densities of objects.

####  3.2.3 Void constrained trajectory planning

To minimize the disturbance of UAV operations to wildlife, we incorporated a
void constraint into our planner. The void constraint provides a probabilistic
approach to maintaining distance to an object without knowing the exact state
of the object.

Given a region $S\subseteq\mathbb{X}$ and Bernoulli density
$\Psi=(r,q(\cdot))$ on $\mathbb{X}$ where $p$ is approximated by set of
weighted particles:
$q(\mathbf{x})\approx\sum^{N_{s}}_{i=1}\omega^{(i)}\delta(\mathbf{x}-\mathbf{x}^{(i)})$.
The void probability function can be expressed as [61]:

$B_{\Psi}(S)\approx(1-r)+r\cdot\big{(}1-\sum_{i=1}^{N_{s}}\omega^{(i)}\mathbf{1}_{S}(\mathbf{x}^{(i)})\big{)}$
(26)

where $\mathbf{1}_{S}(\cdot)$ is the indicator function of the region $S$
equal to $1$ if $\mathbf{x}^{(i)}\in S$ and $0$ otherwise. We can interpret
(26) as the probability of an object with belief density $\Psi$ that is
outside the region $S$. While the void region can be an arbitrary shape, we
use a cylindrical void region with radius $\iota_{\min}$, where
$V(\mathbf{u},\iota_{\min})$ denote the void region given UAV state
$\mathbf{u}$, given by:

$V(\mathbf{u},\iota_{\min})=\bigg{\\{}\mathbf{x}\in\mathbb{X}\Big{|}\sqrt{(p_{x}-u_{x})^{2}+(p_{y}-u_{y})^{2}}<\iota_{\min}\bigg{\\}},$
(27)

Now, the planning constraint can be expressed as:

$\min\\{{B_{\Psi_{t}}}(V(\mathbf{u}_{t},\iota_{\min}))\\}>P_{v\min}$ (28)

where $P_{v\min}\in[0,1]$ is a user-defined void probability threshold. Figure
7 illustrates the resulting void region and the application of the constraint
defined in (28) with two object densities as examples.

Figure 7: Illustration of a cylindrical void region $V$ with two object
densities. The void constraint may be violated for object A if the probability
of the non-overlapping region (red shaded area) between object A’s belief
density and void region is less than desired bound set by $P_{v\min}$.

Importantly, a cylindrical void region is a natural choice for two reasons: i)
when the radio signal is transmitted from a radio tag directly below the
antenna, due to the orientation of the antenna onboard the UAV and the
resulting lower gain, it can lead to increasing the missed detection rate. A
cylindrical void region can potentially eliminate this scenario since a
minimum horizontal distance can be maintained between the UAV and radio tags;
and ii) because the UAV will maintain a constant altitude during a mission to
conserve limited onboard battery power. Provided the flight altitude is high
enough, it is not necessary to consider the minimum vertical separation
distance.

####  3.2.4 Implementation considerations for a real-time system

We considered a myopic planning formulation with a discrete action space to
manage the complexity of the planning problem. To reduce the computational
demands and realize a real-time planner without sacrificing the system’s
localization performance, we considered the two following approaches.

_Planning for the closest unlocalized object._ At every planning iteration,
given a set of unlocalized objects’ densities
$\bm{\Psi}=\\{\Psi_{1}(\mathbf{X}),\ldots,\Psi_{n}(\mathbf{X})\\}$, instead
solving for the optimal action that maximized the total reward for all
densities $\bm{\Psi}$, we consider maximized the expected reward for the
closest belief density $\Psi_{c}(\mathbf{X})$ to the UAV as adopted in [90].
where

$\Psi_{c}(\mathbf{X})=\underset{\Psi(\mathbf{X})\in\bm{\Psi}}{\operatorname{argmin}}~{}d(\bar{\mathbf{x}},\mathbf{u})$
(29)

with $\bar{\mathbf{x}}$ being the mean of object state given PDF
$\Psi(\mathbf{X})$. Once an object meets the condition to be considered
localized, the object’s belief density will be excluded from the next planning
iteration and, therefore, reduce the number of densities the planner needs to
process over time.

Planning for the closest unlocalized object has the benefit of reducing the
computational complexity of calculating the reward. Limiting the number of
planning densities makes the planner focus on computing actions that best
minimize localization uncertainty for the closest object and, consequently,
reduces the number of densities that need to be considered by the planner from
$n$ to one. Interestingly, conservation biologists in the field also follow an
identical strategy to locate multiple animals; they employ a handheld receiver
system to home in on the closest perceived wildlife based on their
determination of signal strength from audible beeps from the receiver.

_Predicted ideal measurement set (PIMS)._ In general, Monte Carlo integration
is used to evaluate the expected reward in (21). This process requires drawing
$M$ measurements $\mathbf{Z}^{(i)}_{t+1:t+H}(\mathbf{a}),i=1,\ldots,M$ which
is obtained by sampling the belief density $\mathbf{\Psi}_{t+H|t}$ followed by
generating a simulated measurement according to the measurement model. Then
the estimated expected reward is given by:

$\mathbb{E}[\mathcal{R}_{t+H}(\mathbf{a})]\approx\frac{1}{M}\sum_{i=1}^{M}\mathcal{R}^{(i)}_{t+H}(\mathbf{a})$
(30)

As the number of samples $M$ increases, the estimated reward converges to the
true expectation. However, this method is computationally intensive, so
instead, we adopted the _predicted ideal measurement set_ (PIMS) approach [85]
to compute the reward where only one instance ($M=1$) of future measurement
set under an ideal condition is generated. The future measurement
$\mathbf{Z}_{t+1:t+H}(\mathbf{a})$ is now computed by: i) computing the
expected state of the belief density $\mathbf{\Psi}_{t+H|t}$; and ii)
generating the expected measurement following the measurement function (9) or
(19) in the absence of measurement noise, false measurements, and miss
detections ($P_{D}=1$). Therefore, the estimated reward using PIMS is

$\mathbb{E}[\mathcal{R}_{t+H}(\mathbf{a})]\approx\mathcal{R}^{(\text{PIMS})}_{t+H}(\mathbf{a})$
(31)

Following the above implementation approach, the measurement and trajectory
planning algorithm we developed is succinctly summarized in Algorithm 1.

1

input : Set of unlocalized objects’ belief densities $\bm{\Psi}_{t}$, UAV
state $\mathbf{u}_{t}$, action execution time $T_{p}$, reward function
$\mathcal{R}(\cdot)$ , void radius $\iota_{\min}$, void probability threshold
$P_{v\min}$, RSSI measurement action space $\mathbb{A}_{RSSI}$, AoA
measurement action space $\mathbb{A}_{AoA}$

output : action $\mathbf{a}$

2

3$\Psi_{t}(\mathbf{X})\leftarrow\text{ClosestObject}(\bm{\Psi}_{t})$

4 // Find the closest belief density for the planning iteration, see (29)

5

6foreach  _$\mathbf{a}^{(k)}\in\\{\mathbb{A}_{RSSI},\mathbb{A}_{AoA}\\}$_ do

7 for  _$i=1:T_{p}$_ do

8 $\bar{X}_{t+i}\leftarrow\mathbb{E}[\Psi_{t+i-1}(\mathbf{X})]$

9 // Compute the expected object state

10 $\mathbf{Z}_{t+i}\leftarrow
h_{\mathbf{a}_{t}^{(k)}}(\bar{X}_{t+i},\mathbf{u}_{t+i})$

11 // Generate simulated measurements using PIMS

12
$\Psi_{t+i}(\mathbf{X})\leftarrow\text{BernoulliFiltering}(\Psi_{t+i-1}(\mathbf{X}),\mathbf{Z}_{t+i})$

13 // Filtering, see (5) and (6)

14

15 if
_$\textsc{checkVoidConstraint}(\Psi_{t+i}(\mathbf{X}),\mathbf{u}_{t+i},\iota_{\min},P_{v\min})$_
then

16 $R^{(k)}\leftarrow 0$

17 break

18 // Void Constraint violated. Evaluate next action

19

20

21 $R^{(k)}\leftarrow\mathcal{R}^{(PIMS)}_{t+T_{p}}(\mathbf{a}_{t}^{(k)})$

22 // Compute the expected reward. See (31) where $H=T_{p}$

23

24$k\leftarrow\text{argmin}(R)$

return : $\mathbf{a}^{(k)}$

Algorithm 1 Information theoretic measurement and trajectory planner (Meta-
Pilot)

##  4 Simulation Experiments

To reduce development time and risks associated with evaluating concepts with
a physical UAV system, and to investigate a wide range of settings we employed
simulation-based experiments to evaluate our proposed approach to answer the
following questions:

  * •

Robustness under various terrain conditions. Our approach aimed to provide a
robust, fast tracking and localization method under various terrain
conditions. How does our proposed joint measurement and trajectory planning
for tracking algorithm perform compared to existing approaches under different
terrain conditions?

  * •

Impact of information-based reward functions. We investigated three different
information-based reward function formulations. Does the choice of
information-based reward functions provide a performance advantage?

  * •

Effectiveness and impact of void constrained trajectories. We employ a void
constraint to maintain a safe distance between the UAV and our target
wildlife. However, the void-constrained trajectories could impact the duration
of a mission to localize wildlife. Is the approach effective and what is the
impact on localization performance?

  * •

Robustness under practical signal detection limitations. In the field, missed
detections can occur and negatively impact performance. Hence, how does our
approach perform under the different measurement detection probabilities
compared to prior state estimation methods employed for localizing wildlife?

First, we elaborate on the complex VHF signal propagation model necessary to
generate signals impacted by terrain conditions in our simulations, in Section
4.1. Then, we describe the simulation settings in Section 4.3 and discuss the
results from the simulations in Section 4.4.

###  4.1 Complex VHF Signal Propagation Model

One of the key properties of our proposed formulation is the ability to relax
the requirement for an accurate radio propagation model by incorporating an
imprecise likelihood. To validate our approach in simulation settings, we
employ a radio propagation model that captures the effects of: i) vegetation;
and ii) terrain variations for generating the radio tag signals. We illustrate
both types of signal propagation loss and parameters related to the model in
Figure 8 and briefly describe the formulation of the model used for generating
signals below.

Figure 8: Illustration of simulated VHF signal propagation model and related
parameters. Radio signal strength at receiver RX is influenced by the line-of-
sight distance $d$, distance from the transmitter to most significant path
blockage $d_{1}$, distance from the receiver to blockage $d_{2}$, height
difference $h$ between the blockage and the path trajectory, vegetation depth
$L_{v}$, and elevation angle $\varphi$

##### Vegetation loss.

We used the International Telecommunication Union (ITU) vegetation loss model
to capture the effect of vegetation on VHF radio signals [80]. The loss due to
vegetation (assumed to be pine woodlands in our model) is defined as:

$h_{v}=0.25f^{0.39}L_{v}^{0.25}\varphi^{0.05}$ (32)

where $f$ is the signal frequency in $\text{\,}\mathrm{MHz}$, $L_{v}$ is the
vegetation depth in meters, and $\varphi$ is the elevation angle in degrees.
We use $f=$150\text{\,}\mathrm{MHz}$$ in our simulations.

##### Terrain shadowing and diffraction.

To model diffraction and shadowing effects from terrain conditions, we adopted
the ITU terrain model where the additional loss is given by [79]:

$h_{d}=-20\cdot\frac{h}{F_{1}}+$10\text{\,}\mathrm{dB}$$ (33)

where $h$ is the height difference between the most significant path blockage
and the path trajectory, $F_{1}$ is the radius of the first Fresnel zone given
by [79]:

$F_{1}=17.3\cdot\sqrt{\frac{d_{1}d_{2}}{f\cdot d}}~{}$\text{\,}\mathrm{m}$,$
(34)

where $d$ is the distance between signal transmitter and receiver in
$\text{\,}\mathrm{km}$, $d_{1},d_{2}$ are the distances from transmitter and
receiver to the blockage in $\text{\,}\mathrm{km}$ and $f$ is the signal
frequency in $\text{\,}\mathrm{GHz}$. Overall, by subtracting (32) and (33)
from the ideal RSSI measurement model (8), the propagation model that
considers the complexities imposed by vegetation and terrain conditions
related losses can be described as:

$h(\mathbf{x,u})=\tilde{\Gamma}(d_{0})-\underbrace{10n\log_{10}(d(\mathbf{x,u})/d_{0}))}_{\text{distance
loss}}+\tilde{G}_{a}(\zeta(\mathbf{x,u}))-\underbrace{h_{v}}_{\text{vegetation
loss}}-\underbrace{h_{d}}_{\text{terrain loss}}$ (35)

An illustration of the impact of vegetation and terrain loss alone, over a
physical terrain obtained from [59] is presented in Figure. 4 in Section
3.1.3.

###  4.2 Comparison Approaches

We consider previous planning and measurement methods employed for tracking
and locating wildlife to understand and evaluate the effectiveness of our
proposed measurement and trajectory planning formulation for the problem.

We employed the Bernoulli filter formulation we proposed for the state
estimator for all methods. This decision benefits all other methods because
the filter formulation is inherently capable of dealing with practical issues
such as miss detections. Importantly, employing the Bernoulli filter
formulation for all comparison methods ensures the differences in performance
are related to demonstrating that the proposed trajectory and measurement
planning is a more effective approach for the task. This strategy can more
clearly demonstrate the performance advantages gained from our proposed
measurement and trajectory planning approach (abbreviated as Meta-Pilot).
Further, we use mobile radio tags to better capture wandering wildlife. Given
the objective of void-constrained trajectories is to reduce disturbances, we
employ void-constrained trajectory planning for all comparison methods. In the
following, we describe previous approaches and our specific improvements to
facilitate a more useful comparison, especially in challenging settings.

  * •

RSSI-only approach. We adopt the RSSI-only approach described in [90] where
the UAV receives RSSI measurements from each radio tag, and the planner
considers all future measurements RSSI only. The study in [90] used a two-ray
model to describe the propagation effect on RSSI over mostly flat terrains and
was therefore not expected to perform well in more complex terrains. As a
result, we introduced our imprecise RSSI measurement model to improve the
robustness of the original method in both filtering and planning algorithms.
The RSSI-only approach with our proposed imprecise model is referred to as
Imp-RSSI in the following sections.

  * •

AoA-only approach. The AoA-only approach uses rotation actions to acquire
bearing measurements [77, 108, 113, 65, 106]. Instead of the AoA detector
methods in prior work, we employed the improved detector proposed in Section
3.1.4 to generate AoA measurements. Further, for this approach, we propose
using $20\text{\,}\mathrm{s}$ to complete an AoA measurement, instead of the
$45\text{\,}\mathrm{s}$ described in prior work [65] using AoA only
measurements. Consequently, we keep the AoA measurement acquisition action and
detector to that used in our Meta-Pilot in this setting; hence, we can expect
the performance improvement to relate to our proposed measurement and
trajectory planning approach in contrast to the detector improvements. We
refer to this approach as cAoA(20 s) to highlight the use of the proposed
compensated AoA detector and the time duration for the measurement action.

  * •

AoA-with-RSSI-update approach. The method described in [66] sought to combine
the benefits reported in [90] with an AoA method. Here, rotation-correlation-
based AoA measurements are used for object state estimation and trajectory
planning, but an RSSI measurement update is also performed after generating
each AoA measurement. The method in [66] takes $45\text{\,}\mathrm{s}$ to
acquire a single AoA measurement and uses a log-path loss measurement model,
given in 9, for the RSSI measurement update. Given the problems we have
outlined in using RSSI models in complex terrains, we used a higher
measurement noise in the log-path loss measurement model for hilly and
mountain terrain to attempt to manage the RSSI model mismatch in complex
terrains and ensure the comparison method remains competitive. We evaluate two
variants. We employed implemented AoA-RSSI(20 s)—using $20\text{\,}\mathrm{s}$
for an AoA measurement—and AoA-RSSI(45 s)—using $45\text{\,}\mathrm{s}$ for an
AoA measurement–to compare with potential advantages with a longer measurement
duration selected in [66].

###  4.3 Simulation setup

We describe the experimental settings and parameters employed in our extensive
simulation-based study below. Notably, we employed Digital Elevation Model
(DEM) data from [59] with $1\text{\,}\mathrm{m}$ resolution to create real-
world terrain conditions for our experiments. We consider three terrain
conditions with increasing signal propagation complexity:

  * •

Flat Terrain. The data is obtained from Parkes, New South Wales (NSW), where
elevation changes from $233\text{\,}\mathrm{m}$ to $239\text{\,}\mathrm{m}$.
This terrain is representative of a simple environment for localization since
the area has small elevation variations, and an accurate measurement model can
be easily obtained for state estimation.

  * •

Hilly Terrain. The hilly terrain is in Flinders Chase National Park, South
Australia (SA), where the elevation changes from $40\text{\,}\mathrm{m}$ to
$77\text{\,}\mathrm{m}$. The hilly terrain is more challenging than the flat
terrain, given the higher elevation variation.

  * •

Mountain Terrain. The mountain terrain is in Rugby, NSW, where elevation
changes from $595\text{\,}\mathrm{m}$ to $704\text{\,}\mathrm{m}$. The
mountain terrain is the most challenging, given the large elevation variance
and terrain obstructions.

Settings. In each terrain, a UAV is tasked with localizing $N=20$ mobile
objects within a $$2000\text{\,}\mathrm{m}$\times$2000\text{\,}\mathrm{m}$$
area. Each radio tag object generates an RSSI measurement every
$1\text{\,}\mathrm{s}$. The initial state of UAV is
$\mathbf{u}_{1}=[1,1,80+h_{0},\pi/4]^{T}$ where $h_{0}$ is the elevation of
terrain at the UAV’s initial position. The UAV has a maximum velocity
$v_{\text{max}}=$10\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$$ and rotation
angular velocity of $\pi/3~{}$\text{\,}\mathrm{rad}\mathrm{/}\mathrm{s}$$. A
cylindrical void region with radius $\iota_{\min}=$50\text{\,}\mathrm{m}$$ and
void probability threshold $P_{v\min}=0.95$ is used to constrain the UAV’s
trajectories. For the RSSI measurement model,
$\tilde{\Gamma}(d_{0})=$40\text{\,}\mathrm{dBm}$$, $n=4$,
$\sigma_{R}=$4\text{\,}\mathrm{dB}$$ are used. For the bearing measurement
model, $\sigma_{A}=$0.095\text{\,}\mathrm{rad}$$ is chosen. The rotation time
to collect RSSI measurements to generate a bearing measurement is set to
$20\text{\,}\mathrm{s}$ except when evaluating the AoA-RSSI(45 s) method in
[66]. The measurement and trajectory planner evaluates actions every
$T_{p}=$30\text{\,}\mathrm{s}$$. For the Rényi divergence reward, $\alpha=0.1$
is selected based on the study in [90]. The Bernoulli filter implementation,
in all of the methods, uses birth probability
$r_{b}=$1\text{\times}{10}^{-5}$$, expected number of clutters $\lambda=0.05$
with clutter density
$c_{\text{RSSI}}(z)=\mathcal{U}[-120,0]~{}$\text{\,}\mathrm{dBm}$$ and
$c_{\text{AoA}}(z)=\mathcal{U}[0,2\pi]~{}$\text{\,}\mathrm{rad}$$ for the
clutter density of RSSI and AoA measurement updates, respectively—here,
$\mathcal{U}[a,b]$ is continuous uniform distribution with interval $[a,b]$.

Detection Probability. To simulate the limited sensitivity of the radio
receiver in practice, a sensitivity threshold
$h_{Th}=$-120\text{\,}\mathrm{dBm}$$ is implemented such that any simulated
radio signal received with signal strength less than the threshold are
discarded. Due to the effect of limited receiver sensitivity, the detection
probability can vary as the state of UAV and radio tags changes. Therefore,
given the RSSI measurement model has Gaussian noise (9), we can express the
detection probability $P_{D}(\cdot)$ of the radio signal as the following
equation for use in the Bernoulli update step expressed in (6)

$P_{D}(\textbf{x,
u})=\int_{h_{Th}}^{\infty}\mathcal{N}(z_{R};h(\mathbf{x,u}),\sigma^{2}_{R})dz_{R}=1-\mathcal{C}(h_{Th};h(\mathbf{x,u}),\sigma^{2}_{R}),$
(36)

here, recall that $\mathcal{C}(;)$ is the Gaussian CDF mentioned in (14).

Mobile radio tag objects. Radio tag objects to track and locate were randomly
placed in the testing environment with elevation $0.2\text{\,}\mathrm{m}$
above ground. All objects were placed under vegetation with depth
$L_{v}=$1\text{\,}\mathrm{m}$$ to generate complex VHF signal propagation
artifacts and create challenging conditions for the proposed measurement and
trajectory planner operating without an accurate measurement model and using
an imprecise model instead. We modeled the object dynamics using a wandering
model [91] with transitional density given by:

$q_{t|t-1}(\mathbf{x}_{t}|\mathbf{x}_{t-1})=\mathcal{N}(\mathbf{x}_{t};\mathbf{Fx}_{t-1},\bm{\Sigma})$
(37)

where $\mathbf{F}=\mathbf{I}_{3}$ with $\mathbf{I}_{3}$ being $3\times 3$
identity matrix,
$\bm{\Sigma}=~{}\text{diag}([2.5,2.5,0.0025]^{T})~{}$\text{\,}\mathrm{m}$^{2}$.

We assume the radio tag carried by each object emits an on-off-keying pulse
signal with a unique frequency as illustrated in Figure 3. Therefore, each
object can be uniquely identified by estimating its signal frequency and this
significantly reduces computation-intensive data association procedures.
Recall, to reduce the computational complexity of planning, the planning
algorithm only selects optimal actions to reduce the estimation uncertainty
associated with the object with the smallest Euclidean distance to the UAV.
Once an object is considered localized, it will no longer be considered by the
path-planning algorithm to control measurement and trajectory-planning
actions. An object is considered localized when the estimation uncertainty has
reduced to a sufficiently small level; for this, the determinant of its
estimated covariance on the $x-y$ axis, $N_{\text{th}}$, being less than or
equal to $2\text{\times}{10}^{4}\text{\,}{\mathrm{m}}^{4}$ was used in our
simulations. We only use the $x-y$ axis to determine the termination condition
for tracking because, generally, elevation resolution is not as important and
to provide a fair comparison with the AoA method, which is not able to obtain
elevation measurements.

Performance measures. For each simulation, $100$ Monte-Carlo runs were
performed. Given the key objectives of the UAV task, we used the following
metrics to evaluate and compare the performance of each method.

  * •

_Estimation Error._ We are interested in the accuracy of estimating the
location of wildlife. Hence, we use mean error of $N$ objects given by
$\frac{1}{N}\sum_{i=1}^{N}\sqrt{(x_{truth}^{(i)}-x_{est}^{(i)})^{2}+(y_{truth}^{(i)}-y_{est}^{(i)})^{2}}$;

  * •

_Localization time._ We want to minimize the flight time to locate radio-
tagged wildlife since a UAV has limited onboard battery capacity and returning
the UAV to the home base and changing batteries for a new mission is
undesirable. Therefore, we measure the total time the UAV spends in the air to
locate all objects.

###  4.4 Simulation Experiments and Results

Figure 9: Comparing performance with mobile radio tags under various terrain
conditions and measurement and planning methods with different information-
based reward functions under investigation. Performance is compared between
different methods in terms of localization time and estimation error in flat,
hilly, and mountain terrains over 100 MC runs where all of the planning
methods use void-constrained trajectories. The time required for each AoA
measurement is marked in brackets. (Note: Imp-RSSI∗ method in mountain terrain
uses a localization termination condition of
$2\text{\times}{10}^{6}\text{\,}{\mathrm{m}}^{4}$) since the tighter
uncertainty bound employed in other methods prevents localization of objects
under less informative RSSI measurements.

Robustness under various terrain conditions.  These experiments aim to
quantify advantages in terms of localization time and accuracy under different
environments based on the information-based reward functions under
investigation. We examined the performance of our proposed method in three
distinct terrains: i) flat; ii) hilly, and iii) mountain terrains.

Figure 9 shows the Monte-Carlo simulation results in flat, hilly, and mountain
terrains. Our proposed method, Meta-Pilot, is able to locate all $20$ radio
tags consistently and faster—see localization times–than all AoA-based
methods—cAoA(20 s), AoA-RSSI(20 s), AoA-RSSI(45 s)—across all terrain
conditions while maintaining low localization errors. Then, given the action
choices the planner is able to make over the relatively flat terrain, where
Imp-RSSI methods are expected to perform well, our proposed method was able to
acquire the location of all $20$ radio tags as fast as the RSSI-based method
whilst being significantly faster than AoA-based methods and without
compromising localization accuracy.

As the terrain complexity increases (Hilly to Mountain terrains), our method
is able to select AoA measurement actions when necessary and achieve faster
localization times than the Imp-RSSI and all AoA-based methods without
sacrificing localization accuracy. In the mountain terrain, our planning for
tracking approach performed better than all of the AoA-based
methods—localization error is the same or better whilst the localization time
is the least. Notably, in the mountain terrain, the Imp-RSSI method is
inherently not able to meet the tight termination condition set at
$2\text{\times}{10}^{4}\text{\,}{\mathrm{m}}^{4}$ due to the complexity of the
terrain. Therefore, a higher localization termination condition (more relaxed)
of $2\text{\times}{10}^{6}\text{\,}{\mathrm{m}}^{4}$ is used for the Imp-RSSI
method instead. As a result, we can observe the localization error of the
method to be significantly larger than other methods.

Impact of information-based reward functions. In the series of experimental
results described in Figure 9, all three reward functions resulted in
approximately similar localization times and errors across all of the
measurement and planning methods across all of the environments. However,
Rényi divergence indicates a slight advantage in localization time. Hence,
Rényi divergence was selected as the reward function to employ in field
experiments.

Robustness under practical signal detection limitations.  In this experiment,
we investigated the performance of our proposed approach under different
measurement detection probabilities to understand the impact of our formation
to address the practical problems experienced by signal detectors—missed
detections. The parameters used in this experiment are those used for the
hilly terrain and Rényi divergence was used as the reward function.

Figure 10: Detection Probability Impact Experiments — Comparison between
Bernoulli filter (BF) formulation to explicitly consider miss detections and
Particle filter (PF) under varying detection probability $P_{D}$ for the
tracking and localization task over the hilly terrain with $100$ MC trials.
The BF formulation is able to maintain a low localization error across
different detection probabilities.

Figure 10 shows the Monte-Carlo-based comparison results of localization error
between the Bernoulli filter and the particle filter (employed in prior work)
implementations as the detection probability $P_{D}$ varies from $0.7$ to
$0.99$. As $P_{D}$ decreases, the particle filter implementation suffers from
low measurement detections, leading to high localization errors. In contrast,
as expected, the Bernoulli filter formulation with explicit consideration for
measurement detection probabilities is able to maintain a consistent
localization accuracy under different detection probabilities.

Figure 11: Void Impact Experiments With Mobile Radio Tags — UAV trajectory
heatmap over 100 MC trials. (a) Without void constraint; and b) with void
constraint on the flat terrain. Green circles mark the initial ground truth
location of mobile radio tags, while green paths denote the traversal paths of
the radio tags.  Figure 12: Void Impact Experiments — Comparison with and
without void constrained trajectories over $100$ MC trials in flat, hilly, and
mountain terrain.

Effectiveness and impact of void constrained trajectories. The void
probability functional constraint applied to planning aims to minimize the
disturbances to wildlife by distancing UAV trajectories away from the wildlife
of interest. This experiment investigates the performance impact of void
constraints in terms of localization time and error.

Figure 11 illustrates $100$ trajectories for the UAV (generated over $100$ MC
trials) in a task to localize $20$ mobile radio tags over the flat terrain.
With the void constraint applied, as shown in Figure 11(b), the flight path is
changed noticeably as the UAV attempts to maintain a safe distance to each
radio tag. Since radio tags are mobile, only the initial ground truth position
and their path are marked in the figure; hence, the mobility results in some
trajectories appear to violate the void constraint. Notably, without the void
constraint, the planner is expected to select the shortest path over the flat
terrain, and the planner is expected to select RSSI-based measurement actions
over AoA measurement actions, resulting in the UAV moving directly towards
each radio tag.

Figure 12 shows performance comparisons with and without void constraints on
flat, hilly, and mountain terrains. In these terrains, with the void-
constrained trajectories, the localization time with different reward
functions all increase from $10\%\sim 80\%$ as the terrain becomes more
complex. The increase in localization time is an expected result from both the
void constraint trajectories and the less informative RSSI measurement model
in the mountain terrain. Due to the void constraint, the UAV needs to maintain
a safe distance to radio tags and therefore requires spending extra time to
navigate around each tag. In addition, in the mountain terrain, the RSSI
measurement model is less effective in improving state estimation, while its
use is conflicted by the need to maintain a minimum distance under void-
constrained planning where the planner prevents the UAV from approaching the
target to improve estimates. Consequently, the UAV is more reliant on time-
consuming AoA measurements and this results in increased mission times for the
localization tasks in more complex terrains under void-constrained planning.
In contrast, over the flat terrain, the RSSI measurement imprecision is
relatively low, and the measurements are more useful in improving state
estimations even in the presence of trajectory constraints imposed by void
preventing the approach of a UAV to a radio tag to obtain more informative
RSSI measurements.

In terms of localization error, we can observe void-constrained trajectories
to lead to comparable performance with planning without void constraints.
Interestingly, the results in the mountain terrain show that with void-
constrained trajectory and measurement planning, the increased mission time to
locate all radio tags has led to slight improvements in median localization
accuracy.

##  5 ConservationBot Prototype

Figure 13: (a) A system overview. The UAV state, control actions, and RSSI
measurements are denoted by $\mathbf{u}_{t}$, $\mathbf{a}_{t}$ and
$\mathbf{Z}_{\text{R}}$ respectively; (b) Lotek VHF Wildlife Radio Collar used
in field experiments; (c) ConservationBot.

An overview of the prototype system—ConservationBot–we built is shown in
Figure 13. We employed a commercial directional H-type VHF antenna (Telonics
RA-2AK) with $4\text{\,}\text{dBd}$ gain and $10\text{\,}\mathrm{dB}$ front-
to-back gain ratio and a Software Defined Radio (SDR) to construct the
receiver. Given the significant advances in software-defined radios, their
small form factor, and low weight (giving us the ability to reduce the payload
of the sensor subsystem), we employed an SDR in our receiver. We selected the
USRP B200mini-i because its lightweight has an adequately large
$$70\text{\,}\mathrm{MHz}$-$6000\text{\,}\mathrm{MHz}$$ receiving frequency
range, high sensitivity, and large bandwidth for simultaneously detecting
multiple radio tags. We employed a DJI Manifold 2-C companion computer to
implement the digital signal processing blocks of the receiver’s detector
module as well as the planning for tracking and localization algorithms.

The signal processing components of our receiver system are shown in Figure
13(a) and is implemented using GNURadio. The SDR is configured with a sample
rate of $3\text{\,}\mathrm{MS}\text{\,}{\mathrm{s}}^{-1}$. We implemented
matched filters to detect and measure the RSSI value of each radio tag. The
digitized RF data from the SDR are first channelized and down-sampled into a
series of sub-channel with $80\text{\,}\mathrm{kHz}$ bandwidth. In each
channel, the data is further decimated into $5\text{\,}\mathrm{kHz}$ bandwidth
signal to further improve SNR (signal-to-noise ratio) and reduce the
computation complexity needed in later processing stages. The data is then
passed through a matched filter, and the RSSI value is identified by using a
peak detector to generate the measurement $\mathbf{Z}_{\text{R}}$.

##  6 Field Experiments

We describe our extensive experimental regime to validate our approach and
evaluate the performance of our aerial robot in the field. Our aims were to:

  * •

Evaluate the detection range of the software-defined receiver architecture and
hardware to understand the scanning range and the effectiveness of the
proposed compensated AoA detector (Section 6.1 and 6.2)

  * •

Conduct field experiments to evaluate and compare performance between the
proposed measurement and trajectory planning for tracking method with prior
approaches (Section 6.3.1, 6.3.2) and illustrate the effectiveness of our
approach (Section 6.3.3).

  * •

Conduct field experiments to demonstrate the significant advantage provided by
our aerial field robot over the manual methods employed for wildlife tracking
(Section 6.3.4) and evaluate the proposed aerial field robot using Southern
Hairy Nosed Wombats as a model species (Section 6.4).

We used Lotek VHF wildlife radio collars in our field experiments. The radio
collar is designed for continuous operation of $18$ months, and as a result of
limited on-board battery power, its output power is limited to
$$200\text{\,}\mathrm{\SIUnitSymbolMicro
W}$-$500\text{\,}\mathrm{\SIUnitSymbolMicro W}$$. It transmits a
$18\text{\,}\mathrm{ms}$ pulse every $1\text{\,}\mathrm{s}$ as illustrated in
Fig. 3.

###  6.1 Software defined radio receiver detection range

Figure 14: (a) The measured gain pattern of antenna used by the receiver; (b)
Detection range experiment: SNR at varying distances for radio collars placed
at $0.5\text{\,}\mathrm{m}$ and $0\text{\,}\mathrm{m}$ above the ground
measured at or above $15\text{\,}\mathrm{dB}$ SNR.

To understand the maximum detection range possible with our receiver
architecture and hardware components, we performed multiple flights at a fixed
$50\text{\,}\mathrm{m}$ altitude and measured the RSSI and SNR values of two
radio collars placed at $0\text{\,}\mathrm{m}$ and $0.5\text{\,}\mathrm{m}$
above the ground. The $0.5\text{\,}\mathrm{m}$ height was chosen to represent
the typically expected antenna height for above-ground wombats and the
$0\text{\,}\mathrm{m}$ height represents a more challenging scenario where
wombats are at the entrance of their warrens and are also representative of
smaller wildlife dwelling closer to ground level. During the flights, the
heading of the UAV and antenna is fixed and directed such that the antenna’s
maximum gain is directed towards radio collars. Importantly, the detection
range demonstrates the scanning area possible for the receiver for a typically
low-power, long-life, VHF radio collar—such as the one we used in our
experiments—even without the ability of the platform to travel and cover a
larger territory.

The detection distance is determined by the maximum distance between the
receiver and radio collar when the received signal’s SNR reached
$15\text{\,}\mathrm{d}\mathrm{B}$. Here, we used a conservative SNR level to
yield minimal false alarms and a high detection probability. Consequently, in
practice, a significantly longer detection range can be achieved and
successfully employed given the capability of the Bernoulli filter formulation
to accommodate false alarms and miss detections in real-world settings.

Figure 14(a) shows the measured gain pattern $\tilde{G_{a}}(\cdot)$ of the
antenna used in our system; the deviations from an ideal pattern in free-space
is expected as the gain of the antenna is modified once mounted onto the UAV.
Hence, the measured pattern is used in the measurement models we employ.
Figure 14(b) shows the resulting detection range measurements. For the radio
collar placed $0.5\text{\,}\mathrm{m}$ above ground, the signal can be
reliably detected up to $2000\text{\,}\mathrm{m}$. As the height of the radio
collar decreases, the system detection range reduced as expected, but even
when the collar is placed directly on the ground, the range consistently
exceeds $1000\text{\,}\mathrm{m}$.

Figure 15: AoA measurements statistics at different distances. (a) Percentage
of RSSI measurements collected during each AoA measurement, the shaded area
shows one standard deviation. Each data point was built using AoA measurements
of size $10$. (b) AoA measurement error using correlation coefficient (15),
error close to $None$ can be observed when radio collar is above
$1\text{\,}\mathrm{km}$. (c) AoA measurement error using cross-correlation
(16), no significant outlier is observed but overall has higher variance than
(c) when radio collar distance is less than $1\text{\,}\mathrm{km}$. (d) AoA
measurement error using (17).

###  6.2 Compensated AoA detector evaluation and measurement model parameter
estimation

The AoA measurement errors can result from the accuracy of the UAV heading at
the time of each RSSI detection since each AoA measurement requires the UAV to
perform a full rotation and weak radio collar signals; for instance, at longer
distances, we can expect the number of RSSI detections to reduce and
potentially increase the AoA errors.

To validate the effectiveness of our proposed compensated AoA measurement
method and determine the AoA measurement noise variance, we collected 10 AoA
measurements with a stationary radio collar at distances from
$45\text{\,}\mathrm{m}$ to $1509\text{\,}\mathrm{m}$ while flying the UAV at a
fixed altitude of $50\text{\,}\mathrm{m}$. Figure 15 illustrates the AoA
measurement errors and the percentage of detections. As shown in Figure 15(b),
at distances larger than $1000\text{\,}\mathrm{m}$, the correlation
coefficient based AoA measurement calculation produced outlier measurements
with significant errors while the cross-correlation methods shown in Figure
15(c) generates AoA measurements with relatively large variance. But the
measurements are less sensitive to the detection rate. The results in Figure
15(d) demonstrate our proposed compensated AoA measurement method described in
(17); we can observe the errors to be reasonably consistent across varying
distances with small variances; notably, with the exception of one outlier at
$45\text{\,}\mathrm{m}$, the majority of errors are within $None$. Although
the variation of AoA measurement noise can be modeled as a function of
correlation coefficient [65] or distance, we opt for a fixed variance Gaussian
noise model since the variation of AoA error with increasing distance is
observed to be minimum with the compensated detector and detailed modeling
would likely yield only marginal improvements.

Figure 16: Contour map of hilly terrain field experiment site, Inman Valley,
South Australia.

###  6.3 Field Experiments

We conducted our field experiments to evaluate our prototype ConservationBot
implementation over a more challenging, hilly terrain. The field experiments
were conducted in the Inman Valley, approximately $10\text{\,}\mathrm{km}$
from Victor Harbor, SA, Australia—the area that the field experiments were
conducted in was $40.86\text{\,}\mathrm{ha}$ in size. The terrain at this
location is hilly and vegetated with remnant eucalypt forest to the height of
approximately $12\text{\,}\mathrm{m}$ interspersed with thick shrubs to the
height of approximately $1\text{\,}\mathrm{m}$, making it difficult for humans
to traverse and an ideal environment to test our system. Figure 16 shows the
contour map of the field test area.

####  6.3.1 Localization Performance

The first set of field trials was designed to evaluate the localization
performance of our proposed Meta-Pilot method. For comparison, we selected
Imp-RSSI and cAoA(20 s) measurement methods without measurement planning.
Here, Imp-RSSI method is able to account for uncertainty in the measurement
model resulting from the hilly terrain and we can expect the approach to
provide lower localization times due to the fast measurement acquisition
times; and, the cAoA(20 s) with compensated AoA measurements minimize outliers
and we expect the approach to provide improved localization performance
because AoA measurement is less affected by terrain condition. (Please see
Section 4.2 for detail descriptions of each method)

We selected a dispersed but stationary set of radio collars (placed at fixed
locations). This setting not only ensures the safety of the personnel involved
but also allows us to design a consistent and repeatable experimental setting
for conducting multiple missions to compare different approaches. A radio
collar or radio-collared wildlife was considered localized if its location
uncertainty, evaluated by the determinant of its estimated covariance $N_{th}$
is sufficiently small; we employed
$N_{th}\leq$1\text{\times}{10}^{5}\text{\,}{\mathrm{m}}^{4}$$ and imprecision
range of $[-16,9]~{}$\text{\,}\mathrm{dB}$$. The ConservationBot was tasked to
take off to $50\text{\,}\mathrm{m}$ above the launch position and execute the
measurement and trajectory planning for the tracking algorithm to localize all
radio-tagged objects.

Table. 1 summarizes localization times and error results. We found that our
proposed approach Meta-Pilot provided the best set of localization and total
mission duration results (lowest mean error with the smallest standard
deviation and shortest mean localization time with the smallest standard
deviation). As expected, confirming our results in the simulation study for
hilly terrain, Meta-Pilot significantly outperformed the cAoA(20 s) method in
terms of localization time in field trials, where Meta-Pilot required only
one-third of the time on average to successfully locate the four stationary
radio collars with better mean localization accuracy. We found that the mean
localization time of Imp-RSSI is significantly better than the cAoA(20 s)
method. Notably, we observed a similar result for the flat and hilly terrains
in our simulation study and confirmed that the proposed imprecise RSSI models
were able to account for the measurement model uncertainty and improve
localization time and accuracy results (see Fig. 9). But, the ability to
flexibly employ AoA measurement planning actions in Meta-Pilot achieved much
better localization accuracy (highest mean and smallest standard deviation
demonstrating consistent performance) compared to Imp-RSSI.

####  6.3.2 Tracking and localizing mobile objects

In this set of field experiments, we employed the same settings used in
Section 6.3.1, with the exception of having two of the four VHF radio collars
mobile to validate the capability of ConservationBots to track and locate
mobile radio collars. Here, two VHF radio collars were carried by human
volunteers tasked with performing a wandering motion from their starting
locations at approximately
$$1\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$\sim$2\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}$$.
The trajectory of the mobile objects was captured using a phone-based GPS data
logger and later compared to the reported object location to obtain the
localization error.

Table. 1 summarizes the results for localizing mobile objects. The results
demonstrate that our proposed Meta-Pilot can track and locate mobile and
stationary objects. When comparing mobile objects to the results for
localizing only stationary objects, we observed a decrease in accuracy and a
slightly larger variation in localization times as the moving radio collars
can impact the time to reduce the uncertainty associated with estimated
positions to a desirable level whilst also planning for void constrained
trajectories.

Table 1: Comparison of localization performance for stationary and mobile objects in a hilly environment where our ConservationBot was configured with: i) our proposed imprecise RSSI model alone; ii) compensated AoA detector alone as described in Section 4.2; and iii) our proposed measurement and trajectory planner with the imprecise RSSI model and compensated AoA detector. Method | Setting | Trials |  Error $\pm~{}1\sigma$ ($\text{\,}\mathrm{m}$) |  Time $\pm~{}1\sigma$ ($\text{\,}\mathrm{s}$)
---|---|---|---|---
| Measurement and Trajectory Planner
---
(Meta-Pilot)
Stationary radio collars | 8 | $\mathbf{34.5\pm 8.5}$ | $\mathbf{231\pm 23}$
| Imprecise RSSI only
---
(Imp-RSSI)
Stationary radio collars | 8 | $43.3\pm 11.2$ | $245\pm 30$
| Compensated AoA only
---
(cAoA(20 s))
Stationary radio collars | 8 | $40.0\pm 12.7$ | $745\pm 123$
| Measurement and Trajectory Planner
---
(Meta-Pilot)
| Mobile & Stationary
---
radio collars
8 | $45.1\pm 17.5$ | $230\pm 83$
Figure 17:  Instances of intermediate belief density representing the
estimated location of radio collars for two scenarios selected from our field
trials: (a) localizing $4$ stationary VHF radio collars, (b) localizing $2$
stationary collars (1 and 2) and $2$ mobile collars (3 and 4). The effect of
void-constrained trajectories can be observed as the UAV navigates around
(unlocalized) radio collars to maintain a safe distance. Here we can observe
the convergence of belief densities of all radio collar location estimates and
the operation of the planner generating trajectories to maintain the void
constraint.

####  6.3.3 Minimizing Disturbances with Void Constrained Trajectories

We present two missions as examples to illustrate the progression of the
tracking and localization task and the manner in which the void-constrained
trajectories are able to maintain a safe distance from the VHF radio collars
of interest. Figure 17(a) depicts the evolution of belief densities for each
radio collar over time. From these snapshots, we can observe a typical
trajectory and behavior as a result of the void constraints. At time
$t=$80\text{\,}\mathrm{s}$$, the UAV is focusing on locating collar $2$.
Shortly after collar $2$ is located, the UAV proceeds to navigate toward the
next closest collar (collar $1$). We can observe that during this process, the
majority of collar $2$’s belief density (represented by orange particles)
remains outside the void region of the UAV (green dashed circle). After time
$t=$150\text{\,}\mathrm{s}$$, the UAV finishes locating collar $1$ and
subsequently heads toward collar $3$ while locating collar $4$ during the
process and return to the home-base location after all collars have been found
at time $t=$252\text{\,}\mathrm{s}$$. Here the effect of void constraint
becomes more prominent as illustrated by the UAV navigating around collar $1$.

Figure 17(b) shows another instance of intermediate belief densities for the
task of locating two stationary (collar $1-2$) and two mobile (collar $3-4$)
VHF radio collars. A similar planning strategy illustrated in Figure 17(a) can
also be observed here. At time $t=$85\text{\,}\mathrm{s}$$ the UAV moves
towards the collar determined to be the closest (collar $2$). However, due to
the void constraint, the UAV is unable to move too close to collar $2$ and
instead plans a trajectory around collar $2$ as seen at time
$t=$120\text{\,}\mathrm{s}$$. Then, after both collar $1$ and $2$ are located,
the UAV traverses towards collar $3$ and completes locating all of the collars
at time $t=$190\text{\,}\mathrm{s}$$. These results from field experiments
demonstrate that our proposed planning method is able to locate all stationary
or mobile radio collars while maintaining a safe distance.

Figure 18: Results from conducting the tracking task with a human expert with
over 20 years of field experience using the manual method with $4$ stationary
VHF radio collars in a hilly environment. Radio collars are found in the order
of $2,3,4,1$ by the expert human tracker. Completing the localization task
took $37$ minutes for the human expert and only $4$ minutes for our
ConservationBot.

####  6.3.4 Comparisons with a Human Expert

In order to demonstrate the benefits of the autonomous method of tracking
wildlife we developed here using our Conservationbot, compared to traditional
wildlife tracking methods (involving a field scientist trekking, often through
difficult terrain, carrying bulky radio-telemetry equipment), we invited an
expert conservation biologist with over 20 years wildlife tracking experience,
to compete with our robotic platform. To ensure comparable settings, $4$
stationary radio collars were used in this experiment. The human expert was
given the list of radio collar frequencies at the start but had no prior
knowledge of the positions of the radio collars. The human expert and the
ConservationBot set off from the same starting position.

The localization time for each radio collar and the traveled path of the human
expert is shown in Figure 18. As expected, the results show a significant
difference in search and localization time between the manual method and the
ConservationBot, demonstrating the effectiveness of the ConservationBot as a
field robot for the task. Human expert, first localized collar $2$ after $13$
minutes of search time (notably, during this time-lapse, the ConservationBot
has located all 4 radio collars and returned to the home base). Due to the
terrain and vegetation coverage impacts on VHF signal propagation, collar $3$
was selected by the human expert as the next collar to localize, although
collar $1$ was closer. Completing the localization task took $37$ minutes;
this was significantly higher than the $4$ minutes required for our
ConservationBot. Notably, the equipment used by the human tracker was superior
to that employed on the ConservationBot; specifically, a three-element Yagi
antenna with a higher gain and front-to-back ratio, compared to the lower gain
two-element model used by the ConservationBot, along with a more sensitive
radio receiver—an Australis 26K radio receiver—was used by the human expert.

###  6.4 Field trials with Southern Hairy Nosed Wombats

We participated in a field experiment where our ConservationBot was deployed
to localize radio-tagged wombats in a conservation project. The trials were
performed near Swan Reach SA, Australia. A total of $6$ southern hairy-nosed
wombats (Lasiorhinus latifrons) were captured, radio-tagged, and released
prior to the trials. The terrain at this location is comprised of remnant
mallee vegetation interspersed with native grasslands, eucalyptus trees and
is, thus, representative of flat terrain with less than $5\text{\,}\mathrm{m}$
elevation variations across the site as shown in Figure 20.

Trials were conducted during the daytime to comply with university health and
safety regulations, legal and risk implications, as well as regulations and
procedures governing the testing of autonomous aerial vehicles. Southern
hairy-nosed wombats, a nocturnal species, are usually less active and located
in warrens underground [104] during daylight hours. While this behavior meant
that wombats were mostly stationary, the radio signal would be greatly
attenuated by the ground resulting in a significant reduction in the maximum
detection range of signals. These attributes provided a very challenging
setting for a field trial. The UAV was launched to a fixed altitude of
$50\text{\,}\mathrm{m}$ and tasked to localize all of the detectable radio-
tagged wombats. Subsequently, manual tracking was undertaken to determine the
ground truth of each wombat’s location and compare it to the reported location
of our system to determine the reported accuracy.

Table.2 presents a quantitative summary of the results of our field
experiments. Five missions were carried out to localize two radio collars
found to be detectable from Wombat dwelling underground. With the exception of
the last mission, we were able to localize both wombats within an average of
$252\text{\,}\mathrm{s}$ with a mean localization error of
$40\text{\,}\mathrm{m}$. In mission 5, after $200\text{\,}\mathrm{s}$, the
signal from wombat $2$ could no longer be detected before it was localized. We
suspect that the wombat moved deeper underground, resulting in further signal
attenuation. The intermediate belief density (particle distributions) from
mission 1 are illustrated in Figure 21 and demonstrate the effectiveness of
the information-theoretic planning objective to reduce the uncertainty of the
estimated location of Wombats.

Figure 19: (a) Photograph showing a southern hairy-nosed wombat captured and
released after radio tagging into the habitat at Swan Reach in Australia. (b)
Main figure: Current (dark color) and extrapolated (light color) distribution
of hairy-nosed wombats—based on Figure 1 in [103]. Inset: map of the terrain
at Swan Reach in Australia. The ground truth location of tagged wombats is
marked by ’$\times$’.

Figure 20: Contour map of wombat habitat terrain in Swan Reach, South
Australia.

Table 2: Results from field trials where the ConservationBot was deployed to
track and locate underground radio-tagged southern hairy-nosed wombats in a
conservation project.

| Error (m) | Time (s)
---|---|---
| Wombat 1 | Wombat 2 | Mean | Total
Mission 1 | 48.4 | 8.0 | 28.2 | 203
Mission 2 | 43.4 | 62.2 | 52.8 | 291
Mission 3 | 49.4 | 25.7 | 37.5 | 231
Mission 4 | 31.5 | 52.6 | 42.1 | 281
Mission 5† | 35.1 | 84.9 | - | 200
Mean‡ | 43.2 | 37.1 | 43.3 | 252

  * †

Mission did not locate Wombat 2 due to loss of detections from Wombat 2’s VHF
radio collar tag, potentially as a result of the Wombat moving deeper
underground during the trial.

  * ‡

Excluding mission 5

Figure 21: Intermediate distributions of belief density representing the
estimated location of the underground VHF radio collared southern hairy-nosed
wombats. The UAV first moves toward Wombat 1 ($t=50$ to $t=90$). Then moves
around Wombat 1 due to the void-constrained trajectory planner and navigates
to Wombat 2 after Wombat 1 is localized ($t=203$). The $\square/\triangle$
denotes the truth—determined by manual tracking methods–and estimated wombat
positions by the ConservationBot, respectively; the green dashed line denotes
the void region employed, and the solid black line denotes the trajectories of
the UAV.

###  6.5 Ethics and Regulatory Compliance

This study was conducted under the University of Adelaide Animal Ethics permit
number S-2018-112a. All of the flights were undertaken with the Civil Aviation
Safety Authority (CASA, Australia) approvals and followed the safety protocols
mandated by The University of Adelaide as such our experiments were designed
around the University of Adelaide and CASA regulations governing the conduct
of UAV research. The two pilots conducting and supervising the experiments had
a Remote Pilot License (RePL).

##  7 Lessons Learned

This study describes, for the first time, the development and optimization of
an aerial robotic system for the tracking and monitoring of wildlife across a
variety of vegetation and terrain conditions. We present innovative solutions
that address practical and technical issues impacting radio tag
detection—speed, accuracy, and reliability, and evaluate the proposed
algorithms, their integration, and operation in field conditions. In this
section, we reflect upon our observations and lessons learned during our
extensive field experiments as well as potential future work.

Given the significant improvements to the detection range of the software-
defined VHF receiver, the maximum search area of our system is primarily
limited by its flight time. For a given UAV platform, flight time is dependent
on the weight of the payload. The total mass of the payload of the sensing and
computing hardware is $550\text{\,}\mathrm{g}$, where the antenna we employed
contributes to more than $45\%$ of the total payload. To reduce the mass of
the payload, and increase flight times, a customized directional antenna
design with lighter materials can be investigated in further research.

Our software systems onboard the UAV employed the existing
$915\text{\,}\mathrm{MHz}$ telemetry channel used for communication between
the UAV and the ground station to provide data for the localization and
planning algorithm executed on the ground control station as well as the
transmission of control action to the UAV. The choice of
$915\text{\,}\mathrm{MHz}$ provided a superior range compared to the
$2.4\text{\,}\mathrm{GHz}$ wireless link used in [90] and removed the need for
an additional transceiver onboard the UAV. We found the exploitation of the
telemetry channel to be convenient and use the full capability to monitor the
UAV operations and meet regulatory compliance requirements with the benefit of
being able to use open-source hardware and software to support the development
of the robotic platform. But, we observed a packet drop rate of around 10%,
predominantly due to the limited communication channel quality. Although
executing the algorithms onboard the companion computer for better reliability
and ease of use addressed the problem, for safety reasons, in the testing
phase, we could not employ this mode of operation.

The software-defined radio receiver design allows us to easily facilitate the
simultaneous detection of multiple radio collar signals at different
frequencies whilst facilitating the realization of the receiver in a small
form factor and a lightweight hardware realization. The software programmable
hardware simplifies the reconfiguration on the fly, such as receiver SNR and
radio tag frequencies. Despite the advances made compared to previous
software-defined receiver designs [90] to increase the scanning range,
tracking underground radio-collared wildlife was a challenging proposition.
For our detector, a $-70\text{\,}\mathrm{dBm}$ SNR threshold is used to
minimize false detections (false alarms); this setting achieved a scanning
range of over $2\text{\,}\mathrm{km}$. However, as shown in 6.4, detecting
very weak signals from underground VHF radio emitters due to significant
signal attenuation through the soil was challenging in this setting.

Reducing the detector threshold could increase the probability of weak signals
being detected, but it will also increase the probability of receiving false
alarms. Notably, our current detector implementation only reports up to one
peak detection per radio tag transmit period; whenever a false alarm is
reported, the truth signal (if present) will be suppressed, which also
effectively reduces the detection probability. To allow using a lower SNR to
improve the detection range further, the detector architecture can be modified
to report all signal detection peaks (from the peak detection stage in our
detector). This will allow us to fully utilize the Bernoulli filter’s ability
to handle object state estimation in the presence of multiple false alarms in
addition to missed detections and, therefore, increase the capability of our
estimation algorithm to function under increased false alarms. Consequently,
the operating range of our ConservationBots will effectively increase—more
importantly, enable the tracking and localization in the presence of weak VHF
radio collar tag signals, such as those from underground dwelling animals.

##  8 Conclusion

We have validated the capability of our proposed approach to rapidly localize
multiple mobile objects in different environments through extensive
simulation-based experiments and field experiments with a prototype robotic
platform—ConservationBot. Further, we have shown that our approach, which
utilizes both RSSI and AoA measurements and performs measurement and
trajectory planning to locate radio-collared wildlife, delivers consistently
fast, robust, and better performance over traditional RSSI-only or AoA-based
approaches, even when the proposed imprecise RSSI model formulation and
compensated AoA detector are employed with previous approaches. Importantly,
the ability to plan for measurements allows the robot to benefit from robust
AoA measurements without the impact of the increased time needed to complete a
mission. Although the use of the imprecise likelihood method is not a perfect
replacement for the precise and correct likelihood function, it greatly
simplifies the difficult task of modeling and building the often complex
likelihood model significantly impacted by environmental conditions.

Our field experiments confirm that autonomous aerial robots capable of fast,
robust tracking of multiple wildlife can provide benefits over the labor-
intensive manual tasking to gather precise information from wildlife for their
conservation and management.

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