=Paper=
{{Paper
|id=Vol-2498/short1
|storemode=property
|title=Fusion of time of arrival and time difference of arrival for ultra-wideband indoor localization
|pdfUrl=https://ceur-ws.org/Vol-2498/short1.pdf
|volume=Vol-2498
|authors=Juri Sidorenko,Volker Schatz,Norbert Scherer-Negenborn,Michael Arens,Urs Hugentobler
|dblpUrl=https://dblp.org/rec/conf/ipin/SidorenkoSSAH19
}}
==Fusion of time of arrival and time difference of arrival for ultra-wideband indoor localization==
https://ceur-ws.org/Vol-2498/short1.pdf
Fusion of time of arrival and time difference of
arrival for ultra-wideband indoor localization?
Juri Sidorenko1,2[0000−0003−0089−967X] , Volker Schatz1 , Norbert
Scherer-Negenborn1 , Michael Arens1 , and Urs Hugentobler2
1
Fraunhofer Institute of Optronics, System Technologies and Image Exploitation
IOSB, Germany juri.sidorenko@iosb.fraunhofer.de
2
Institute of Astronomical and Physical Geodesy, Technical University of Munich,
Germany
Abstract. This article presents a time of arrival and time difference of
arrival fusion for Decawave ultra-wideband transceivers. The presented
techniques combine the time-of-arrival and time-difference-of-arrival mea-
surements without losing the advantages of each approach. The precision
and accuracy of the distances measured by the Decawave devices depends
on three effects: signal power, clock drift, and uncertainty in the hard-
ware delay. This article shows how all three effects may be compensated
with both measurement techniques.
Keywords: Time Of Arrival · Time Difference Of Arrival · Two-Way
Ranging.
1 Introduction
Localization systems have become indispensable for everyday life. Satellite nav-
igation[1, 2] has displaced paper maps and is now essential for the autonomous
operation of cars and airplanes. As the requirements of logistics and manufac-
turing processes increase, access to precise positional information is becoming
a necessity. Depending on the operating conditions for the localization applica-
tion, different measurement principles [3–5] and techniques [6–8] are available.
Two of the most common measurement techniques are based on the time of ar-
rival (TOA) [6] and the time difference of arrival (TDOA) [7]. The measuring
equipment is just as important as the measurement technique itself. This article
focuses on indoor radio frequency (RF)-based localization systems. In general,
indoor positioning applications are a challenge for RF-based localization systems.
Reflections can generate interference with the main signal and lead to fading.
Compared to narrowband signals, ultra-wideband (UWB) signals are more ro-
bust against fading [9, 10]. The Decawave transceiver [11] uses ultra-wideband
(UWB) technology and is compliant with the IEEE802.15.4-2011 standard [12].
It supports six frequency bands with center frequencies from 3.5 GHz to 6.5 GHz
and data rates of up to 6.8 Mb/s. Depending on the selected center frequency, the
?
Fraunhofer Institute of Optronics, System Technologies and Image Exploitation.
2 Juri Sidorenko et al.
bandwidth ranges from 500 to 1000 MHz. Various methods for wireless TDOA
clock synchronization are presented in [13–15]. One aspect shared by all of them
is that they use a fixed and known time interval for the synchronization sig-
nal. In our case, the synchronization signal is part of the localization and the
time interval does not need to be known. The solution presented here merges
TOA and TDOA measurements to increase the number of equations without los-
ing the specific advantages of each method. The measurements are provided by
Decawave EVK1000 transceivers without additional synchronization hardware.
This system can operate in indoor environments due to its ability to deal with
fading. The precision and accuracy of the Decawave UWB depend primarily on
three factors: the received signal power, the clock drift, and the hardware de-
lay. In [16], we showed how the signal power correction curve can be obtained
automatically and how the clock drift can be corrected in every measurement.
In the present publication, we demonstrate how to apply these corrections for
TOA and TDOA localization.
2 Time of arrival
Figure 1 illustrates the concept of TWR and the timestamp shift caused by signal
power, as well as the error due to hardware delay. In our implementation, the
reference station is the initiator. The first message is sent by the reference station
with timestamp T1R . The timestamp of the received message at the tag is affected
by the signal power, resulting in a timestamp shift of E1 . The same applies to
the response message, this time at the reference station. It is important to note
that the timestamps T1R and T2T are not affected by the receiving signal power.
However, the hardware delay (A,B) must always be considered. The sending
delay is assumed to be equal to the receiving delay. Without
correction, the
TWR signal travel time is 0.5· T2R − T1R − T2T − T1T .
TR1 TR2 TR1 TR2
E2 A A
Reference station Reference station
TOA TOA TOA TOA
Tag Tag
E1 B B
TT1 TT2 TT1 T T2
Fig. 1. Left: Effect of the power on the TOA, Right: Effect of the hardware delay on
TOA
Title Suppressed Due to Excessive Length 3
The values E1 and E2 are deduced from the signal power correction curve.
Note that the signal power may affect the tag and the reference station differ-
R
ently. At lower signal power, the time difference ∆T1,2 increases.
In the previous section, we showed that the clock drift can be corrected by
three messages. Figure 2 demonstrates how this principle can be adapted for
two-way ranging. The last message is used to calculate the clock drift error
RT R T
C1,3 = ∆T1,3 − ∆T1,3 . Observe that the signal power E1 does not affect the
T
timestamp difference ∆T1,3 .
TR1 TR2 TR3
E2
Reference station
TOA TOA Clock drift correction TOA
Tag
E1 E1
TT1 TT2 TT3
Fig. 2. TWR clock drift correction
3 Time difference of arrival
The previous section showed how the clock drift and the hardware offset influence
the time-of-arrival position estimate. In this section, we show how to combine
TOA with TDOA. Unlike TDOA, two-way ranging (TWR) based on TOA does
not require clock synchronization. One approach to synchronizing the TDOA
clock is to use an additional signal [3]. This signal is already present in the
two-way ranging (TWR) approach, so a combination of both techniques seems
natural. This principle is illustrated in figure 4. The effect of the clock drift and
the hardware delay on the TDOA can be seen in figure 3. Two-way ranging
is performed between the tag and the reference station. The other stations are
passive and do not respond to the reference station or tag. The difference between
timestamps two and one at each anchor depends on the positions of the reference
station and the tag with respect to the anchor. Unlike the TWR application
presented earlier, the influence of the signal power and the hardware delay differs
in the TDOA application.
In the TDOA application, the influence of the hardware delay is assumed to
be the same for both timestamps T1S and T2S . Therefore, the TDOA equation
4 Juri Sidorenko et al.
TOA TOA
Reference station Tag Reference station Tag
TDOA
TDOA
TS1 TS2 TS1 TS2
E3 E4 C C
Station N Station N
Fig. 3. Left: Effect of power on the TDOA, Right: Effect of the hardware offset on the
TDOA
is independent of the hardware delay. However, a new offset K appears, repre-
senting the delay between the signal of the tag with respect to the signal of the
reference station. If both stations send the signal at exactly the same time, this
offset K is zero.
4 Two-dimensional position estimation with four stations
In this section, the theoretical concepts are verified with real measurements. The
first test scenario uses TOA measurements to estimate the unknown position of
the tag. In the second test scenario is the position of the tag estimated by
the fused measurements of TDOA and TOA. The tests were carried out with a
Decawave EVB DW1000. The Decawave supports different message types, which
are specified for the discovery phase, ranging phase and final data transmission.
Depending on the update rate and the preamble length, each message can vary
from 190 s to 3.4 ms. In our experiments, we only used 190 s messages, also called
blink messages. The general settings of the Decawave transceivers are listed in
table 1.
Table 1. Test settings
Channel 2
Center Frequency 3993.6 MHz
Bandwidth 499.2 MHz
Pulse repetition frequency 64 MHz
Preamble length 128
Data rate 6.81 Mbps
Figure 5 and table 2 show the constellation of the stations. The ground
truth data were obtained by laser distance measurement. The position of the
Title Suppressed Due to Excessive Length 5
TR1 TR2 TR3
E2
Reference station
2. 3.
Clock drift correction
1.
TS1 TS2 TS3
1.
E3 E4 E3
Station N
2. 3.
Clock drift correction
Tag
E1 E1
TT1 TT2 TT3
Fig. 4. TOA and TDOA clock drift correction
tag with identification number (ID) 2 is assumed to be unknown. The other
stations are used to estimate the position of this tag. The station identified
as the reference station changes during TWR positioning. This is because the
distances between the tag and the other stations must be calculated successively
for TWR trilateration. Unlike TWR, the reference station remains the same for
TDOA; in this example, the reference station is the station with ID 1. This also
explains why TDOA is much faster than TWR.
Table 2. Position of the stations obtained by laser distance measurements
Station ID X-Axis [m] Y-Axis [m]
1 0 0
2 0 1.5134
3 1.27 1.643
4 1.1439 0.0385
Figure 6 shows the results of the TOA and TDOA position estimate of station
2. The mean values of TOA and TDOA differ by 0.0023 m on the x-axis and
0.0006 m on the y-axis. This difference is small, indicating that the assumptions
regarding the offset and the clock drift are correct. The deviation between the
mean values of the TOA and TDOA measurements and the ground truth data
may be explained by uncertainty in the hardware delay and the ground truth
data estimate.
6 Juri Sidorenko et al.
Fig. 5. Constellation of the stations
The following table 4 shows the standard deviation of the precision of the
TOA and TDOA position estimates. The y-axis scattering is almost exactly equal
for both measurement techniques. On the other hand, the x-axis scattering of
TDOA is higher than that of TOA, depicted in Table 3.
Table 3. Covariance matrix of the TOA and fused TDOA measurements in m2
0.0023 0.0001 0.0003 0.0001
Cov (T DOA) = Cov(T OA) =
0.0001 0.0007 0.0001 0.0006
This effect is due to the asymmetry of the TDOA, which is actually a fusion
of TWR and TDOA. An alternative reference station would change the distri-
bution. The compensation of this effect is described in a previous publication
[?]. When combined with a filter, highly accurate results can be obtained. The
position of the anchors affects the tag localization; better results are obtained
with tags that are more centered with respect to the anchors [?].
Table 4. Precision: Standard Deviation in m
TOA TDOA
X-axis [m] 0.0175 0.0479
Y-axis [m] 0.0249 0.0256
Title Suppressed Due to Excessive Length 7
1.65 TDOA
TOA
1.6
Y-Axis [m]
1.55
1.5
1.45
-0.1 -0.05 0 0.05 0.1 0.15
X-Axis [m]
Fig. 6. X/Y positions of the TOA and TDOA fused with TOA position estimates
The accuracy depends on the true position of the anchors and the offset
estimate. This topic will be explained in detail in an upcoming publication.
5 Conclusion
This paper introduces a method for TOA and TDOA fusion for Decawave ultra-
wideband transceivers, which is able to use clock drift correction and the power
correction curve. We showed how wireless clock calibration can be performed for
the time difference of arrival using an additional station. The corrected time of
arrival and time difference of arrival measurements were combined to increase
the number of equations for the time difference of arrival position estimate.
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