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Performance Evaluation of UWB Active-Passive
Two-Way Ranging Distance Estimation Matrix
Weighting Methods
Taavi Laadung
1,2,∗
,Sander Ulp
2
,Muhammad Mahtab Alam
1
and Yannick Le Moullec
1
1Tallinn University of Technology, Ehitajate tee 5, Tallinn, 19086, Estonia
2Eliko Tehnoloogia Arenduskeskus OÜ, Aiandi 13/1, Tallinn, 12918, Estonia
Abstract
This paper explores least squares (LS), median (MED), inverse distance weighting (IDW), distance
weighted estimator (DWE) and three dierent weighted least squares (WLS) methods for Ultra-Wideband
(UWB) active-passive two-way ranging (AP-TWR) measurement matrix estimation. The proposed
methods were tested with practical experiments in line-of-sight (LOS) and two dierent non-line-of-
sight (NLOS) conditions, and were benchmarked against an active-only single-sided two-way ranging
(SS-TWR) method.
The results show that the proposed methods MED, IDW and DWE achieve comparable standard
deviation values, while outperforming the root-mean-squared-error (RMSE) of SS-TWR ranging by up to
14.3% in LOS and 19.08% in NLOS conditions. The experiments validate that the MED, IDW and DWE
methods for AP-TWR are NLOS-robust and achieve better RMSE performance than active-only SS-TWR
ranging.
Keywords
Active-Passive Two-Way Ranging, Ultra Wideband, Line-of-Sight, Non-Line-of-Sight
1. Introduction
During recent years, Ultra-Wideband (UWB) technology based positioning has been considered
as an attractive and one of the most promising method to provide various location-based services.
The increased interest for UWB can be explained by various traits that it oers: in addition to
positioning, it can be also be used for data transfer, it provides high robustness to multipath, it
does not strictly require line-of-sight (LOS) conditions, and it provides high accuracy in the
order of centimeters [1].
Typically, UWB positioning is based on exploiting the propagation time of radio frequency
signals due to the usage of temporally very short pulses. The main time-based methods are Time
of Flight (ToF), which estimates the propagation time between two nodes, and time dierence
IPIN 2022 WiP Proceedings, September 5 - 7, 2022, Beijing, China
∗Corresponding author.
taavi.laadung@taltech.ee (T. Laadung); sander.ulp@eliko.ee (S. Ulp); muhammad.alam@taltech.ee (M. M. Alam);
yannick.lemoullec@taltech.ee (Y. Le Moullec)
0000-0002-7909-5385 (T. Laadung); 0000-0002-3497-4204 (S. Ulp); 0000-0002-1055-7959 (M. M. Alam);
0000-0003-4667-621X (Y. Le Moullec)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
of arrival (TDoA), which estimates the dierences of arrival time of a signal between multiple
nodes [2].
TDoA oers an air time advantage, where only a single packet per position estimate is needed,
which decreases the overall energy consumption of the system and could theoretically support
a high device density in the service area. The main disadvantage of TDoA is that the anchors of
a system need to be synchronized very accurately, adding to the complexity of the system. Time
of ight (ToF) estimates are typically achieved via two-way ranging (TWR) methods, which
remove the need for tightly synchronized anchors at the expense of additional air time. This in
turn increases the energy consumption and lowers the tag density in the service area [3].
In order to overcome the shortcomings of both methods, a compromise is found by using
passive anchor nodes to assist in the positioning process. The estimates supplied by passive
nodes allow to reduce the number of packets a system has to transmit in a TWR sequence,
eectively allowing to reduce the energy consumption and increase the air time eciency, while
still beneting from the relaxed anchor synchronization requirement.
For example, Hepp et al. in [
4
] provide an anchor-initiated active-passive ranging protocol,
mounted on a quadcopter. Horváth et al. proposed another passive ranging method used in
conjunction with double-sided (DS) TWR with an alternative calculation method for increased
robustness [5]. These methods have been more focused on increasing the air time eciency.
Although the seminal concept of tag-initiated Active-Passive Two-Way Ranging (AP-TWR)
was published in [
6
], the concept of generalized tag-initiated AP-TWR was introduced in [
7
].
This method was further expanded in [
8
] to include an additional passive ranging method and
assess the performance of AP-TWR in conjunction with dierent active ranging methods.
The main idea of AP-TWR is to employ a priori information about anchor locations to calculate
extra passive range estimates in addition to standard TWR estimates, without any additional
impact on the air time. When maximum air time eciency is not critical, the system can be
scaled such that multiple active anchors are used, so the ranging performance can be increased.
The achieved range estimates can then be arranged in a measurement matrix, which holds all the
ranging data for a single ranging sequence. The previous papers have only utilized averaging
of the measurement matrix rows to provide nal range estimates, without looking into other
methods. Additionally, the experiments were exclusively in line-of-sight (LOS) propagation
conditions [7,8].
In this paper we investigate methods to further improve AP-TWR range estimation via the
manipulation of the resulting measurement matrix. These methods are then compared in various
locations, in LOS and two separate non-line-of-sight (NLOS) propagation conditions. The rest of
this paper is structured as follows: in Section 2we give the theoretical background for AP-TWR,
Section 3lists the estimation methods to process the measurement matrix, Section 4provides
information on the experimental test setup, Section 5presents the experimental results and the
analysis; nally, the conclusions are drawn.
2. AP-TWR
AP-TWR denes two types of anchors, active-passive and passive-only, the former taking
part of the ranging via standard TWR methods and listening to other transmissions while
not transmitting. The second type of anchors only listen to ongoing transmissions in the air,
providing range estimates without actively partaking in them.
The work in [
8
] dened separate AP1-TWR and AP2-TWR methods, where the results showed
that AP2-TWR is the better performing method. Therefore, in the scope of this paper we will
be focusing on this method, while calling it just AP-TWR in order to avoid confusion.
The UWB ranging protocol is pictured in Fig. 1, where tag T initiates a ranging sequence by
starting its internal timer and transmitting an UWB frame to active anchor Ai, which starts its
timer and responds aer its processing time
𝐴𝑖,𝑇
. Upon receiving Ai’s reply, T sends out a nal
UWB frame aer its processing time
𝑇 ,𝐴𝑖′
. Passive anchor Aj listens in on all the transmissions
during the ranging sequence and records the corresponding times.
All the relevant time intervals for AP-TWR are described in more detail aer the introduction
of
(1)
. As per Fig. 1and [
8
], the AP-TWR employing Single-Sided Two-Way Ranging (SS-TWR)
active method is described as
𝑇 ↔𝐴𝑗|𝐴𝑖
𝑇 ,𝐴𝑖 𝐴𝑖,𝑇
for
𝐴𝑖,𝑇 𝑇,𝐴𝑖
𝐴𝑖↔𝐴𝑗 𝐴𝑗,𝐴𝑖for (1)
where
𝑇 ↔𝐴𝑗|𝐴𝑖
is the calculated time of ight (ToF) between the tag T and the
-th passive
anchor Aj, while the
-th active anchor Ai is partaking in the ranging sequence. This distinction
is made because a single passive anchor can produce an estimate of the ToF between T and Aj
following each Ai’s response. In the special case where
, only the active range estimate
can be calculated; in this case it is calculated using SS-TWR. This is done by time intervals
𝐴𝑖,𝑇
- the time interval measured by Ai corresponding to reception of T, and
𝑇 ,𝐴𝑖
- time interval
measured by T corresponding to the reception of Ai. In other cases, the passive estimate is
calculated using the above mentioned
𝐴𝑖,𝑇
,
𝑇 ,𝐴𝑖
, the known ToF between Ai and Aj -
𝐴𝑖↔𝐴𝑗
,
and 𝐴𝑗,𝐴𝑖 - the time interval measured by Aj corresponding to the reception of Ai.
Calculating all possible
𝑇 ↔𝐴𝑗|𝐴𝑖
values via
(1)
results in the following
-by-
ToF measurement
matrix T:
𝑇 ↔𝐴1|𝐴1 𝑇 ↔𝐴1|𝐴𝑚
𝑇 ↔𝐴𝑛|𝐴1 𝑇↔𝐴𝑛 |𝐴𝑚(2)
where
,
and the total number of anchors
consists of the
number of active-passive anchors and passive-only anchors , such that .
It can be observed that the ToF estimates achieved via active TWR methods are located on
the main diagonal of
T
, and the passive estimates of AP-TWR are situated o the main diagonal,
so rows contain only passive ToF estimates.
The active SS-TWR method, as a result of its shorter measurement period, provides a lower
relative motion induced error than the eectively longer Asymmetric Double-Sided Two-Way
Ranging (ADS-TWR). The larger error is on account of including the nal frame of the tag in
the calculation of the range estimate [9].
It can be observed from Fig. 1that the duration of the frame exchange regarding the calcula-
tion of the passive range estimates is in the same range as SS-TWR, since the time intervals
incorporating the third UWB frame of the tag are not used in
(1)
. Therefore we can assume
that the relative motion error for AP-TWR passive range estimates is lower than ADS-TWR, for
example.
Figure 1:
AP-TWR: Message exchange of tag T and active anchor Ai, while passive anchor Aj listens to
the transmissions.
Moreover, assuming that the total length of the ranging protocol is in the order of milliseconds,
we can infer that the error originating from the tag’s relative movement to the anchors can
altogether be omitted [10,11].
AP-TWR cases
produce a ToF estimate matrix
(2)
consisting of more than one column
and row, where the elements of each row are individual estimates of the true ToF between T and
Aj,
𝑇 ↔𝐴𝑗
. Considering all the above, we can assume that elements of each row are independent
estimates of
𝑇 ↔𝐴𝑗
, the values of which can be considered as constants for the duration of a
single ranging sequence.
The number of rows show the number of unique distance measurements between the tag and
anchors, and the values in each row are separate estimates of a single anchor-to-tag distance
value. That is, the number of columns represents the number of measurements that can be
processed to provide a nal range estimate for that specic anchor. The row values need to be
processed in order to provide a more accurate, precise and robust nal distance estimate.
The following section focuses on the methods of estimating the values of
𝑇 ↔𝐴𝑗
from the
measurement matrix presented by (2).
3. Estimation methods
This section describes the methods of processing the raw measurement matrix values to achieve
the nal distance values as inputs for a positioning system. Many of the described methods
employ estimation of
𝑇 ↔𝐴𝑗
via calculating a weighted arithmetic mean, diering by only how
the weights are generated.
The weighted mean (WM) of the -th row of the measurement matrix can be expressed as:
𝑇 ↔𝐴𝑗|𝐴1∶𝑚
𝑚
𝑖=1𝑗,𝑖 𝑇 ↔𝐴𝑗|𝐴𝑖
𝑚
𝑖=1 𝑗,𝑖 (3)
where
𝑗,𝑖
are the non-negative weights corresponding to each of the measurement matrix
element
𝑇 ↔𝐴𝑗|𝐴𝑖
. The special case where all the weights are equal, the solution simplies to a
standard arithmetic mean:
𝑇 ↔𝐴𝑗 |𝐴1∶𝑚
𝑚
𝑖=1 𝑇 ↔𝐴𝑗|𝐴𝑖
(4)
which will be discussed in the following Section.
3.1. Least Squares
In order to better describe the concept, we deconstruct the measurement matrix
(2)
to a set of
row vectors: 𝑇 ↔𝐴1 𝑇↔𝐴1|𝐴1 𝑇 ↔𝐴1|𝐴𝑚
𝑇 ↔𝐴𝑛 𝑇↔𝐴𝑛 |𝐴1 𝑇 ↔𝐴𝑛|𝐴𝑚(5)
The problem of estimating the value of a constant using Least Squares (LS) is reduced to
nding the mean value of the individual elements of the input vector [
12
]. The method is
desirable because no additional information of the ToF estimates is needed and thus calculating
weights is not needed.
As stated above, the LS solution for estimating a constant simplies to calculating the
arithmetic mean by applying (4) to (5):
𝐿𝑆 𝑇 ↔𝐴1|𝐴1∶𝑚
𝑇 ↔𝐴𝑛|𝐴1∶𝑚(6)
where
𝐿𝑆
is a vector containing
nal LS estimates of the ToF between the tag and the anchors.
3.2. Median
Like in the previous section, we adopt the vector notation of
(5)
to provide the solution of the
next method.
Then the vector of nal ToF estimates can be found as the median values of each vector of
(5)
as follows:
𝑀𝐸𝐷 𝑇 ↔𝐴1|𝐴1∶𝑚
𝑇↔𝐴𝑛 |𝐴1∶𝑚(7)
where the tilde accent notes the mathematical operation of median, which does not require
extra information on measurements, while being a more robust estimator in presence of outliers
than LS.
3.3. Inverse Distance Weighting
The Inverse Distance Weighting (IDW) method was introduced by Shepard in [
13
], which was
devised as an interpolation function to produce a continuous surface from discrete data points.
Following the idea of Shepard, we take the liberty to rewrite the concept of IDW into the
context of the current paper:
𝑇 ↔𝐴𝑗
𝑚
𝑖=1𝑇 ↔𝐴𝑗|𝐴𝑖 −1
𝑗,𝑖
𝑚
𝑖=1 −1
𝑗,𝑖 if 𝑗 ,𝑖 for all
𝑇 ↔𝐴𝑗|𝐴1∶𝑚 if 𝑗,𝑖 for some
(8)
where 𝑗,𝑖 𝑇 ↔𝐴𝑗 |𝐴𝑖 𝑇 ↔𝐴𝑗 |𝐴1∶𝑚 (9)
Equation
(9)
is the rst-order distance function of
𝑇 ↔𝐴𝑗|𝐴𝑖
. Since we are working in one
dimension, the value of the distance function
𝑗,𝑖
is calculated as the absolute value of the
dierence of 𝑇 ↔𝐴𝑗|𝐴𝑖 and the arithmetic mean of row .
The value of
𝑗,𝑖
is in turn used in the calculation of the rst-order IDW estimate by
(8)
, where
the order is specied by the magnitude of the negative exponent of
𝑗,𝑖
. Larger exponent values
eectively give larger weight to ToF estimates which are closer to the arithmetic mean.
3.4. Distance Weighted Estimator
Dodonov and Dodonova introduced the Distance Weighted Estimator (DWE) in [
14
], which
provides a robust estimate of central tendency without the need of separately calculating a
mean value.
Adopting our notation to (9) of [
14
], we get the expression to calculate the DWE weights as
follows:
𝑗,𝑖
𝑚
𝑙=1 𝑇 ↔𝐴𝑗 |𝐴𝑖 𝑇 ↔𝐴𝑗 |𝐴𝑙(10)
where each of the weights are calculated as the inverse mean distance of
𝑇 ↔𝐴𝑗|𝐴𝑖
and other
elements of row
. These weights are in turn used in
(3)
, to provide the set of nal ToF estimates
𝑇 ↔𝐴𝑗.
3.5. Weighted Least Squares 1
The solution to Weighted Least Squares (WLS) estimation reduces to weighting the measured
values with their corresponding noise variance, keeping in mind that the noise for each mea-
surement is considered zero-mean and independent [12].
Firstly, we consider the theoretical noise variance values as the basis for the weights to
calculate an estimate for the WLS1 method.
Considering the results of [
6
,
8
], we can assume that active ranging (SS-TWR and AltDS-TWR,
respectively) performs at about 3.2 cm root-mean-square error (RMSE) and passive ranging of
AP-TWR in the range of 5.2 to 5.5 cm RMSE.
The RMSE values are presented in centimeters to reect the nal product of ranging, as
opposed to providing the RMSE in picoseconds for the ToF measurements. Both representations
can be used interchangeably, since the ToF time
𝑇 𝑜𝐹
and the distance value
are related to
each other via the propagation speed
(in this case, the speed of light) through the expression
𝑇 𝑜 𝐹.
As the WLS solution employs weighting based on the noise variance, the WLS1 weights for
the measurement matrix can be written as
𝑗,𝑖
2
𝑎for
2
𝑝for (11)
where
2
𝑎
is the variance of the active measurements, and
2
𝑝
is the variance of the AP-TWR
passive measurements. The calculated weights
𝑗,𝑖
are in turn used in
(3)
for the calculation of
the nal estimate.
The calculation of RMSE and standard deviation is somewhat similar, where the former is
calculated using the known true value and the latter employing the sample mean value [
8
].
Therefore when the true value is equal to the sample mean, the RMSE and standard deviation
values are also equal. Assuming the same data, but where the true value is not equal to the
sample mean, the RMSE value is higher than the standard deviation of the data set.
Therefore in the scope of this paper we assume the value of standard deviation for the passive
range estimates at
𝑝
cm, and for active estimates
𝑎
cm, inferred from the RMSE
results of previous papers.
3.6. Weighted Least Squares 2
Following the approach of weights calculated using the theoretical variances, we propose the
second method of weighted least squares (WLS2).
Firstly, we nd each elements’ distance from their corresponding row mean of the ToF
measurement matrix
by adopting
(9)
. By doing so, we formulate a mean-shied measurement
matrix 𝑆:
𝑆1,1 1,𝑚
𝑛,1 𝑛,𝑚(12)
Since the newly formed
𝑆
is centered around its mean values, we can calculate column-wise
variances:
2
𝑖
𝑛
𝑗=1𝑗,𝑖 1∶𝑛,𝑖2
(13)
where
1∶𝑛,𝑖
is the mean value of column
of
(12)
and
2
𝑖
are the calculated column-wise variances.
Then the according weights can be calculated as
𝑗,𝑖
2
𝑖for all (14)
The weights calculated by this method are the same for each row of the measurement matrix,
changing only with each successive ranging sequence. Similarly to the previous section, the
resulting weights are then used in (3) for the nal ranging estimates.
3.7. Weighted Least Squares 3
In this section, we propose a third method for Weighted Least Squares (WLS3), for which the
noise variance-based weights are also calculated for each row separately.
In order to calculate the nal weights, the measurement matrix needs to be centered via
(12)
and the column-wise variances calculated, similarly to the previous section. Then the row-wise
variances of 𝑆need to be calculated as well:
2
𝑗
𝑚
𝑖=1𝑗,𝑖 𝑗,1∶𝑚 2
(15)
where
𝑗,1∶𝑚
is the mean value of row
, and
2
𝑗
is the row-wise variance of the measurement
matrix. Following the calculation of
2
𝑖
and
2
𝑗
, we then combine them into
2
𝑗,𝑖
by the following
expression: 2
𝑗,𝑖 2
𝑗2
𝑖
(16)
Based on (16), we can then calculate the weights by
𝑗,𝑖
2
𝑗,𝑖 (17)
which are in turn used as weights in (3) for the nal AP-TWR ranging estimates.
0 1 2 3 4 5 6 7
0123456
x (m)
y(m)
A1
A2
A3
A4
A5
A6
L1
L2
L3
L4
L5
Figure 2:
Representation of the test room setup in XY-plane. Anchors are marked with red circles and
the test locations of the tag with green triangles.
4. Test Setup
In order to assess the performance of each of the previously specied methods, practical
experiments were conducted. In this section we describe the preliminaries for the experiments.
The tests were ran in a 7.2 m by 6 m university laboratory room with concrete-walls, furnished
with desks and computers. The UWB system used for experiments was the Eliko UWB RTLS
[
15
] consisting of 6 active-passive anchors and a single tag. The active and passive range
estimates were gathered via a laptop connected to the ranging engine of the Eliko UWB RTLS.
The active range estimates were attained using SS-TWR, and the passive estimates via the AP-
TWR passive method described in Section 2. The gathered estimates were post-processed using
a custom script written in R, implementing all the methods described in Section 3. Additionally,
the script also calculates various statistical parameters, including RMSE and standard deviation,
which are the basis for the results presented in Section 5. Apart from the proposed estimation
methods, no additional ltering or trimming was applied to the measurement matrix.
The true coordinates of the anchors and of the tag at various positions were measured with
a Leica Disto S910 laser distance meter [
16
]. In addition, the anchor-tag true distances were
also veried with the Leica Disto S910, in order to calculate some of the needed performance
parameters.
The data was gathered with a tag installed on a tripod at 5 arbitrarily chosen points in the
room, which are marked on Fig. 2alongside the locations of the anchors; the anchors are
Table 1
Test setup: anchors (Ax) subjected to NLOS in the 5 test locations (Loc x).
Loc 1 Loc 2 Loc 3 Loc 4 Loc 5
A1, A2, A4, A5 A2, A4 A1, A2, A4, A5 ALL A3, A6
marked with red circles and the locations of the tag with green triangles.
In each location 3 separate tests were conducted: one line-of-sight (LOS) test and two separate
non-line-of-sight (NLOS) tests. The NLOS tests were conducted by disrupting the LOS between
anchors and a tag by either a 40 cm by 20 cm, 0.8 mm thick sheet of metal (NLOS1) or a human
body chest area (NLOS2), placed at a distance of about 5 cm from the tag. Note that for both
NLOS tests, the propagation paths to the same exact anchors were disrupted to have a fair
comparison of the dierent NLOS conditions. Table 1gives the details of NLOS tests, i.e. which
anchors have NLOS propagation conditions at each of the test locations.
During each separate test, data from a minimum of 1200 separate ranging sequences were
collected. Considering that the setup consisted of AP-TWR
, this amounts to at a
minimum of 43200 raw range values across all the captured measurement matrices.
5. Experimental Results
The results of the experiments are given in Fig. 3, where the RMSE and standard deviation (SD)
values for each of the test locations is given, depending on the propagation conditions. Fig. 3a,
b and c give the RMSE values for LOS, NLOS1 and NLOS2, respectively. Fig. 3d, e, f give the
respective SD values for the same propagation conditions. Additionally, a zoomed-in region of
each of the sub-gures is given four location 4 since the traces can be placed quite densely.
Alongside the seven proposed methods (LS, Med, IDW, DWE, WLS1, WLS2, WLS3), the
performance of active-only (SS-TWR) and AP-TWR passive-only ranging estimates from the
same exact measurements is also given. They are separately pictured in order to give a baseline
comparison of the performance of the proposed methods.
It can be observed from Fig. 3a - c that the RMSE of passive measurements is almost always
lower than the active-only method, with the exception of locations 1 and 2 in Fig. 3a. On
the other hand, the results for SD show the opposite: active-only estimates outperform the
passive-only methods in every single test and location by a very slight margin. This is also in
line with the results attained in previous publications regarding AP-TWR [6,7,8].
Although in regards of SD, the proposed methods’ performance always places between the
active and passive-only methods, the RMSE values show that many of the proposed methods
provide better results than even the baseline better-performing passive-only estimates.
The average SD across all locations, depending on the method used, is shown as the bars on
Fig. 4. From these results we can again see that the active estimates provide the lowest SD,
while the passive estimates perform the least. The results from all three propagation condition
tests show that utilizing the MED, IDW or DWE methods provide comparable performance to
the most precise active-only estimates.
Across all locations the average RMSE values of LOS, NLOS1 and NLOS2 conditions depending
on the method are given in Fig. 4, pictured by the lines+markers. The following analysis focuses
on the RMSE improvements compared to a active-only SS-TWR method (Active method RMSE
of Fig. 4), which achieved an RMSE of 24.209 cm in LOS, 36.006 cm in NLOS1 and 37.123 cm in
NLOS2.
The WLS3 method provides the lowest RMSE of all the methods in LOS conditions at 20.742
cm (decrease of 14.3%), followed closely by IDW (20.785 cm, decrease of 14.14%) and DWE
10
20
30
1 2 3 4 5
Location
RMSE (cm)
LOS
a.
10
20
1 2 3 4 5
Location
SD (cm)
LOS
d.
10
20
30
40
50
60
1 2 3 4 5
Location
RMSE (cm)
NLOS1
b.
5
10
15
20
25
1 2 3 4 5
Location
SD (cm)
NLOS1
e.
20
30
40
50
1 2 3 4 5
Location
RMSE (cm)
NLOS2
c.
10
15
20
25
30
1 2 3 4 5
Location
SD (cm)
NLOS2
f.
Method
Active
Passive
LS
Med
IDW
DWE
WLS1
WLS2
WLS3
Figure 3:
Results of experiments at each individual location. Parts a, b, c present the RMSE of the
proposed methods in LOS, NLOS1 and NLOS2 propagation conditions; parts d, e, f present the respective
standard deviation (SD) values. Lower is better for all of the figures, note the dierent scales on each
figure.
(20.795 cm, decrease of 14.10%), up to the least performing method of WLS2 (21.064 cm, decrease
of 13.00%). The results show that in LOS conditions all of the proposed methods perform
similarly, with a dierence of 0.322 cm between the best and worst performing method.
NLOS1 conditions showed the best performing method to be MED at 29.135 cm RMSE
(decrease of 19.08%), followed by DWE at 29.169 cm (18.99% decrease) and IDW at 29.210 cm
(18.87% decrease), with the lowest performing method WLS1 at 30.727 cm (14.66% decrease). It
can be observed that in NLOS1 the absolute dierence of the best and least performing methods,
at 1.592 cm, is larger than in LOS.
NLOS2 conditions produced similar results where MED achieved the best results at 32.183
cm (13.31% decrease), followed by DWE at 32.190 cm (13.29%) and IDW at 32.251 cm (13.12%)
1
5
10
14
18
20
25
30
35
Active Passive LS Med IDW DWE WLS1 WLS2 WLS3
Method
SD (cm)
RMSE (cm)
LOS NLOS1 NLOS2
Figure 4:
The average RMSE (lines+markers) and SD values (bars) for the proposed methods across all
locations, depending on the tested propagation conditions. Lower is better.
with WLS1 landing at the last place with 33.157 cm RMSE (decrease of 10.68%). Similar to the
previous result, the absolute dierence of the methods is lower than NLOS1 but is still about 3
times as large as in LOS with 0.974 cm.
In terms of RMSE, the LS, MED, IDW and DWE methods show millimeter level dierences
between each other in LOS and NLOS, providing essentially the same performance. Coupled
with the fact that MED, IDW and DWE oer comparable SD performance to active estimates, it
can be claimed that the MED, IDW and DWE methods are the best-suited measurement matrix
estimation methods.
Compared to results shown in previous papers reporting on AP-TWR [
6
,
7
,
8
], the attained
RMSE values were slightly higher than expected. This is partly due to the fact that earlier
papers ran only LOS tests, so naturally the added NLOS would provide degraded performance
due to the impairment of propagation conditions, but the reported LOS results showed slightly
lower performance as well.
This could be explained by some systematic errors introduced in the system. These errors
could be attributed to imperfect calibration of antenna delays, range bias (eect of signal strength
to the reported ranging value) [
17
], multipath propagation [
18
] or even errors originating from
the physical orientation of the devices in regards to each other [19].
6. Conclusion
The experiments validated that all of the methods decrease the ranging RMSE in LOS propagation
conditions, while also showing that NLOS propagation conditions do not break down the
methods but rather increase the performance in demanding propagation conditions.
Results also showed that the selection of the specic method is not so critical in LOS conditions,
as all the methods perform equivalently. The two tested NLOS conditions showed that in both,
absolute values and relative decrease of RMSE, are further increased by selecting the appropriate
method, meaning that the choice of methods becomes more crucial for real-life applications
experiencing mixed LOS/NLOS conditions.
In LOS, all the methods perform almost identically - achieving up to 14.3% lower RMSE when
using WLS3 method compared to SS-TWR. NLOS conditions showed that up to 19.08% decrease
of RMSE can be achieved compared to SS-TWR by employing MED to the measurement matrix,
whereas the LS, IDW and DWE methods’ performance lies within a few millimeters of it.
Comparing with the standard deviation of the best-performing SS-TWR active ranging, it
was observed that the MED, IDW and DWE achieve comparable results, implicating that the
precision of these methods is approximately on the same level. Meaning that these methods
oer no signicant degradation of the precision when compared to the active-only ranging.
In conclusion, across the tested LOS, NLOS1 and NLOS2 propagation conditions the methods
MED, IDW and DWE showed similar SD, while providing considerably higher RMSE perfor-
mance compared to SS-TWR. Taking into account these results it can be claimed that either
one of the MED, IDW or DWE methods are sucient for the AP-TWR measurement matrix
estimation, while showing that these methods are also robust in NLOS conditions.
For future work, new experiments could be conducted in larger and more complex en-
vironments with harsher multipath eects present. Moreover, additional locations and tag
orientations should be investigated to average out the device orientation errors and tests with
varying number of active-passive anchors (
) should be conducted to see how it aects the
performance of the proposed methods.
Acknowledgments
This project has received funding from the European Union’s Horizon 2020 Research and
Innovation programme under grant agreement No 951867, 101058505 and 668995. This research
has also been supported in part by the European Regional Development Fund, Study IT in
Estonia Grant, and Estonian Research Council under Grant PUT-PRG424.
References
[1]
A. Alari, A. Al-Salman, M. Alsaleh, A. Alnafessah, S. Al-Hadhrami, M. A. Al-Ammar,
H. S. Al-Khalifa, Ultra wideband indoor positioning technologies: Analysis and recent
advances, Sensors (Switzerland) 16 (2016) 1–36. doi:
10.3390/s16050707
.
[2]
H. Liu, H. Darabi, P. Banerjee, J. Liu, Survey of wireless indoor positioning techniques and
systems, IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and
Reviews 37 (2007) 1067–1080. doi:
10.1109/TSMCC.2007.905750
.
[3]
M. Ridol, S. van de Velde, H. Steendam, E. De Poorter, Analysis of the scalability of UWB
indoor localization solutions for high user densities, Sensors (Switzerland) 18 (2018) 1–19.
doi:
10.3390/s18061875
.
[4]
B. Hepp, T. Nägeli, O. Hilliges, Omni-directional person tracking on a ying robot using
occlusion-robust ultra-wideband signals, in: IEEE International Conference on Intelli-
gent Robots and Systems, volume 2016-Novem, 2016, pp. 189–194. doi:
10.1109/IROS.2016.
7759054
.
[5]
K. A. Horvath, G. Ill, A. Milankovich, Passive extended double-sided two-way ranging with
alternative calculation, in: 2017 IEEE 17th International Conference on Ubiquitous Wireless
Broadband, ICUWB 2017 - Proceedings, 2017, pp. 1–5. doi:
10.1109/ICUWB.2017.8250972
.
[6]
S. Shah, T. Demeechai, Multiple simultaneous ranging in IR-UWB networks, Sensors
(Switzerland) 19 (2019) 1–14. doi:
10.3390/s19245415
.
[7]
T. Laadung, S. Ulp, M. M. Alam, Y. Le Moullec, Active-Passive Two-Way Ranging Using
UWB, in: 2020 14th International Conference on Signal Processing and Communication
Systems (ICSPCS), IEEE, 2020, pp. 1–5. doi:
10.1109/ICSPCS50536.2020.9309999
.
[8]
T. Laadung, S. Ulp, M. M. Alam, Y. L. Moullec, Novel Active-Passive Two-Way Ranging
Protocols for UWB Positioning Systems, IEEE Sensors Journal 22 (2022) 5223–5237.
doi:
10.1109/JSEN.2021.3125570
.
[9]
C. Lin, X. Jin, S. Mo, C. Hou, W. Zhang, Z. Xu, Z. Jin, Performance analysis and vali-
dation of precision multisatellite RF measurement scheme for microsatellite formations,
Measurement Science and Technology 33 (2022). doi:
10.1088/1361-6501/ac37ea
.
[10]
Y. Jiang, V. C. Leung, An asymmetric double sided two-way ranging for crystal oset,
in: Conference Proceedings of the International Symposium on Signals, Systems and
Electronics, Crdpj 320552, 2007, pp. 525–528. doi:
10.1109/ISSSE.2007.4294528
.
[11]
J. Cano, G. Pages, E. Chaumette, J. LeNy, Clock and Power-Induced Bias Correction
for UWB Time-of-Flight Measurements, IEEE Robotics and Automation Letters 7 (2022)
2431–2438. doi:
10.1109/LRA.2022.3143202
.
[12]
D. Simon, Optimal State Estimation: Kalman, H Innity, and Nonlinear Approaches,
Wiley-Interscience, USA, 2006.
[13]
D. Shepard, A two- dimensional interpolation function for irregularly- spaced data, in:
Proceedings of the 1968 23rd ACM national conference, 1968, pp. 517–524.
[14]
Y. S. Dodonov, Y. A. Dodonova, Robust measures of central tendency: Weighting as
a possible alternative to trimming in response-time data analysis, Psikhologicheskie
Issledovaniya 5 (2011) 1–11.
[15]
Eliko Tehnoloogia Arenduskeskus OÜ, Eliko UWB RTLS, 2022. URL: https://eliko.ee/
uwb-rtls-ultra-wideband-real-time-location-system/, accessed May 5, 2022.
[16]
Leica Geosystems AG, Leica DISTO S910 User Manual, 2019.
URL: https://shop.leica-geosystems.com/sites/default/files/2019-04/
leica-disto-s910-user-manual-805080-808183-806677-en.pdf, accessed May 5, 2022.
[17]
Decawave/Qorvo, APS011 Application Note: Sources Of Error In DW1000 Based Two-
Way Ranging (TWR) Schemes, 2018. URL: https://www.qorvo.com/products/d/da008446,
accessed July 13, 2022.
[18]
A. D. Preter, G. Goysens, J. Anthonis, J. Swevers, G. Pipeleers, Range bias modeling and
autocalibration of an UWB positioning system, in: 2019 International Conference on
Indoor Positioning and Indoor Navigation, IPIN 2019, IEEE, 2019, pp. 1–8. doi:
10.1109/
IPIN.2019.8911815
.
[19]
P. Krapež, M. Vidmar, M. Munih, Distance measurements in uwb-radio localization
systems corrected with a feedforward neural network model, Sensors 21 (2021) 1–18.
doi:
10.3390/s21072294
.
