Citation: Grasso, P.; Innocente, M.S.;
Tai, J.J.; Haas, O.; Dizqah, A.M.
Analysis and Accuracy Improvement
of UWB-TDoA-Based Indoor
Positioning System. Sensors 2022, 22,
9136. https://doi.org/10.3390/
s22239136
Academic Editor: Andrzej Stateczny
Received: 31 October 2022
Accepted: 18 November 2022
Published: 24 November 2022
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Article
Analysis and Accuracy Improvement of UWB-TDoA-Based
Indoor Positioning System
Paolo Grasso
1
, Mauro S. Innocente
1,
* , Jun Jet Tai
1
, Olivier Haas
2
and Arash M. Dizqah
3
1
Autonomous Vehicles & Artificial Intelligence Laboratory (AVAILAB), Centre for Future Transport and Cities,
7th Floor Friars House, Manor House Drive, Coventry CV1 2TE, UK
2
Centre for Future Transport and Cities, 7th Floor Friars House, Manor House Drive, Coventry CV1 2TE, UK
3
Smart Vehicles Control Laboratory (SVeCLab), University of Sussex, Brighton BN1 9RH, UK
* Correspondence: mauro.s.innocente@coventry.ac.uk
Abstract:
Positioning systems are used in a wide range of applications which require determining
the position of an object in space, such as locating and tracking assets, people and goods; assisting
navigation systems; and mapping. Indoor Positioning Systems (IPSs) are used where satellite and
other outdoor positioning technologies lack precision or fail. Ultra-WideBand (UWB) technology is
especially suitable for an IPS, as it operates under high data transfer rates over short distances and at
low power densities, although signals tend to be disrupted by various objects. This paper presents
a comprehensive study of the precision, failure, and accuracy of 2D IPSs based on UWB technology
and a pseudo-range multilateration algorithm using Time Difference of Arrival (TDoA) signals. As
a case study, the positioning of a 4
×
4
m
2
area, four anchors (transceivers), and one tag (receiver)
are considered using bitcraze’s Loco Positioning System. A Cramér–Rao Lower Bound analysis
identifies the convex hull of the anchors as the region with highest precision, taking into account the
anisotropic radiation pattern of the anchors’ antennas as opposed to ideal signal distributions, while
bifurcation envelopes containing the anchors are defined to bound the regions in which the IPS is
predicted to fail. This allows the formulation of a so-called flyable area, defined as the intersection
between the convex hull and the region outside the bifurcation envelopes. Finally, the static bias is
measured after applying a built-in Extended Kalman Filter (EKF) and mapped using a Radial Basis
Function Network (RBFN). A debiasing filter is then developed to improve the accuracy. Findings and
developments are experimentally validated, with the IPS observed to fail near the anchors, precision
around
±
3
cm
, and accuracy improved by about 15
cm
for static and 5
cm
for dynamic measurements,
on average.
Keywords:
IPS; ultra-wideband; time difference of arrival; Cramér–Rao lower bound; CRLB; bifurcation
curve; debiasing; filtering
1. Introduction
Positioning that is accurate and precise as well as robust and reliable has become an
essential part of many applications which require determining the position of an object in
space, such as monitoring the location of assets, people, and goods and assisting navigation
systems with varying degrees of autonomy while operating within potentially complex
and dynamic environments [1,2]
A variety of positioning systems exist which make use of different (i) technologies,
(ii) signal properties, and (iii) positioning algorithms. Technologies include inertial navigation
systems (INS) [
3
,
4
], sound waves [
5
,
6
], infrared [
7
], visible light [
8
], and radio frequency,
including Ultra-Wide Band (UWB) [
9
], Bluetooth [
10
], Bluetooth Low Energy (BLE) [
11
],
ZigBee, Wireless Local Area Network (WLAN) [
12
,
13
], and Wireless Underground Sensor
Network [
14
]. Signal properties used for positioning include Angle of Arrival (AoA) [
7
],
Time of Arrival (ToA) [
14
], Time Difference of Arrival (TDoA), Received Signal Strength
Sensors 2022, 22, 9136. https://doi.org/10.3390/s22239136 https://www.mdpi.com/journal/sensors
