# XRLoc: Accurate UWB Localization for XR Systems

Aditya Arun  University of California San DiegoCaliforniaUnited States
<EMAIL_ADDRESS>,  Shunsuke Saruwatari  Osaka UniversityOsakaJapan
<EMAIL_ADDRESS>,  Sureel Shah  University of California San
DiegoCaliforniaUnited States<EMAIL_ADDRESS>and  Dinesh Bharadia  University
of California San DiegoCaliforniaUnited States<EMAIL_ADDRESS>
(Date: July 2023)

###### Abstract.

Understanding the location of ultra-wideband (UWB) tag-attached objects and
people in the real world is vital to enabling a smooth cyber-physical
transition. However, most UWB localization systems today require multiple
anchors in the environment, which can be very cumbersome to set up. In this
work, we develop XRLoc, providing an accuracy of a few centimeters in many
real-world scenarios. This paper will delineate the key ideas which allow us
to overcome the fundamental restrictions that plague a single anchor point
from localization of a device to within an error of a few centimeters. We
deploy a VR chess game using everyday objects as a demo and find that our
system achieves $2.4$ cm median accuracy and $5.3$ cm $90^{\mathrm{th}}$
percentile accuracy in dynamic scenarios, performing at least $8\times$ better
than state-of-art localization systems. Additionally, we implement a MAC
protocol to furnish these locations for over $10$ tags at update rates of
$100$ Hz, with a localization latency of $\sim 1$ ms.

††conference: ; 2023††journalyear: ;††copyright: none

##  1\. Introduction

Extended Reality (XR), broadly encompassing virtual, augmented, and mixed
reality technologies, can potentially revolutionize fields such as education,
healthcare, and gaming (Thomas, 2012; Alizadehsalehi et al., 2020; Xi et al.,
2022). The primary ethos for XR is to provide immersive, interactive, and
realistic experiences for users. A key component of delivering this user
experience is to transfer the physical world into the virtual space. For
example, our everyday spaces and objects can be transformed into video game
assets (like tennis racquets, swords, or chess pieces) for interactive gaming
applications.111 in a demo, we transform mugs and a desk into our lab to a
life-size chess board (link:https://bit.ly/3q7DKKy) To enable these
applications, we find a common thread — any XR system should localize and
track objects in an environment. Specifically, this object-tracking system
needs to satisfy three key requirements to realize XR applications:

Figure 1. XRLoc enables users to play a life-size chess game with everyday
objects. XRLoc localizes mugs retrofitted with off-the-shelf UWB tags from a
single vantage point with a few cm of location accuracy, which are then
translated to chess pieces in the virtual world.

R1. Ease of anchor deployment: Any asset localization system must have low
deployment efforts, which can potentially be embedded within common
electronics like TVs or soundbars. This single module should be smaller than
$1$ m. 222Most consumer electronics like TVs or soundbars are around $1$ m in
length.

R2. Accurate and reliable: Assets must be localized to an accuracy within a
few centimeters in room-scale scenarios. We place a stringent requirement of a
few centimeters of accuracy to provide a glitch-free user experience.
Providing immersive XR experiences consequently means small user or object
tracking errors are more obvious and severely impede the adoption of XR (Wang
and Dunston, 2007). Specifically, the localization system must be reliable
during movement, under occlusions, and consistently track assets within an
accuracy of a few cm.

R3. Multi-asset low latency localization: Finally, an XR system needs to
localize multiple objects in an environment in real time. In dynamic
scenarios, this can mean we must localize tens of objects with a $60$–$80$ Hz
update rate as people naturally perceive their surroundings at 60–75 Hz
(Deering, 1998), and delays in updates of object locations in a dynamic
scenario can break away from an immersive experience.

| Visual | Acoustic | Radar | RFID | Single anchor | XRLoc
---|---|---|---|---|---|---
R1: Ease of anchor deployment | ✓ | ✓ | ✓ | $\times$ | ✓ | ✓
R2: Accuracy and reliability | $\times$ | ✓ | $\times$ | ✓ | $\times$ | ✓
R3: Multi-asset and low latency | ✓ | $\times$ | ✓ | ✓ | ✓ | ✓
Table 1. Existing technologies do not satisfy the 3 key requirements for an XR
localization/tracking system.

However, none of the existing asset localization systems meet these three key
requirements to deliver XR applications in everyday scenarios (see Table 1).
Camera and visual sensors are susceptible to poor lighting and visual
occlusions, consequently failing to provide reliable localization (R2).
Additionally, deploying a camera-based system can be privacy invasive
(Russell, 2013) in home and public settings. Acoustic systems (Liu et al.,
2020) provide accurate localization but are difficult to localize multi-asset
with low latency simultaneously (R3). Radar systems (Kong et al., 2022;
Mukherjee et al., 2022; Xue et al., 2021) can provide low-latency object
tracking from a single module but fail to track occluded objects or those
which have small radar cross-sections (RCS). Some RFID systems have succeeded
in realizing low latency (Luo et al., 2019; Shangguan and Jamieson, 2016; Yang
et al., 2014). Their asymmetric architecture (cost-effective tags and
expensive readers) better suits large-scale deployments in retails and
industrial sectors. However, long-range RFID systems ($>$ 6m) are expensive
and bulky to integrate into consumer electronics, precluding wide-scale
deployments (R1).

Altenatively, many single RF module localization solutions (Chen et al., 2019;
Ge and Shen, 2021; Giorgetti et al., 2009; Großwindhager et al., 2018; Groth
et al., 2021; Kotaru and Katti, 2017; Li et al., 2020b; Meissner and Witrisal,
2012; Soltanaghaei et al., 2018; Wang et al., 2019a, b; Zhang et al., 2022)
leveraging WiFi/BLE or ultra-wideband (UWB) are easy to deploy because of
transceivers which can be inexpensively deployed in consumer electronics.
However, they fail to provide the necessary cm-level accuracy. None of the
existing systems simultaneously satisfy all three stringent requirements to
enable XR applications, and prior art will be more carefully considered in
Sec. 8.

To address the need for XR-compliant localization, we develop XRLoc, which
consists of two parts — a localization tag, attachable to objects of interest,
and a single localization module to furnish few-cm level locations from a
single vantage point. The localization module is less than $1$ m and can be
easily incorporated within everyday electronics such as televisions or
soundbars (satisfying R1). It leverages the tag’s single UWB transmission for
a few cm accurate localization. An accompanying MAC protocol also supports the
localization of multiple tags at an update rate of $100$ Hz (satisfying R3).
An example deployment of XRLoc is showcased in Fig. 1, where beverage cups are
attached with off-the-shelf UWB tags. XRLoc is leveraged to transform an
office space into a life-sized chess board, with these cups taking the place
of chess pieces and localized with cm-level accuracy. A video demo of this
case study is also included as well${}^{\ref{fn:demo}}$. However, to
simultaneously meet all the aforementioned requirements, we need to solve four
key challenges:

1\. Geometric dilution of precision: In most UWB localization systems, three
or more UWB anchors need to be placed in diverse locations in a room to
localize the UWB tag, increasing deployment efforts and breaking away from R1.
Alternatively, we can place these UWB anchors within a single localization
module constrained to a $1$ m space. However, reducing the spatial diversity
can worsen the localization accuracy by $10\times$. This accuracy degradation
is called ‘geometric dilution of precision’ (Spilker Jr et al., 1996) (GDOP).
A potential strategy to overcome GDOP is to borrow techniques from RFID-
systems (Yang et al., 2014; Luo et al., 2019; Shangguan and Jamieson, 2016)
that achieve real-time cm-scale accuracy from a single RFID reader. However,
we observe UWB systems provide $15\times$ worse measurement accuracy compared
to RFID systems (Yang et al., 2014), owing to an RFID system sharing the same
clock at the transmitter and receiver (mono-static architecture). Hence a
direct consequence of GDOP is a XRLoc’s reduced resilience to measurement
noise, which precludes us from directly borrowing techniques from RFID-based
systems.

To reduce our measurement noise, we could increase transmit power to improve
signal quality, increase transmission length for better averaging, or choose
better hardware with lower noise floors. However, these solutions come at the
cost of increased battery consumption at the tag, increased localization
latency, or expensive tag design, respectively. Alternatively, XRLoc makes a
key observation when looking at the phase difference of the received UWB
signal measurements (PDoA) between a pair of anchors — PDoA measurement
quality can be improved proportionally to the distance between the pair of
anchors. This simple observation forms the cornerstone of XRLoc’s design and
allows us to satisfy the first requirement R1.

2\. Ambiguous location predictions: However, this improved PDoA measurement
quality comes at a detrimental cost — increasing the anchor spacing creates
multiple ambiguous location predictions as phase measurements wrap around at
$2\pi$. The changes in these ambiguities mirror the changes in the true
location of the tag, and they do not affect tracking systems (Wang et al.,
2014; Cao et al., 2021), which leverage phases to provide cm-level tracking
accuracy for handwriting recognition. However, incorrectly choosing an
ambiguous absolute location can degrade the accuracy by several tens of
centimeters and may create glitches within the XR system.

To predict accurate locations despite phase wrap-around, XRLoc leverages a
simple observation — unlike phase measurements, time of arrival measurements
do not suffer from ambiguity. Specifically, the time difference of arrival
(TDoA) between a pair of anchors, although inaccurate in furnishing cm-level
localization, can help to detect and filter out ambiguities. By cleverly
fusing these time-difference and phase-difference measurements, XRLoc can
provide cm-level accurate locations from a single UWB transmission and satisfy
the second requirement R2.

3\. Measurement bias-aware localization: However, as we push the envelope on
cm-accurate location predictions, we find that hardware biases can corrupt our
location estimates and degrade our location accuracy by over $2\times$.
Specifically, through empirical measurements, and as observed in previous
studies (De Preter et al., 2019), UWB modules (Decawave, 2020) suffer from a
distance-sensitive measurement bias. We model, estimate, and calibrate for
these biases via a three-point calibration procedure. We fuse the time and
phase measurements with a corrected PDoA and TDoA measurement model by
leveraging a particle filter to provide cm-accurate and low-latency location
estimates, satisfying R2.

4\. High update rate multi-tag operation: In addition to providing low-latency
localization, XRLoc must furnish locations for multiple objects in the
environment. Often, the UWB transmissions for localization from multiple tags
in an environment can cause packet collisions at XRLoc’s module. The collision
causes localization failure $25\%$ of the time. We leverage a low-power
wireless side channel to alleviate packet collisions to design a power-
efficient medium access control (MAC) protocol. Specifically, XRLoc deploys a
LoRa-based MAC to support consistent localization for tens of tags at over
$80$ Hz, satisfying R3.

XRLoc brings together these key techniques to build a $1$ m sized module,
consisting of $6$ Decawave DW1000 (Qorvo, Inc., 2016) UWB modules for
localization, along with a Semtech LoRa SX1272 (Semtech Corp., 2022) to
furnish a side-channel for the MAC protocol. Additionally, we prototype a
simple UWB + LoRa Tag using the Decawave EVB1000 and a LoRa SX1272. Through
extensive evaluations, we find that XRLoc satisfies all the three stringent
requirements with

  1. (1)

Static localization error with median and 90th percentile accuracy of $1.5$ cm
and $5.5$ cm, an improvement of $9.5\times$ and $5.2\times$ from state-of-art
systems (Zhao et al., 2021).

  2. (2)

Dynamic localization error with median and 90th percentile accuracy of $2.4$
cm and $5.3$ cm, an improvement of $11\times$ and $8\times$ from state-of-art
systems (Zhao et al., 2021).

  3. (3)

Localization failure rate of $0.5\%$ when using the MAC protocol as compared
to a failure rate of $~{}25\%$ without a MAC protocol, a $50\times$
improvement, for $10$ tags operating simultaneously at $100$ Hz location
update rate.

  4. (4)

Location compute latency of $1$ ms, allowing for real-time localization ($60$
Hz) of 16 tags.

##  2\. Why is this problem hard?

Figure 2. (a) Spatially-diverse placement of UWB anchors (red diamonds) near
the walls provides median accuracy with TWR of $2.9$ cm (b) when receivers are
constrained near the bottom wall, median accuracy degrades by $~{}8\times$
when using TWR (c) fusion of TDoA, TWR, and AoA does not help in these
scenarios either, providing median accuracy of $23.3$ cm. (d) XRLoc solves the
challenges associated with dilution of precision, achieving median accuracy of
$3.3$ cm (e) Summary of errors when leveraging various UWB measurements and
XRLoc.

We have established the need for localizing users and objects within a few
centimeters of a single vantage point. In this section, we will find that
restricting our sensing to within a space of $1$ m reduces our geometric
diversity leading to localization errors of many $10$’s of centimeters. This
phenomenon is commonly referred to as geometric dilution of precision. We will
explore the use of three common UWB measurements – two-way-ranging (TWR),
time-difference-of-arrival (TDoA), and angle-of-arrival (AoA) – and find
systems that rely on these measurements fail to furnish the required accuracy.
Additionally, we’ll explore fusing and jointly optimizing for these
measurements to improve localization accuracy. However, even this measurement
fusion is insufficient. To test this hypothesis, we build a simple simulation
environment described below.

Simulation environment: We perform extensive simulation in a $3\times 3$
environment, a standard room size, to find the best case localization
accuracy. We use $6$ UWB transceivers, placed either diversely in the
environment (red diamonds in Fig. 2 (a)) or in a limited space near the bottom
wall (see Fig. 2 (b, c, d)). Next, we divide this space into a $1$ mm grid and
place tags in each position to measure the location accuracy. The pixels of
the ‘heatmaps’ represent these tag locations, and the pixel color intensity
quantifies the median localization accuracy across $100$ simulated trials.

Simulating TWR: Many UWB radios measure the time of flight (ToF) of the signal
between the transmitter and receiver with up to a resolution of $15.6$ ps
(Dotlic et al., 2017). The ToF is measured via multiple packet exchanges,
taking at least $0.3$ ms (Corbalán and Picco, 2020). And clock drifts at the
receiver during this TWR event can lead to a ToF measurement deviation of
$150$ ps for a $0.5$ ppm clock crystal. Hence, we characterize our simulated
TWR measurements with a zero-mean Gaussian with a standard deviation of $150$
ps.

Simulating TDoA: Instead of an absolute time of flight measurement, we can
measure the difference in the time of arrivals across a pair of synchronized
receivers. However, TDoA measurements depend on the receivers’ clock
synchronization accuracy. Our measurements, independently verified by Decawave
(Qurvo, Inc., 2014), show clock-sync errors in best-case wired synchronization
can cause a TDoA measurement deviation of $140$ ps. Hence, our simulated TDoAs
are Gaussian distributed with a standard deviation of $140$ ps.

Simulating AoA: Some UWB systems (Zhao et al., 2021; Heydariaan et al., 2020)
alternatively measure the angle of arrival of a signal between a pair of
receivers placed half-wavelength apart (see close pairs of red diamonds in
Fig. 2(c)). We can measure AoA with noise deviation of $1.5^{\circ}$, as
independently verified in (Zhao et al., 2021; Heydariaan et al., 2020).
Consequently, we simulate our AoA measurements as zero-mean Gaussian with
$1.5^{\circ}$ standard deviation.

###  2.1. Quantifying localization errors

TWR, or distance measurements between a tag and multiple receivers placed
diversely in an environment, can be used to trilaterate the tag’s position to
achieve a few cm-level accuracies. From Fig. 2(e), we find that the median
localization error is $2.9$ cm. Additionally, this error is consistent (with a
variation of a few centimeters) across the space (see heatmap in Fig. 2(a)).
However, when we place all the receivers within a $1$ m linear form factor to
satisfy R1, we find that the accuracy degrades by over $8\times$ as compared
to the diverse antenna placement. Additionally, we observe a non-uniform
performance with errors as large as $1$ m. To meet R2, we have made our
localization system too erroneous to be usable.

The fundamental reason for the performance degradation is the reduced
geometric diversity when the antennas are closer. With the antennas placed
around the environment, trilateration is more resilient to errors in distance
measurements. We quantify the localization errors by leveraging TDoA or AoA
measurements and summarize the results in Fig. 2(e). We find under low
geometric diversity, the median localization errors can be close to $54.4$ cm
and $40.9$ cm for TDoA and AoA measurements, respectively.

###  2.2. Fusing all measurements

Similar to many robotics applications (Alatise and Hancke, 2020), we can use
TWR, AoA, and TDoA measurements to provide higher accuracy. This fusion is
done by jointly optimizing the error function from TWR, AoA, and TDoA (Liu et
al., 2013) measurements. Specifically, in Fig. 2(c), we measure $6$ TWR
measurements from each receiver (red diamonds), $3$ AoA measurements from each
closely-spaced pair of UWB receivers, and $3$ TDoA measurements between one
antenna from each of these paired groups. The measurement-fusion efforts
provide median localization of $23.3$ cm. However, it still fails to meet our
criteria of a few-cm error in localization.

None of the existing states of art systems can surmount the challenge of
localizing from a single vantage point and deliver the stringent requirements
set forth by our application use case. In XRLoc, we develop the algorithm
(Sec. 3) and prototype a system (Sec. 4 and 5) to achieve this small-form-
factor, high accuracy (median accuracy of $3.3$ cm as seen from Fig.2(d) and
Fig. 2(e)), and multi-asset localization system, for use within VR systems and
immersive audio applications. In the following section, we will delineate the
key ideas which allow XRLoc to circumvent the challenges posed by geometric
dilution of precision.

##  3\. Circumventing low-spatial diversity

In the following sections, we tackle the fundamental challenge in single-
vantage point localization. First, we will explore improving our phase
measurements to improve location accuracy by increasing the antenna separation
(Sec. 3.1). However, this comes with the unintended side-effect of introducing
ambiguities to our location prediction. So, we explore the use of time
difference of arrival (TDoA) measurements to combat these ambiguities (Sec.
3.2). Finally, we explore fusing these measurements in an accurate and low-
latency fashion by leveraging a particle filter (Sec. 3.3). By exploring the
key ideas here, XRLoc will fulfill R2 and furnish few-cm level localization.

###  3.1. Improving localization resolution

The prior learning from Sec. 2 is that we reduce our resiliency to noise when
we try to localize tags from a single vantage point. Lacking spatial diversity
adds vulnerability to the optimization creating large outlier measurements and
preventing few-cm scale localization. However, when we have two closely (less
than half-wavelength) separated antennas, we can find the phase difference
($\Delta\phi$) between this pair as

$\displaystyle\Delta\phi=\frac{2\pi d}{\lambda}\sin(\theta)$

where $\theta$ is the incoming angle of arrival w.r.t. to the normal of this
pair of antennas, $d=\frac{\lambda}{2}$ is the distance between them, and
$\lambda$ is the wavelength at $3.5$ GHz UWB center frequency.333we develop
this intuition assuming far field, but later in Sec. 3.3 we consider the exact
phase difference measurement However, the typical UWB phase has a resolution
of around $8$ bits 444For example, although having a 16-bit real part and a
16-bit imaginary part in each CIR sample, DW1000 has a 7-bit phase resolution
because the phase must be corrected by RCPHASE register, which is a 7-bits and
for the adjustment of receiver carrier phase., which provides a phase
resolution of $1.4^{\circ}$, and consequently a localization resolution of
$~{}2.1$ cm at a distance of $3$ m from the localization module. However,
increasing the inter-antenna separation, $d$, linearly increases the measured
phase difference. We can leverage this to improve our localization resolution
to the $\sim 1$ mm limit when the antenna separation is $1$ m.

Prior works (Wang et al., 2014; Cao et al., 2021) have leveraged this fact to
increase accuracy for handwriting tracking purposes. But, widening this
separation comes at the cost of introducing more phase ambiguities. This is
apparent when we return to the AoA equation and observe that our phase-
difference measurements, $\Delta\phi$, wrap over $2\pi$ for a larger
separation than half-wavelength separation for angles between
$-90^{\circ}<\theta<90^{\circ}$. This is not an issue for tracking purposes,
where the changes in location of these ambiguities mirror the true changes in
the location and continue to provide a similar trajectory estimate. However,
for XRLoc, we find predicting and tracking these incorrect locations can
degrade the localization accuracy by an order of magnitude to several tens of
centimeters.

###  3.2. Ruling out ambiguities

To overcome ambiguities, a simple solution is adding more antennas between the
two we have placed so far. These additional antennas will help eliminate phase
ambiguities by reducing the consecutive antenna distance while employing a 1-m
antenna array aperture. Fig. 3 (a, b) depicts these ambiguities that exist in
such a system by showing the likely positions of the tag. Considering the
simulation environment from Sec. 2, we deploy two arrays with spacing $33.3$
cm and $25$ cm for the same antenna aperture of $1$ m. Next, we deploy a tag
at the center of the space and predict its potential locations (pixel color
intensities) in both scenarios. We observe that keeping the same aperture of 1
m, we have similar measurement errors (peak widths) in both cases, consistent
with our previous findings, but reducing separation creates fewer ambiguities.
Deploying $23$ antennas within this $1$ m, each spaced half-wavelength apart,
will remove all our ambiguities at the cost of increased hardware complexity.

Alternatively, we observe TDoA measurements are free from ambiguities and can
potentially be leveraged to disambiguate the predictions from PDoA. Similarly
to the previous PDoA images, in Fig. 3 (c, d), we only show the tag’s location
likelihoods when relying on TDoA measurements. The TDoA peak, although very
erroneous (larger peak widths), is unambiguous. Additionally, increasing the
number of antennas reduces this error/peak width. To recap, by reducing the
antenna separation (or increasing the number of antennas), we increase the
separations between the ambiguities coming from PDoA measurements and tighten
our peak widths coming from TDoA. Consequently, at the correct antenna
spacing, our ambiguous peaks will be wide enough to be rejected by our TDoA
measurements. We find this sweet spot when we use $6$ antennas, $4\times$
fewer antennas than would have otherwise been required.

###  3.3. Jointly optimizing for TDoA and PDoA measurements

We can now extend the key intuitions to leverage TDoA and PDoA to develop a
localization algorithm to meet our few-cm accuracy requirement. As further
explained in Sec. 4, via careful engineering and hardware design choices, we
measure PDoA with a standard deviation $\sigma_{\theta}=5^{\circ}$ and TDoA
with a standard deviation of $\sigma_{t}=150ps$. This measurements can be
modeled as a zero-mean Gaussian:

$\displaystyle\mathrm{TDoA\ between\ Rx\ i\ and\ j:}\ $ $\displaystyle
t_{i,j}\sim\mathcal{N}(0,\sigma_{t})$ $\displaystyle\mathrm{PDoA\ between\ Rx\
i\ and\ j:}\ $ $\displaystyle\theta_{i,j}\sim\mathcal{N}(0,\sigma_{\theta}).$

Additionally, given a candidate tag location, $\vec{p}$, and receiver
locations $\vec{x_{i}},\forall i\in[1,2,\dots,N]$ we can also compute the
expected PDoA and TDoA as

$\displaystyle\mathrm{TDoA:}\ $
$\displaystyle\hat{t}_{ij}=\frac{|\vec{p}-\vec{x_{i}|}}{c}-\frac{|\vec{p}-\vec{x_{j}}|}{c}$
(1) $\displaystyle\mathrm{PDoA:}\ $
$\displaystyle\hat{\theta}_{ij}=\mod\left(2\pi\left(\frac{|\vec{p}-\vec{x_{i}}|}{\lambda}-\frac{|\vec{p}-\vec{x_{j}}|}{\lambda}\right),2\pi\right)$

where $\vec{p}$ is the location of the tag and $\vec{x}_{i}/\vec{x}_{j}$ are
the locations of the 6 UWB antennas placed within a linear $1$ m array. $c$
and $\lambda$ are the speed of light and UWB wavelength, respectively. Note
here we forgo the far-field assumption made in Sec. 3.1.

Figure 3. Log-likelihood heat map of PDoA and TDoA when changing the number of
antennas $N$.

The location ($\vec{p}$) which gives the closest expected measurements to the
actual measurements is the likely tag location,

(2)
$\displaystyle\min_{\vec{p}}\begin{bmatrix}\vec{e_{t}}^{T}&\vec{e_{\theta}}^{T}\end{bmatrix}^{T}\Sigma^{-1}\begin{bmatrix}\vec{e_{t}}^{T}&\vec{e_{\theta}}^{T}\end{bmatrix}$

where $\vec{e}_{t}$ and $\vec{e}_{\theta}$ measure the error between our
predictions and the actual measurements, and

$\displaystyle\Sigma=\mathrm{diag}(\sigma_{t}^{2},\cdots,\sigma_{t}^{2},\sigma_{\theta}^{2},\cdots\sigma_{\theta}^{2})$

is a diagonal covariance matrix containing the TDoA and PDoA measurements
standard deviations. Note here that since each receiver on XRLoc’s
localization module is independently measuring the TDoA and PDoA, we have a
diagonal covariance matrix.

The simplest way to find this best tag location is to perform a grid search
over our space to find the minimum point for Eq. 2. Aiming for cm-level
localization, we choose a grid size of $1\times 1$ mm. But this exhaustive
search can be time-consuming (around $61.2$ s / location on a 12-core CPU),
precluding real-time localization in dynamic situations. Alternatively, we can
leverage gradient descent-based optimization techniques (Gil et al., 2007) to
arrive at the most likely tag position. However, these techniques fail when we
do not have a good initial estimate of the location, which is the case when
looking to localize a tag in a large environment (Glorot and Bengio, 2010).

To surmount this challenge, we provide the final insight —selectively
searching over the large space instead can reduce the computation complexity
for localization. The brute force approach unnecessarily searches over each
grid point for every packet. We can instead sample our environment more
sparsely and slowly converge to our ideal location over a few packets. This
is, in fact, the key idea behind particle filters (Aernouts et al., 2020),
which are commonly used in state estimation scenarios with highly non-convex
error functions and poor initialization.

Armed with this insight, for the first packet we receive, we uniformly
distribute a set of particles (500 particles/$\mathrm{m}^{2}$) in our
environment and compute the likelihood of these positions. When we receive
consecutive packets, we can re-sample the set of particles with the highest
probability and continue converging to our true locations. However, despite
the fewer likelihood computations required, particle filters commonly furnish
non-real-time estimates (with a latency of $~{}7.2$ ms on a 12-core CPU). To
combat this problem, XRLoc adaptively re-samples and reduces the number of
particles based on the current confidence of the estimate. As we do not know
the tag’s location, many particles are initially required to sample the search
space uniformly. However, our particles converge close to the true location
over time, improving our confidence in the location estimate. We can reduce
the number of particles needed as we no longer need to explore the space
uniformly. Empirically, this adaptive particle filter implementation converges
within five measurements and provides a location estimate with a $1.2$ ms
latency on a 12-core CPU.

##  4\. Challenges with prototyping XRLoc

Additional considerations arise when employing the ideas from Sec. 3 while
prototyping XRLoc using off-the-shelf components. First, we need to acquire
low-noise phase measurements. In Sec. 4.1, selecting the right clock is
imperative to ensure a low phase noise. Second, due to hardware imperfections,
we find that the expected PDoA measurements (Eq. 1) do not match the real-
world measurements. To account for the offsets, we devise a calibration scheme
and re-consider the formulation of the expected PDoA measurements in Sec. 4.2.
Finally, we explore the effects of multipath reflection on the TDoA
measurements in Sec. 4.3.

###  4.1. Acquiring accurate time and phase

Before prototyping XRLoc, we conducted extensive simulations to investigate
the minimum phase and time acquisition accuracy needed to achieve few-
centimeter positioning accuracy, assuming 6 antennas were equally spaced in a
1-meter region. In a $3\times 3$ environment, we implemented the algorithm
presented in Sec. 3.3 at varying phase and time acquisition noise levels. Our
simulation results are presented in Fig. 4(a), where the horizontal axis
represents the standard deviation of the phase error, and the vertical axis
represents the 50 percentile of the localization error. Each line shows the
standard deviation of the time error.

From this simulation, we make two key observations. First, we see that time
errors between 3–250 ps provide similar localization accuracy, and these lines
are grouped in the plot. However, exceeding $300$ ps in time error
significantly increases localization error, as TDoA fails to segregate
ambiguity made by PDoA. Second, these simulations clarify that few-cm level
accurate localization requires high phase accuracy. Specifically, the red
vertical line marks a threshold of $5^{\circ}$ of standard deviation in phase
measurement needed to achieve few-cm accurate locations.

The synchronization clock is the main factor affecting this phase noise in our
system. The phase of the UWB signal is measured by first down-converting the
received signal with the carrier signal. It is measured relative to this
carrier signal by the baseband processing unit (Dotlic et al., 2017). And when
we consider measuring the PDoA, we look at the difference in the phase of any
two receivers. In this situation, if both receivers share the same carrier
clock, then the PDoA they measure will be induced purely from the relative
distance traveled by the signals to each receiver (see Eq. 1). A simple way to
achieve this is to connect the two receive antennas to the same UWB module
(Cao et al., 2021). However, we observed the overhead of extracting the
complete CIR when implementing these systems is large ($\sim 1.2$ ms),
precluding low-latency localization. Specifically, we have the API overhead to
measure the data and the data extraction overhead over USB, requiring 599
$\mu$s and 612 $\mu$s, respectively.

Alternatively, we prototype our system using independent UWB modules (Qorvo,
Inc., 2016) for each receiver, eliminating the need to export CIR
measurements. This reduces the data acquisition latency by $\sim 4\times$ to
$\sim 340~{}\mu$s. However, we cannot synchronize the carrier clocks on these
independent modules, but instead, synchronize a lower $38.4$ MHz clock leading
to phase measurement errors. Via measurements with different clocks, we find
that the phase noise in this input clock can largely influence the noise in
the PDoA measurements. Specifically, from the oscillator’s data sheet (Crystek
Corp., 2022), we can obtain the phase noise of the oscillator,
$N_{\phi}(f_{\rm offset})$ where $f_{\rm offset}$ is the frequency offset from
the center frequency of the oscillator. Using the $N_{\phi}(f_{\rm offset})$,
the standard deviation of clock jitter, $\sigma_{\rm jitter}$, can be
expressed as follows.

(3) $\displaystyle\sigma_{\rm jitter}=\frac{\sqrt{2}}{2\pi f_{\rm
osc}}\sqrt{\Delta fN_{\phi}(f_{\rm offset})}$

where, $\Delta f$ is the bandwidth of the measurement and $f_{\rm osc}$ is the
oscillator frequency. We measure the standard deviation of the phase error
($\sigma_{\phi}$) and time stamping error ($\sigma_{t}$) as:

$\displaystyle\sigma_{\phi}=\frac{c}{\lambda}\frac{f_{\rm osc}}{2\pi
f_{s}}\sigma_{\rm jitter}\ ;\quad\sigma_{t}=\frac{f_{\rm
osc}}{f_{t}}\sigma_{\rm jitter}$

where, $f_{s}$ is the sampling frequency, $f_{\rm t}$ is the frequency of the
clock used for to measure time-of-arrival and $c$ is the speed of light. We
can choose an appropriate clock to meet our phase and time measurement
thresholds by modeling this noise behavior. Many off-the-shelf (Crystek Corp.,
2022; Abracon LLC, 2022) clocks satisfy these requirements at reasonable price
points and employ (Crystek Corp., 2022) in prototyping XRLoc. For example,
according to the datasheets provided by Crystek (Crystek Corp., 2022) and
Abracon (Abracon LLC, 2022), their respective phase noise values at 100 kHz
offset are $-160$ dBc/Hz and $-150$ dBc/Hz, while their respective phase noise
values at 100 Hz offset are $-115$ dBc/Hz and $-109$ dBc/Hz.

Figure 4.  (a) Localization error vs. PDoA error standard deviation, with TDoA
error standard deviations as each line in the legend. For few-cm level
localization, the threshold, per the red line, is $\sigma_{t}=5^{\circ}$ and
$\sigma_{t}=150$ ps. (b) Phase measurements (green) deviate from ideal (black)
measurements. Performing appropriate calibration fixes these deviations (red).

###  4.2. Combating hardware biases

In Eq. 1, we provided an expression for the expected PDoA measurement if we
know the underlying tag and receiver locations. In reality, however, we see a
large deviation when we compare the expected PDoA measurements with true PDoA
measurements. To verify this, we perform an experiment varying the distance of
a tag from XRLoc’s localization module. In Fig. 4(b), the green‘RAW’
measurements are shifted from black ground truth ‘GND’ measurements. Visually,
we observe three deviations — a constant additive bias ($\alpha$) which
contributes to a downward shift, a multiplicative bias ($\beta$) w.r.t.
distance affecting the slope of the line, and an exponential bias ($\gamma$)
w.r.t. distance affecting the curvature (non-visualized in the figure). We
assume these biases result from the ADC saturation when the distances are too
close and propose a 3-point calibration to compute these hardware-specific
calibrations below. Subsequently, we modify our expected PDoA measurements
from Eq. 1 as

$\displaystyle\hat{\phi}_{i,j}=\mod\bigg{(}$ $\displaystyle\left\\{\frac{2\pi
d_{i}}{\lambda}-\alpha_{i}-\beta_{i}d_{i}^{\gamma_{i}}\right\\}-$
$\displaystyle\left\\{\frac{2\pi
d_{j}}{\lambda}-\alpha_{j}-\beta_{j}d_{j}^{\gamma_{j}}\right\\},2\pi\bigg{)}$

where, $\alpha_{i}$, $\beta_{i}$, $\gamma_{i}$ are the calibration parameters
and $d_{i}=|\vec{p}-\vec{x_{i}}|$ is the distance between the tag and UWB
receiver. We replace Eq. 1 with this updated expected PDoA equation for the
particle filter described in Sec. 3.3.

To estimate these calibration parameters, we perform a three-point
calibration. First, we model the phase ($\tilde{\Phi}$) measured at each UWB
module according to these biases as

$\displaystyle\tilde{\Phi}_{i}=\Phi_{i}+\alpha_{i}+\beta_{i}(d_{i})^{\gamma_{i}},\quad
i\in[1,N],$

where $\tilde{\Phi}$ is the calibrated phase. Next, we measure the received
phase ($\Phi$) at each UWB receiver for three known locations within our
space. Finally, we use regression to find the expected calibration parameters,
which minimize the deviation between the measured and expected phases
according to the above equation.

###  4.3. Handling multipath reflections

However, in common indoor settings, reflections of the RF signal can
potentially lead to ambiguities in TDoA measurement (Scheuing and Yang, 2006).
Despite our best efforts to acquire bias-corrected PDoA measurements, the
presence of multipath can prevent us from ruling out ambiguous location
predictions. However, UWB signals sample at the rate of $1$ GHz, implying a
time resolution of $1$ ns. This fine-time resolution implies we are only
corrupted by reflected paths whose additional travel distance is within $30$
cm. In indoor environments, finding such close-by reflected paths is unlikely,
and we find that our direct path and reflected signals are separable in the
time domain. With this in mind, we measure the time of arrival and phase of
the signals at the hardware reported first peak index, FPI (Qurvo, Inc.,
2016), at the 6 UWB receivers in XRLoc’s localization module.

Figure 5. Implementation: (a) Block diagram showcasing interconnections
between the $6$ UWB receivers (Qorvo, Inc., 2016), the clock synchronization
scheme (blue), “SYNC” implementation (red), and data back-haul via USB
(black). (b) real-world implementation of block diagram; inset: external
modification to UWB receiver. (c) block diagram for Tag showcasing the UWB and
LoRa radios, the interrupt line (blue) to schedule UWB transmission and LoRa
clock-sync broadcasts (dotted green) (d) real-world implementation of Tag. (e)
UWB/LoRa radio parameters.

##  5\. Enabling multi-tag operation

Through the ideas presented in Sec. 3 and 4, XRLoc fulfills the first two
requirements for a localization system to be compatible with XR applications —
ease of deployment (R1) and accuracy (R2). However, when we extend the current
system to localize multiple tags in an environment, packet collisions amongst
various tags can detrimentally affect our localization rates, resulting in a
packet drop of $25\%$. Alternative to allowing tags to transmit arbitrarily,
we can schedule individual tags at specific time intervals and leverage time-
division multiple access (TDMA) to prevent collisions.

We seek to enable a total localization rate of $1000$ Hz at XRLoc’s receiver
means localizing a $1000$ tags at a rate of $1$ Hz or $10$ tags at $100$ Hz.
Specifically, we explore leveraging low-power wireless technologies (Sanchez-
Iborra and Cano, 2016; Gupta, 2016) as a side channel for MAC protocol
operation. A MAC controller needs to perform three tasks — onboarding new
tags, providing time synchronization, and applying corrections to tags that
deviate from their time slots. Existing systems (Tiemann et al., 2019; Macoir
et al., 2018; Bauwens et al., 2021) leverage UWB signals for providing this
MAC control. However, we observe when a large number of tags need to be
onboarded or corrections to the tag’s time slots need to be made, frequent
collisions between UWB beacons for localization and UWB transmission for MAC
control can exacerbate the problem we seek to solve. Alternatively, we propose
using an additional side-channel leveraging low-power wireless technologies
(Sanchez-Iborra and Cano, 2016; Gupta, 2016) to simplify the MAC control and
allow for independent tag management and localization functions. UWB is known
to have high power consumption (e.g., about 416 mW for DW1000) during
reception due to its use of wide bandwidth and despreading processing (Biri et
al., 2020). From the viewpoint of low power reception, using LoRa (e.g., about
20 mW for SX1280) or BLE (e.g., about 16 mW for nRF52832) for the side channel
is practical. We employ LoRa as a side channel to furnish reliable and low-
power MAC control for multiple tags. LoRa and UWB are at $~{}900$ MHz and
$~{}3.5$ GHz, allowing them to co-exist with minimal interference. We also
note that alternative side channels like BLE be employed; however, we choose
to implement this prototype with LoRa given its simplicity.

The MAC protocol consists of two components — a LoRa MAC controller (gateway),
which is deployed along with the localization module we have built so far, and
a LoRa Receiver (LoRa RX) connected to the UWB tag. The gateway performs the
three core functions of the MAC protocol.

Discovery and Onboarding: New tags introduced to a system transmit beacon
packets to announce their presence. Subsequently, the gateway invites these
new tags to join the network by assigning a specific transmit time slot to
transmit the UWB localization packets. The number and duration of a transmit
slot are determined by the maximum number of tags and their localization rate.
Currently, we support $1000$ slot with a $1$ ms slot width. Fig. 5(c)
illustrates a block diagram of operation.

Global Time sync: Each tag must have a consistent notion of time slots, which
requires a global time synchronization within the accuracy of at least half
the slot width. Previous works (Ramirez et al., 2019) have showcased $\mu$s
accuracy in synchronization clocks, and we leverage these works to provide
time synchronization. Specifically, the gateway transmits time-sync packets
every $100$ s, the time it takes for the $5$ ppm clocks to drift by $500$
$\mu$s, half the slot width for each tag. The LoRa RX receives these sync
packets and corrects for its clock drift.

Correcting erroneous tags: Finally, as a precautionary measure, we develop a
correction mechanism to re-slot colliding tags. There may be a time-sync
failure at tags, resulting in transmission at an incorrect time slot, leading
to consistent collisions among groups of tags. By tracking the tags which
suffer consistent collisions, the gateway broadcasts a correction packet over
LoRa to re-slot the erroneous tag.

##  6\. Implementation

We have seen XRLoc consists of three core components — the localization
module, the LoRa MAC handler, and the UWB+LoRa tag. This section will take a
closer look at prototyping these components.

Localization Module: XRLoc’s primary contribution is a single-vantage point
localization module using off-the-shelf components with a size of $1$ m. This
small size allows the localization module to be deployed within common
electronics like TV’s our soundbars. Fig.5 shows the implemented prototype.
The prototype is built with $6$ UWB receivers EVB1000 (Qorvo, Inc., 2016),
with table 5(e) detailing the configuration parameters. We synchronize the UWB
modules to a common clock (OCXO (Crystek Corp., 2022)) via a clock distributor
module (Texas Instruments, Inc., 2017) as shown by the ‘blue’ path in Fig/
5(a). Additional to the clock modification discussed in Sec. 4.1, we expose
the EVB1000’s ‘SYNC’ pin to reset the time on the UWB modules to reduce bias
in TDoA measurements. This sync is handled by an Arduino Due and is indicated
in the ‘red’ path, with additional details provided in (Qurvo, Inc., 2014).
When each EVB1000 receives a single “blink” signal for localization from the
UWB Tag, the receiver reports the first-peak-index (FPI) of the direct path in
the channel impulse response’s peak, the signal phase at this point, time of
arrival (RXTIME), and a carrier phase correction (RCPHASE) via the data path
(shown in black).

LoRa MAC gateway: The LoRa gateway is the central controller to initialize,
discover, and onboard all the tags in the environment. It is prototyped with a
LoRa SX1272 (Semtech Corp., 2022) transmitter. This handler maintains the MAC
state machine and performs all the functions described in Sec. 5.

Tags: We prototype the tag (shown in Fig. 5(d)) using the EVB1000 (Qorvo,
Inc., 2016) and program it with the parameters in Table 5(e). The tag
transmits ‘blink’ packets at $60$ Hz, with each transmitted frame having 14
bytes of payload, including packet number and MAC address, to facilitate and
test the MAC protocol. Operating in parallel, we have the LoRa SX1272
receiving time-sync packets from the Gateway module maintaining the UWB
transmit slots and providing medium access control. An interrupt pin is raised
by LoRa RX (shown in blue in Fig. 5(d)) to initiate a UWB ‘blink’ transmission
at the accurate time slot.

##  7\. Evaluation

Figure 6. Evaluated in three spaces referred to as (a) Env-1: office-like, (b)
Env-2: large-scale, and (c) Env-3: Non-line-of-sight condition. The tag,
XRLoc’s module, and relevant regions are marked.

XRLoc takes strides in achieving a few cm-scale localization in static and
dynamic conditions. We rigorously test the system over eight different moving
datasets and at multiple static points in various environments, including
line-of-sight (LOS at Env-1 and 2) and non-line-of-sight (NLOS at Env-3)
conditions as shown in Fig. 6. To make the NLOS condition in Env-3, a wooden
board 2.5 cm thick was placed 30 cm forward from the XRLoc anchor.
Additionally, we re-implement state-of-art AoA-based UWB localization system
ULoc (Zhao et al., 2021) based on their open-source documentation. We place
$3$ anchors in a diverse scenario, as a triangle in this space, and a
constrained linear scenario, in a $1$ m straight line. We test ULoc with the
same static and dynamic positions.

(a)

(b)

Figure 7. XRLoc’s Localization performance. (a) Static localization error, (b)
localization accuracy vs. range with LOS (Env-2) and NLOS (Env-3) conditions.

(a)

(b)

(c)

(d)

Figure 8. Dynamic testing scenario: (a, b) Scatter plot of XRLoc’s predictions
(EST), ground truth (GND), and antenna locations (ANT). More examples can be
found in demo video${}^{\ref{fn:demo}}$. (c) CDF of errors compared to AoA-
based localization when three anchors (Zhao et al., 2021) are placed diversely
around the room (AoA-D) and constrained to a $1$ m single line (AoA-L). (d)
time-series errors of movement in (b), with the inset showcasing particle
filter convergence within five packets.

###  7.1. Static Localization Accuracy

One of the key use cases targeted in XRLoc is to provide accurate locations of
real-world objects and place them in the virtual realm. These objects of
interest could be tagged with inexpensive and long-lasting UWB tags, which
will relay their location to the VR system. To simulate this use case, we
place multiple tags in the environment with the simple goal of recreating a
life-size chess game. In this static scenario, from Fig. 7(a), we observe a
median and $90^{\mathrm{th}}$ percentile error of $1.5$ cm and $5.5$ cm,
respectively. We additionally observe XRLoc provides a $9.5\times$ and
$4.0\times$ improvement at the median over using ULoc in a linear (AoA-L) and
diverse (AoA-D) placement scenario which have (median, $90^{\mathrm{th}}\%$)
of (14.6 cm, 28.7 cm) and (6.1 cm, 13.7 cm), respectively. The evaluation of
different ranges shows median errors of 6.8 cm and 15.2 cm at 4m and 5 m in
the LOS condition, respectively, and 35.3 cm and 34.0 cm in the NLOS condition
as shown in Fig. 7(b).

###  7.2. Moving Localization Accuracy

Continuing with the motivation of playing a life-size chess game, we
characterize XRLoc’s localization accuracy in dynamic scenarios. Fig. 8(a) and
8(b) showcase two characteristic movement patterns we tested. We tested $8$
movements, as shown in the demo video${}^{\ref{fn:demo}}$, and achieved median
and $90^{\mathrm{th}}$ errors of 2.4 cm and 5.3 cm, respectively, as shown in
Fig. 8(c). We observe an $11\times$ and $3.2\times$ improvement at median over
using ULoc in a linear (AoA-L) and diverse (AoA-D) placement scenario, which
have (median, $90^{\mathrm{th}}\%$) of (26.0, 43.3 cm) and (7.5 cm, 17.4 cm),
respectively.

In Fig. 8(d), we show the time-series error of localization for the ‘Fig.
8(b)’ movement scenario (Fig. 8(c)). We note that opting to use a particle
filter over a brute force approach provides a localization latency of $~{}1$
ms, compared to exhaustive grid search’s latency of $~{}61.2$ s on a 12 Core
CPU as explained in Sec. 3.3. However, because the particle filter performs a
sparse sampling over the entire space, XRLoc may initialize the tag’s location
incorrectly. This is visible in the inset shown in Fig. 8(d). But, throughout
$5$ received packets, we can see the location converges to the true location,
and XRLoc subsequently provides accurate location predictions.

(a)

(b)

Figure 9. MAC protocol performance: (a) Packet success ratio across ten tags
with (blue) and without (red) mac protocol. (b) packet success ratio over time
for Tag 2 (best performing without MAC) and Tag 9 (worst performing without
MAC). In all cases, MAC protocol provides a success rate of over $99.5\%$.

###  7.3. MAC Protocol Efficacy

In the previous sections, we have shown XRLoc can achieve a few-cm level
localization from a single localization module, meeting the first two
requirements (R1 and R2). To allow multiple tags to be localized with this
accuracy, XRLoc leverages a LoRa side-channel to develop a power-efficient MAC
protocol as described in Sec. 5. To evaluate its efficacy, we set up $10$ tags
to transmit at $100$ Hz for a half-hour period. Fig. 9(a) showcases the packet
success ratio, and we find over $99.5\%$ of the packets are received by
XRLoc’s localization module. Alternatively, when we do not have a MAC
protocol, we have an average success rate of $~{}76\%$, ranging between
$56\%-87\%$. Specifically, considering the best and worst tag, we plot the
packet arrival rate in Fig. 9(b) over the $30$ min period and observe there
are large periods when packets from Tag 09 are not received, likely due to
collision from either Tag 02 or any of the other tags in the environment.
Alternatively, we see a consistent packet arrival rate using a MAC protocol.
Clearly, a MAC protocol is necessary to achieve multi-tag tracking and
localization at high rates and fulfill R3.

(a) TDoA/PDoA

(b) Aperture

(c) # of antennas

(d) Antenna patterns

Figure 10. Microbenchmarks: (a) Using TDoA or PDoA only as opposed to a fusion
(XRLoc). (b) Reducing aperture from $1$ m (XRLoc). (c) Reducing the number of
antennas while keeping the aperture at $1$ m. (d) Leveraging co-prime antenna
array as opposed to uniform linear array (ULA).

###  7.4. Justifying design choices

The evaluations from the previous sections prove XRLoc’s ability to fulfill
the stringent requirements set for Sec. 1. In the following section, we will
answer key questions about the design choices made when developing XRLoc.

TDoA and PDoA are both needed?: As we have discussed, a system relying purely
on time-based measurements will not meet the stringent requirements of few-cm
localization accuracy. We further evaluate this on our datasets in Fig. 10(a).
We see a median localization accuracy of 2.4 cm, deviating over an order of
magnitude from our few-cm level accuracy requirement. This re-iterates the
challenge of achieving single-vantage point localization.

However, we claimed in Sec. 3.2 TDoA measurements play an important role in
ruling out ambiguous initialization caused by PDoA-only localization. To
confirm this, we see in the same figure when PDoA is solely used for
localization, and we have a median accuracy of 49.1 cm. Clearly, ambiguities
from phase wrap-around can be detrimental to XRLoc’s performance, emphasizing
TDoA’s role. Through this micro-benchmark, it is apparent TDoA and PDoA work
hand-in-hand to provide few-cm location accuracy.

How does the aperture effect the localization?: In Sec. 3.1, we discussed the
importance of the antenna aperture in bringing resilience to phase measurement
error. Consequently, a wider distance between the first and last antenna helps
to improve localization accuracy. To ensure easy integration within everyday
consumer electronics (like TVs or soundbars), we restrict XRLoc’s size to less
than $1$ m wide. However, how important is antenna aperture to our
localization performance? For this, we reduce the maximum antenna aperture to
$80$, $60$, and $40$ cm and report the results in Fig. 10(b). Clearly, a
reduction in the aperture size affects the localization accuracy, with median
localization accuracy reducing to 9.6, 19.3, and 35.0 cm, respectively. In
fact, we see a steep drop-off in accuracy when we have an aperture of $40$ cm.
Furthermore, we see that a minimum aperture of $1$ m is required to achieve
the required localization accuracy. Under space constraints, smaller apertures
may be used at the cost of lower accuracy.

How many antennas are needed?: Clearly, a minimum aperture of $1$ m is needed.
However, within this aperture, how many antennas are needed to meet the
localization requirements? This is an important question to consider to make
XRLoc cost-effective. In the previous localization accuracy analysis, we
consider an array with 6 antennas. In Fig. 10(c), we reduce the number of
antennas placed within the $1$ m aperture. For 6, 5, and 4 antennas, we see
the median location accuracy of 4.7, 6.9, and 28.7 cm, respectively. As few as
4 antennas are enough to meet the required few-cm localization accuracy at the
median. Although, we observe a sharp reduction in localization accuracy in the
$90^{\mathrm{th}}$ percentile. More antennas provide a better averaging effect
and reduce erroneous TDoA and PDoA measurements, hence improving the
localization performance at higher percentiles. From these experiments, we
empirically observe choosing at least $6$ antennas meets the required few-cm
level accuracy required for XR applications.

Are there better antenna spacing we can choose?: So far, we have considered
placing our antennas in a uniform linear array (ULA), separated by $20$ cm.
However, many works (Vaidyanathan and Pal, 2010; Wang et al., 2014) showcase
antenna patterns that are more optimal than a ULA. To investigate the
improvements from these co-prime antenna arrays, we leverage our simulator
from Sec. 2 to carry out extensive simulations and showcase the results in
Fig. 10(d). We see slight degradation of error when using co-prime arrays.
However, co-prime arrays can be levered to reduce the number of antennas
required by XRLoc to achieve similar location accuracy.

(a)

(b)

Figure 11. (a) Localization error with and without bias calibration; (b)
measured PDoA and TDoA errors.

Why do we need fine-grained bias compensation?: Finally, we evaluate the
system-level measurements. In XRLoc, we choose the appropriate clock sources
to achieve the required accuracy in both TDoA and PDoA measurements (Sec. 4.1)
and additionally calibrate for TDoA and PDoA hardware biases via a 3-point
calibration scheme (Sec. 4.2). In Fig. 11(a), we showcase the importance of
this bias calibration, observing median localization accuracy degrade by
$1.8\times$ to a median accuracy of 2.4 cm without applying appropriate bias
calibration. In Fig. 11(b), we also observe an average TDoA error of $180.7$
ps and PDoA error of $8.2^{\circ}$.

##  8\. Related Works

Providing indoor location information for people and various in-animate
objects is a well-studied problem. This section will broadly cover various
techniques leveraged to address this problem. We will find that none of the
existing techniques meets the stringent requirements we set up earlier in Sec.
1. Recall that we seek to provide easy-to-deploy (R1), few-cm accurate
localization (R2) in dynamic scenarios for multiple people or objects of
interest (R3). A few key technologies which can be considered are:

Visual sensing: Under this broad umbrella, we have many distinct technologies.
Existing VR systems utilize external IR-based sensors (Borges et al., 2018) or
specialized cameras (Vicon Motion Systems Ltd, 2021) to furnish accurate
ground truth locations. There are also works that deploy a single Lidar (Hasan
et al., 2022) for person tracking or utilize headset-mounted cameras (Monica
and Aleotti, 2022). However, these systems are sensitive to visual occlusions,
hindering a user experience. Recent works (Zhong et al., 2021; Sahin and Itti,
2023; Luo et al., 2022) which leverage machine learning to track objects
despite occlusions. Alternatively, other studies (Guo et al., 2022; Li et al.,
2020c; Xie et al., 2020; Yan et al., 2021; Wang et al., 2023) seek to deploy
multiple cameras, let tag equips with a camera, or utilize special light
sources to be robust to occlusions. However, no studies have simultaneously
solved all the problems of ease of anchor deployment (R1), accuracy (R2), and
the risk of security and privacy (Vigdor, 2019). Moving away from deploying
privacy-invasive cameras, other works (Miller et al., 2022) seek to use the
cameras on-board VR setups fused with occlusion-resilient radio-frequency (RF)
signals like ultra-wideband. These systems have a low deployment cost but do
not achieve a few-cm level accuracy.

Acoustic sensing: Alternative to these systems, various acoustic localization
systems (Famili et al., 2022; Merenda et al., 2022; Murakami et al., 2019; Cao
et al., 2020; Li et al., 2020a; Wang et al., 2020) take advantage of the lower
speed of sound ( $340$ m/s) for fine-grained localization and meet the
required localization accuracy. However, acoustic sensing has a few
fundamental drawbacks (Li et al., 2022). First, acoustic systems (Liu et al.,
2020) are difficult to provide both multi-asset and low latency localization
simultaneously because of narrow bandwidth, deviating from R3. Second, they
hinder music and audio playback, precluding immersive XR applications. Third,
acoustic signals that employ ultrasound (¿ $20$ kHz) for sensing have
considerable audio leakage in the audible frequency range, affecting user
experience.

Radar-based sensing: Mm-wave radars near the $60$ GHz and $77$ GHz bands have
gained recent interest. Many works (Xue et al., 2021; Kong et al., 2022) have
looked at furnishing human pose with these radars from a single radar. Recent
work (Mukherjee et al., 2022) has shown that the human body can act as a
strong blockage at these frequencies. These blockages can hinder tracking
multiple people and objects in an environment and affect user experience.
Additionally, tracking and identifying smaller assets in an environment can be
challenging as radar reflections depend on an object’s radar cross-sectional
area (RCS). Alternatively, many works (Soltanaghaei et al., 2021) propose
placing retro-reflective tags on objects with small RCS to guarantee their
detection; however, these systems suffer from poor localization accuracy.

RF-based sensing: The robustness of sub-6 GHz RF-signals to occlusions (Slezak
and Rangan, 2022) and low privacy risk makes it a promising technology to
consider. The common mode of operation is for multiple RF radios to jointly
localize an active RF transmitter or a passive RF reflector (tags). Many works
have looked at leveraging WiFi (Mostafa et al., 2022; Kotaru et al., 2015;
Xiong and Jamieson, 2013; Vasisht et al., 2016), LoRa (Islam et al., 2019), or
BLE (Ayyalasomayajula et al., 2018) to achieve robust user localization.
However, these systems fail to provide the required localization accuracy due
to bandwidth limitations.

RFID has a strong asymmetry in the reader-tag relationship, and the
transmitter and receiver share the same clock, which allows for highly
accurate phase acquisition. According to (Shangguan and Jamieson, 2016; Yang
et al., 2014; Luo et al., 2019), RFID systems do not have carrier and sampling
frequency offset and enjoy a phase measurement accuracy of $0.085^{\circ}$
(Yang et al., 2014), 15$\times$ better than the UWB, which provides an
accuracy of $1.4^{\circ}$. Using the highly accurate phase, (Yang et al.,
2014; Luo et al., 2019; Wang et al., 2014; Ma et al., 2017; Jiang et al.,
2018) has succeeded with tracking or localization at the few cm levels.
However, due to the asymmetric nature, RFID readers whose range is several
meters are not suitable for embedding into consumer electronics (R1) because
of their power-hungriness and expensiveness (ex. ImpinjJ Speedway R420 costs
$1666). The main target of RFID is industrial or retail store settings where
thousands of tags must be deployed inexpensively, and readers’ one-time cost
is justifiable. For instance, (Shangguan and Jamieson, 2016) looks at item
ordering in manufacturing lines, retail stores, or libraries. (Yang et al.,
2014; Luo et al., 2019) examine industrial robotics or baggage handling tasks.

Unlike RFID, Ultra-wideband provides a more symmetric architecture where
localization modules can cost $\$10-100$. Consequently, we have seen their
increased adoption in smartphones and smart tags. It provides over $500$ MHz
of bandwidth and a time resolution of $1$ ns, providing localization accuracy
to a few tens of centimeters. Many current UWB-localization schemes leverage
the accurate time-resolution for Two-Way Ranging (TWR) (Zwirello et al., 2012;
Ledergerber and D’Andrea, 2019; García et al., 2015; Alarifi et al., 2016;
Bonnin-Pascual and Ortiz, 2019; Kempke et al., 2016; Poulose et al., 2020;
Gowda et al., 2017) and localize objects via trilateration. However, these
multiple-packet exchanges increase localization latency and prevent real-time
tracking of multiple objects of interest (R3). Many works instead leverage the
TDoA or PDoA of the UWB signal to multiple time-synchronized anchors (Chen et
al., 2020; Vecchia et al., 2019; Tiemann et al., 2016; Gro$\beta$windhager et
al., 2019; Cao et al., 2021), or AoA measurements (Zhao et al., 2021;
Heydariaan et al., 2020; Dotlic et al., 2017) at multiple anchors to furnish
locations using a single packet. Some works (Yang et al., 2022) employ
alternative transmission schemes to TWR to reduce the packet overhead.
However, these systems only meet the necessary localization accuracy when the
UWB anchors are placed in diverse locations, increasing deployment efforts and
deviating from R1.

As discussed in Sec. 2, few-cm accurate localization is challenging due to
geometric dilution of precision. To circumvent this problem, three common
techniques are leveraged. First, by leveraging reflected paths in the
environment, many systems (Kotaru and Katti, 2017; Chen et al., 2019; Li et
al., 2020b; Zhang et al., 2022; Soltanaghaei et al., 2018; Meissner and
Witrisal, 2012; Großwindhager et al., 2018) create additional “virtual” radios
in the environment. These “virtual” radios provide the needed spatial
diversity to localize an object of interest. However, multipath is often
unreliable (Almers et al., 2006) in many environments and can lead to
localization failure and poor user experience. Second, many works (Wang et
al., 2019b; Ge and Shen, 2021; Wang et al., 2019a; Rostami and Sundaresan,
2022) look at fusing TWR, TDOA, and AoA information to provide single anchor
localization solutions. However, some systems cannot furnish the few-cm
accurate localization requirement or rely on TWR measurements, increasing the
system’s latency. Finally, some works develop switched beam antennas (Groth et
al., 2021; Giorgetti et al., 2009), which selectively sense signals
approaching the anchor from different directions. However, these systems lack
the required angular resolution to provide localization accuracy of a few cm.

##  9\. Discussion and Future work

XRLoc overcomes the fundamental challenges arising from geometric dilution of
precision to deliver cm-level accurate localization by developing an easy-to-
deploy and low-latency localization module. Through this development, we are
one step closer to achieving immersive XR experiences. However, a few
limitations and possibilities of future work can be explored to build upon
XRLoc.

Extensions to 3D: XRLoc focuses on localizing people and assets on a 2D floor
plane, which is required in various XR applications. However, these ideas can
be extended to the 3D domain by incorporating a vertical array of antennas in
conjunction with the current horizontal linear array. These 3D-compliant
antenna arrays can be retrofitted with television screens or paintings to
allow cm-accurate 3D localization.

Improving power efficiency of XRLoc’s localization module: Various works (Biri
et al., 2020) have noted the $10\times$ higher power consumption of UWB
reception than transmission. Keeping this in mind, we designed a system that
requires only a single transmission from the tag for localization to ensure
long battery life. However, the $6$ receivers on XRLoc’s wall-powered
localization module are power inefficient. To rectify this, antenna switching
schemes (Gu et al., 2021) can be employed, or multiple antennas can be
combined to connect to a single receiver (Cao et al., 2021) to reduce the
number of receivers. However, unlike XRLoc’s system, these alternatives will
not be FiRa compliant (Coppens et al., 2022).

Miniaturized tag design:  We prototype our tag from off-the-shelf EVB1000
(Qorvo, Inc., 2016) and LoRa (Semtech Corp., 2022) evaluation boards. Future
work can look towards miniaturizing these tag designs. Since these radios we
employ are centered at 3.4 GHz and 930 MHz, it allows us to place these radio
modules in close proximity with limited RF interference.

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