=Paper=
{{Paper
|id=Vol-3248/paper30
|storemode=property
|title=SALOS - a UWB Single Anchor Localization System based on CIR-vectors - Design and Evaluation
|pdfUrl=https://ceur-ws.org/Vol-3248/paper30.pdf
|volume=Vol-3248
|authors=Sven Ole Schmidt,Marco Cimdins,Horst Hellbrück
|dblpUrl=https://dblp.org/rec/conf/ipin/SchmidtCH22
}}
==SALOS - a UWB Single Anchor Localization System based on CIR-vectors - Design and Evaluation==
https://ceur-ws.org/Vol-3248/paper30.pdf
SALOS - a UWB Single Anchor Localization System
based on CIR-vectors - Design and Evaluation
Sven Ole Schmidt1 , Marco Cimdins1 and Horst Hellbrück1
1
Technische Hochschule Lübeck - University of Applied Sciences, Mönkhofer Weg 239, 23562 Lübeck, Germany
Abstract
Single anchor localization systems with radio-frequency (RF) signals provide a position estimation for
indoor environments and have unique challenges. For such a position estimation, angle and distance
measurements are required. Whereas distance measurements are a standard in RF localization systems,
angular measurements require either multi-antenna systems or selective shadowing with mechanical
rotation, which is complex and costly. Another approach for resolving the ambiguity of pure distance
measurements is the use of multipath propagation when the location of the anchor and the geometry of
the indoor environment is given. Multipath information is available by channel impulse response (CIR)
measurements. The concept of CIR-vectors for position characterization is already introduced but is not
yet evaluated in real systems. A comparison of similarity metrics has not been investigated for a setup
with off-the-shelf hardware. We introduce our system SALOS, a localization approach to convert real
measurements into CIR-vectors and provide similarity metrics for comparison. We introduce a standard
ℓ1-norm, advanced ℓ1-norm, and ℓ1-norm based on the sliding window. We perform 3-dimensional
measurements with Qorvo’s DW1000 RF chip in a grid. To increase the resolution distinct transmission
bands are assembled. We modeled the expected results of the CIR-vectors based on an optimal anchor
positioning and designed several similarity metrics. We evaluate the resulting position estimation. In the
best case, SALOS estimates 70% of correct positions for the sliding window ℓ1-norm. For this case, the
assessment of ambiguity, our proposed metric to quantify the demand for external information, of 0.89
is reached.
Keywords
single anchor localization, channel impulse response, effective length of CIRs, optimal anchor positioning,
UWB measurements, DW1000, CIR-vector
1. Introduction
In the last ten years radio-frequency (RF)-based indoor localization complements the well-
established satellite localization we all use for outdoor navigation. Successful and robust RF
indoor localization started with multiple anchors. Many products recommend at least four
anchors placed at each corner of a room to perform distance measurements and multilateration
algorithms. If the room is large, cells of four anchors are formed to cover larger areas. Hence,
IPIN 2022 WiP Proceedings, September 5 - 7, 2022, Beijing, China
$ sven.ole.schmidt@th-luebeck.de (S. O. Schmidt); marco.cimdins@th-luebeck.de (M. Cimdins);
horst.hellbrueck@th-luebeck.de (H. Hellbrück)
https://www.th-luebeck.de/en/cosa/team/sven-ole-schmidt/ (S. O. Schmidt);
https://www.th-luebeck.de/en/cosa/team/marco-cimdins/ (M. Cimdins);
https://www.th-luebeck.de/en/cosa/team/horst-hellbrueck/ (H. Hellbrück)
0000-0001-7653-1463 (S. O. Schmidt); 0000-0002-0114-5661 (M. Cimdins); 0000-0001-7619-8015 (H. Hellbrück)
© 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)
these systems require a large number of anchors and each anchor increases the costs for
hardware, deployment, and maintenance. E.g. 50 Ultra-Wideband (UWB) anchors are deployed
to cover a production facility of 1500 m2 in [1].
In the recent past, single anchor localization systems became a cost-effective alternative.
However, such systems for indoor environments have unique challenges. For position estimation,
pure distance measurements are not enough. Additionally, angular measurements are required
that need either multi-antenna systems or selective shadowing with mechanical rotation.
Technologies such as Bluetooth Low Energy (BLE) introduced angle-of-arrival in version 5.1.
Together with distance measurements, single anchor localization will receive more attention
[2, 3]. Grosswindhager et al. present a UWB single anchor localization system in [4]. They
deploy multiple directional antennas to overcome ambiguities in the position estimation since
one single antenna could not avoid a suboptimal anchor position leading to a set of position
estimations instead of on fixed estimation without further processing. In [5], Wang et al. equip
a single UWB anchor with an antenna array and localize tags with the distance extracted from
time-of-flight measurements and the angle-of-arrival extracted from the antenna array. Cao et
al. combined speed estimations extracted from UWB range with an inertial-measurement-unit
to track tags that are attached to a moving robot [6]. However, angular measurements are
complex and costly compared to an anchor that performs only distance measurements but are
more effective than multiple anchors.
An alternative approach for resolving the ambiguity of pure distance measurements is the
use of multipath propagation, exploiting the concept of virtual anchors due to reflections
at walls [7]. This requires knowledge of the location of an anchor and the geometry of the
indoor environment. In [8] Miao et al. discussed the optimal anchor positioning for single-hop
localization systems. For a multipath-based localization system, anchor positioning is very
important. We proposed to convert the given multipath components (MPC) into an overall
channel impulse response (CIR) vector to determine the optimal position of the anchor via
simulation [9]. Multipath information is available by CIR measurements with commercial off-
the-shelf (COTS) anchors based on UWB signals. Furthermore, we have shown that assembling
several UWB channels increases the bandwidth of the UWB signals and thereby the resolution
[10].
In this paper, we investigate SALOS, a single anchor localization system, and perform mea-
surements in a realistic setup with COTS hardware. We model MPCs via raytracing and model
CIRs that we compare with real taken CIR measurements. MPC detection is ambitious, therefore
this paper is also about extracting MPCs from the measured UWB CIR. For efficiency and to
create a similarity metric, we convert these CIR measurements into so-called CIR-vectors. In this
work, we show that the previous set assumptions are valid for measurements that are recorded
by a COTS available low-cost UWB transceiver: the Qorvo DW1000. For this proof-of-concept
for SALOS, we focus on a localization area with a single anchor node. This procedure enables
the evaluation of the concept at all and is covering a minimalized-hardware approach, which is
one of the main arguments for usage of single-anchor localization.
In summary, our contributions are:
• We introduce SALOS, a single anchor localization system based on CIR-vectors.
• We derive a CIR-vector representation of CIR measurements of Qorvo’s Decawave
DW1000 RF chip with a new estimation algorithm for MPCs.
• We assemble DW1000’s CIR measurements of distinct transmission bands to improve the
accuracy of the MPC detection algorithm.
• We introduce two advanced similarity metrics for the comparison of CIR-vectors that
consider typical measurement inaccuracies and evaluate the system performance.
The rest of the paper is organized as follows: Section 2 introduces theoretical basics for SALOS:
a multipath model, a conversion from CIRs to CIR-vectors, as well as optimal anchor positioning,
and a new similarity metric. Section 3 describes the processing of the CIR measurements as
well as the MPC detection algorithm. The evaluation of our deployment is given in Section 4.
Section 5 finally concludes the paper and provides directions for future work.
2. SALOS System Background and Components
In this section, we introduce the theoretical background for SALOS, our single anchor localiza-
tion system based on CIR-vectors. First, we focus on the derivation of multipath components
(MPC) based on a 3-dimensional multipath environment and form the overall channel impulse
response (CIR) ℎ(𝑡). Afterward, we show how to convert ℎ(𝑡) into the corresponding CIR-vector
h. Then, we determine the optimal anchor position based on the effective length of CIRs 𝑙𝑒 , as
introduced in our previous work [9]. Finally, we will introduce three similarity metrics applied
for position estimation in our localization system.
2.1. Modeling 3-dimensional Multipath Propagation
We assume that the electromagnetic signal 𝑥(𝑡) propagates from a sensor node of unknown
position 𝑃𝑇 (e.g. a tag) to a node of known position 𝑃𝐴 (e.g. an anchor). The anchor 𝐴𝑛 does
not only receive the 𝑇 𝑎𝑔’s signal 𝑥(𝑡) via the direct Line-of-Sight-path (LOS) with path length
𝑑0 and transmission delay 𝜏0 = 𝑑0 /𝑐0 , with speed of light 𝑐0 ≈ 3 · 108 m/s. In addition, signal
echoes e.g. reflected from surfaces such as walls or objects will reach the anchor as well. Figure 1
shows an exemplary multipath environment including echo paths (depicted in blue).
Figure 1: 3-dimensional multipath environment including one wall and the ground.
Signal echoes passing the 𝑖-th echo path result in a higher transmission delay 𝜏𝑖 > 𝜏0 since
the path length of the transmission 𝑑𝑖 > 𝑑0 is longer than the LOS. To calculate the path length
of the single echo paths, we introduce the concept of virtual anchors. These virtual anchors
(𝑉 𝐴𝑛) are projections of an anchor 𝐴𝑛, mirrored at the reflection surface. Figure 1 depicts them
in gray. While the path length between one 𝑉 𝐴𝑛 and 𝑇 𝑎𝑔 is identical to the echo path’s length
𝑑𝑖 , the intersection between these pseudo-direct connections and the corresponding surface
indicates the reflection point at the surface (in Figure 1 marked with an orange star).
Each echo path has individual effects on the transmitted signal 𝑥(𝑡), e.g. transmission delay
or received power. In the following, the transmission delay 𝜏𝑖 in combination with the received
signal amplitude 𝑎𝑖 characterizes the multipath component (MPC) of the 𝑖-th echo path. Note,
that the received signal amplitude 𝑎𝑖 is decreasing with increasing path length 𝑑𝑖 due to the
path losses. The channel impulse response (CIR) ℎ(𝑡) is the sum of the effect of all 𝐼 MPCs on
the transmitted signal 𝑥(𝑡) leading to the received signal 𝑦(𝑡) with:
𝐼−1
∑︁
𝑦(𝑡) = 𝑥(𝑡) * ℎ(𝑡), with ℎ(𝑡) = 𝑎𝑖 · 𝛿(𝑡 − 𝜏𝑖 ), (1)
𝑖=0
where 𝛿(𝑡 − 𝜏𝑖 ) is Dirac’s pulse at time 𝑡 = 𝜏𝑖 .
Since the anchor’s position 𝑃𝐴 and the environment (e.g. extracted by a floor plan) are known,
the CIR characterizes the corresponding tag’s position 𝑃𝑇 and enables localization systems
based on a single anchor node. The optimal approach to avoid external information for these
systems is to assure that the mapping from the tag position 𝑃𝑇 to the corresponding CIR ℎ𝑃𝑇 (𝑡)
is bijective. So, both a tag position is leading to a specific CIR, and the CIR is only indicating
exactly this tag position. If the mapping is not designed bijectively, at least one CIR could result
from two different tag positions. Therefore, external information coming from e.g. the prior
position or angular measurements are required for successful localization. This assumption
leads to the optimal anchor position of the localization system covered in Section 2.3.
2.2. Conversion of Channel Impulse Responses to CIR-vectors
In this section, we briefly summarize the conversion of CIRs into their corresponding vectors.
By converting the continuous CIRs ℎ(𝑡) to discrete finite vectors h, we shorten the data set
and enable direct quantitative comparison of the CIR-vectors. Even though we discard addi-
tional information, the remain information covered in the CIR-vectors is enough to ensure an
unambiguous characterization of tag positions with the corresponding CIR-vectors [9].
Assume a fixed anchor in a given three-dimensional multipath environment. So, the unknown
tag position 𝑃𝑇 is characterized based on the received signal 𝑦(𝑡). Therefore, the underlying
multipath propagation needs to be comparable, even with real measurement inaccuracies. For
this purpose, the CIR ℎ𝑃𝑇 (𝑡) at arbitrary tag’s position 𝑃𝑇 is converted into a CIR-vector h𝑃𝑇 .
Figure 2 shows a conversion from ℎ𝑃𝑇 (𝑡) to h𝑃𝑇 . First, we define a bin width Δ𝑏𝑖𝑛 as a fixed
time interval and split the time axis into 𝑁 ⌈𝜏𝐼−1 /Δ𝑏𝑖𝑛 ⌉ bins, where 𝜏𝐼−1 is longest transmission
delay of all echo paths. Now, we check the transmission delay 𝜏𝑖 for each MPC to match the
𝑛-th bin and increment the corresponding entry in h𝑃𝑇 [𝑛] by one (see Algorithm 1).
For detailed information, we refer to previous work [9]. After the introduction of the CIR-
vector representation, we will focus on the optimal anchor position of our localization system.
Figure 2: Conversion of CIR ℎ𝑃𝑇 (𝑡) to CIR-vector h𝑃𝑇 .
Algorithm 1: Conversion of CIR ℎ𝑃 (𝑡) consisting of 𝐼 MPCs to CIR-vector h𝑃 .
Data:
(1×𝑁 )
Assume 𝜏𝐼−1 ⩾ 𝜏𝑖 , ∀𝑖 ∈ {0, ..., 𝐼 − 1}: 𝑁 = ⌈𝜏𝐼−1 /Δ𝑏𝑖𝑛 ⌉ ; h𝑃 = [0, 0, ..., 0];
1 for 𝑖 = 0, ..., 𝐼 − 1 do
2 𝑛 = ⌈𝜏𝑖 /Δ𝑏𝑖𝑛 ⌉;
3 h𝑃 [𝑛] = h𝑃 [𝑛] + 1;
4 end
2.3. Calculation of the Effective Length of CIRs and Optimal Anchor
Positioning
The optimal anchor positioning of our localization system focuses on the idea of bijective
mapping, following an unambiguous correspondence of tag position 𝑃𝑇 and its CIR-vector h𝑃𝑇
(derived from the CIR ℎ𝑃𝑇 (𝑡)). To fulfill the condition of a bijective mapping, we require that
the CIR-vectors of all tag positions differ from each other. Since the multipath environment is
fixed and the tag position 𝑃𝑇 is unknown, the only way to influence the CIR-vectors is by the
positioning of the anchor. To evaluate the bijectivity characteristics of an anchor position in a
multipath environment, we introduced in our previous work the effective length of CIRs 𝑙𝑒 [9].
Next, we describe how we identify bijective mapping and we find the optimal anchor position
based on the results of the comparison of the CIR-vectors. Bijectivity is given, when CIR-vectors
of all tag positions are distinct. Since the MPC’s amplitude, 𝑎𝑖 is decreasing for increasing path
length, we focus on the most powerful signal echoes for distinction. So we start with comparing
the CIR-vectors h[ 𝑛] at 𝑛 = 0 with increasing 𝑛 in each iteration.
Figure 3 depicts an exemplary comparison of three different CIR-vectors h1 , h2 , h3 , at tag’s
position {𝑃𝑇,1 , 𝑃𝑇,2 , 𝑃𝑇,3 , } as well as the resulting effective length 𝑙𝑒 . In the first iteration, the
first bin of length Δ𝑏𝑖𝑛 of all CIR-vectors is compared with each other. Since h2 and h3 both
have a [0] entered in this bin, they are indistinguishable based only on the first bin, leading
to an ambiguous representation with respect to the first bin. Only h1 has a ’1’ noted in the
first bin. Thus, h1 is already unambiguous. When a measured CIR-vector with a [1] in the
first bin appears, it points back to h1 and thus to the tag position 𝑃𝑇,1 . Since there are at least
two tag positions, which do not differ with respect to the first bin, the combination of the first
and the second bin are of interest. Again, h2 and h3 include the same combination with [0,1]
Figure 3: Comparison of CIR-vectors h1 , h2 , h3 the resulting effective length of the CIRs is 𝑙𝑒 = 3Δ𝑏𝑖𝑛 .
and are not yet distinguishable. Therefore, the next iteration including the combination of the
first three bin entries is taken into account. While h2 results in [0,1,0], h3 finally differs with
the entries [0,1,1]. So, this is the first selection that all three tag positions result in distinct
CIR-vectors. Following the example, not more than three bins are needed for unambiguous
characterization. Since three bins are required to enable bijective mapping at the given anchor
position, the smallest length of the CIR-vector to consider is 𝑙𝑒 = 3Δ𝑏𝑖𝑛 , which is the so-called
effective length of CIRs of this anchor position. Taking more bins into account would not add
any further information, but only redundancy.
Different anchor positions result in different effective lengths 𝑙𝑒 for the same set of tag
positions [9]. Therefore, anchor positions must provide unambiguous CIR-vectors for a given
set of tag positions (𝑙𝑒 < ∞) to avoid the need for external information. The smaller 𝑙𝑒 for
different anchors, the more preferable is the anchor position. The anchor position with the
smallest 𝑙𝑒 is defined to be the optimal anchor position.
After determining the optimal anchor position, the localization system finally requires a
similarity metric for accurate position estimation based on the measured CIR-vectors.
2.4. Similarity Metric for CIR-vectors
We base SALOS on a set of modeled CIR-vectors {h𝑚𝑜𝑑 }, which are general constructed as
described in Section 2.2. For position estimation with respect to a measured CIR-vector h𝑚𝑒𝑎𝑠
(also formed as described in Section 2.2), the corresponding similarity metric needs to take
measurement inaccuracies into account following from deviating positioning of the anchor or
rough and bumpy reflection surfaces.
In this work, we compare the result of three different similarity metrics for the comparison of
vectors. These metrics are chosen as examples because they can handle the basic idea of vector
comparison with possible error-ridden bin content. In the following, the metrics’ input is the
general vectors h1 and h2 with the same number of entry bins 𝑁 .
Assume the comparison of 𝑁 bins of the vector h1 and the vector h2 . It is useful to focus on
the difference between the vectors bin by bin. So, the ℓ1-norm is selected as the first metric.
The ℓ1-norm is defined as:
𝑁
∑︁−1
𝑑ℓ1 (h1 , h2 ) = |h1 [𝑛] − h2 [𝑛]|. (2)
𝑛=0
In SALOS, measurement inaccuracies lead to alteration of the MPC’s transmission delays
𝜏 . In the worst case, the altered delay 𝜏 is allocated to a different bin than expected during
CIR-vector conversion. So, even if the corresponding MPC is estimated accurately, the measured
CIR-vector differs. Therefore, we introduce our advanced ℓ1-norm 𝑑𝑎𝑑ℓ1 (h1 , h2 ), which focuses
on the neighboring bins.
Figure 4: Block diagram of the self-developed advanced ℓ1-norm 𝑑𝑎𝑑ℓ1 (h1 , h2 ).
Figure 4 shows the algorithm as a block diagram. As with 𝑑ℓ1 , the 𝑛-th bin of h1 and h2 are
subtracted. When all entries of the measured CIR-vector’s 𝑛-th bin h1 [𝑛] are also contained in
the modeled CIR-vector’s 𝑛-th bin h2 [𝑛], the algorithm increases the considered bin to 𝑛 = 𝑛+1.
If not, subsequently, the previous and then the following bin of h2 [𝑛] are taken into account.
Note, that for 𝑛 = 0 no previous bin exists, therefore we go directly to the following bin. In the
end, the advanced ℓ1-norm 𝑑𝑎𝑑ℓ1 (h1 , h2 ) is the sum of the not-found CIR-vector entries of h1 .
Additionally, a third algorithm is added, which is based on the sliding window concept in
combination with the ℓ1-norm. Algorithm 2 depicts the operation method of the resulting
similarity metric 𝑑𝑠𝑤 (h1 , h2 ):
Algorithm 2: Similarity metric 𝑑𝑠𝑤 (h1 , h2 ).
Data:
{h1 , h2 }∈ N𝑁 ×1 ; window size: 𝑛𝑠𝑊 = 3;
1 for 𝑛 = 0, ..., 𝑁 − 𝑛𝑠𝑊 do
∑︀𝑛+𝑛 ∑︀𝑛+𝑛
2 𝑑[𝑛] = | 𝑛 𝑠𝑊 h1 [𝑛]| − | 𝑛 𝑠𝑊 h2 [𝑛]|;
3 end
∑︀𝑁 −𝑛𝑠𝑊
4 𝑑𝑠𝑊 (h1 , h2 ) = 𝑛=0 |𝑑[𝑛]|;
Here, to catch position estimation errors coming from measurement inaccuracies, we add
up the entries of 𝑛𝑠𝑊 = 3 bins for both h𝑚𝑒𝑎𝑠 and h𝑚𝑜𝑑 and subtract them from each other.
Subsequently, we shift the consideration window by one bin and add up two of the already
considered bins with the next following entry.
In this section, we summarized the CIR-vector representation to characterize tag positions
based on the multipath propagation of the transmit signal 𝑥(𝑡) and the resulting optimal anchor
positioning for our proposed localization system. Furthermore, we presented the algorithms
applied as a similarity metric for the localization system. In the next section, we will focus on
the extraction of MPCs and CIR-vectors from real UWB measurements with Qorvo’s Decawave
DW1000 RF chip.
3. CIR-vector Estimation for UWB Measurements
After proposing the concept of SALOS, we show in this section how to assemble real UWB
measurements recorded with Qorvo’s DW1000 RF chip and the conversion to real CIR-vectors.
The assemblage of multiple transmit signals on distinct transmission bands increases the effective
bandwidth of the system without hardware change.
3.1. Signal Processing and Assemblage of Decawave DW1000 UWB
Measurements
The COTS available DW1000 RF chip provides distance estimation between tag and anchor via
two-way-ranging (TWR). In addition, it records the received signals at predefined transmission
channels. In the following, we will focus on the transmission parameters listed in Table 1:
For details regarding the TWR of the DW1000 we refer to [11]. Note: following [12], we
extract the corresponding received signal of DW1000’s registers in the Final-message of the
TWR. This results in a distance estimation, which is directly correlated to the received signal
recorded by the DW1000 system.
In our previous work [10], we showed that the assemblage of received signals of multiple
transmissions on distinct transmission bands equals the received signal for one simultaneous
transmission at all these transmission bands.
In order to apply this method for the DW1000, we apply pre-processing that is proposed in
previous work [13].
The receive signal consists of 𝐾
^ integer-valued I/Q-samples 𝑦𝑟𝑎𝑤 [𝑘𝑇𝑆 ] with sampling time
𝑇𝑆 ≈ 1 ns= 1/(2𝐵) resulting from bandwidth 𝐵 ≈ 500 MHz for each UWB channel. The
Table 1
Parameters for the DW1000 UWB measurements.
DW1000 parameter value
UWB transmission band channel 1 𝐵𝑇,1 [3.25, 3.75] GHz
UWB transmission band channel 2 𝐵𝑇,2 [3.75, 4.25] GHz
UWB transmission band channel 3 𝐵𝑇,3 [4.25, 4.75] GHz
pulse repetition frequency 64 MHz
preamble length 128
preamble acquisition chunk size 8
Tx and Rx preamble code 9
data rate 6.8 MBit/s
recorded Rmarker indicates the beginning of the received signal in the 𝐾 ′ -sized sample set. The
received signal starts with the sample indicated by the Rmarker, therefore, a total of 𝐾 samples
of the received signal are available leading to 𝑦𝑟𝑎𝑤 [𝑘𝑇𝑆 ], 𝑘 = 0, ..., 𝐾 − 1.
Figure 5: Pre-processing of the DW1000 Received Signals.
Figure 5 depicts the magnitude of an exemplary raw received signal |𝑦𝑟𝑎𝑤 [𝑘𝑇𝑆 ]| in the
baseband at center frequency 𝑓𝑐 = 0, with bandwidth 𝐵 (sampled signal shown with black
dots). We interpolate all 𝐾 samples by convolution with a sinc-function with zero-crossings of
distance 𝑇𝑠𝑖𝑛𝑐 = 1/(2𝐵) = 𝑇𝑆 [13]. This fulfills the Nyquist-Shannon sampling criterion. The
resulting interpolated signal 𝑦𝐼𝑃 (𝑡) is shown in Figure 5 (red line)
𝐾−1
∑︁ sin(𝜋 · 𝑡/𝑇𝑆 )
𝑦𝐼𝑃 (𝑡) = 𝑦𝑟𝑎𝑤 [𝑘𝑇𝑆 ] · · 𝛿(𝑡 − 𝑘𝑇𝑆 ). (3)
𝜋 · 𝑡/𝑇𝑆
𝑘=0
The DW1000 also provides the power 𝐴𝑅𝑋 of the received signal to reconstruct the real
received amplitude of the received signal simply by multiplying the signal. Also, a phase
offset 𝜑0 is included in every measurement. This offset is extracted by setting the phase at a
self-defined time-stamp 𝑇0 to zero. Additionally, the signal is time-shifted by 𝜏0 to include the
TWR distance estimation 𝑑0 and align the signal echo in time. As we record 𝑀 measurements
with the identical setup at the same position, we are able to average these measurements after
normalization with 𝐴𝑅𝑋 and phase correction by 𝜙0 (𝑇0 ) to determine 𝑦𝐵𝐵 (𝑡):
𝑀 −1 √︀ 𝑚
∑︁
𝑦𝐵𝐵 (𝑡) = 𝑚
𝑦𝐼𝑃 (𝑡 − 𝜏0 ) · 10(𝐴𝑅𝑋 /10) · exp(−𝑖 · 𝜙𝑚
0 (𝑇0 )), (4)
𝑚=0
with 𝑀 measurements 𝑚 = 0, ..., 𝑀 . The magnitude of the resulting signal |𝑦𝐵𝐵 (𝑡)| is shown
in Figure 5.b) (red line). Finally, we shift the baseband signal to the transmission band at the
measurement center frequency 𝑓𝑐,𝑘 = {3.5, 4.0, 4.5} GHz where 𝑘 = 1, 2, 3 is the UWB channel
𝑦𝑘 (𝑡) = 𝑦𝐵𝐵 (𝑡) · exp(𝑖 · 2𝜋 · 𝑓𝑐,𝑘 · 𝑡). (5)
The reconstructed received signal is shown in Figure 5.b) (blue line). In previous work [10],
we assembled signals on distinct transmission bands from the same measurement environment
to create a larger transmission bandwidth 𝐵𝑎 > 𝐵. The DW1000 provides measurements on
the transmission bands 𝐵𝑇,1 , 𝐵𝑇,2 , 𝐵𝑇,3 , which are neighboring bands each with a bandwidth
𝐵 = 500 MHz. The assembled received signal 𝑦𝑎 (𝑡) is [10]:
3
∑︁
𝑦𝑎 (𝑡) = 𝑦𝑘 (𝑡), with bandwidth 𝐵𝑎 = 1.5 GHz (6)
𝑘=1
Figure 6: Measured and pre-processed UWB signals 𝑦1 (𝑡),𝑦2 (𝑡) and 𝑦3 (𝑡) of transmission bands
𝐵𝑇,1 , 𝐵𝑇,2 , 𝐵𝑇,3 and the assembled 𝑦𝑎 (𝑡) of one tag position 𝑃𝑇 .
Figure 6 shows the three processed received signals at one tag position as well as the resulting
assembled received signal. We determine the assembled received signal for each tag position as
an input for the peak detection algorithm depicted in the next section.
3.2. MPC Estimation and Real CIR-vector Measurements
After processing our measurements for MPC detection, we will briefly introduce our modified
peak detection algorithm, which evolves based on our previous work [10].
Algorithm 3: Modified pseudo-code for MPC detection from previous work [10].
Data:
received signal 𝑦𝐼𝑡 (𝑡) = 𝑦𝑎 (𝑡) ; amplitude-threshold: 𝑎𝑡 ∈ R+ ;
MPC-threshold:𝐼𝑡 ∈ N ; counter: 𝑐 ← 1;
′ ^ ′
1 while ∄ 𝑐 : |a[𝑐 ]| < 𝑎𝑡 OR 𝑐 ⩽ 𝐼𝑡 do
2 𝑦𝑐𝑜𝑛𝑣 (𝑡) = 𝑦𝐼𝑡 (𝑡) * 𝑥(−𝑡);
3 𝜏^[𝑐] ← arg max(𝑦𝑐𝑜𝑛𝑣 (𝑡));
𝑡∈R+
4 𝑤𝑐 (𝑡) = 𝑥(𝑡 − 𝜏^[𝑐]);
]︀𝑇
= 𝑤 [𝑘𝑇 ]𝑇 , ..., 𝑤𝑐 [𝑘𝑇𝑆 ]𝑇 , 𝑘 ∈ N;
[︀
5 w
⎡ 𝑐𝑚𝑏 ⎤ 1 𝑆
^[1]
a
⎢ .. ⎥ [︀ 𝑇
]︀−1
6 ⎣ . ⎦ = w𝑐𝑚𝑏 · w𝑐𝑚𝑏 × [w𝑐𝑚𝑏 · 𝑦[𝑘𝑇𝑆 ]𝑇 ];
a^[𝑐]
7 𝑐 = 𝑐 + 1; ∑︀𝑐
8 ^[𝑖] · 𝑥(𝑡 − 𝜏^[𝑖]);
𝑦𝐼𝑡 (𝑡) = 𝑦𝑎 (𝑡) − 𝑖=1 a
9 end
For MPC detection, we use the algorithm depicted in 3. We correlate the transmit signal
𝑥(𝑡) with the assembled received signal 𝑦𝑎 (𝑡) to find the most likely position of 𝑥(𝑡) in 𝑦𝑎 (𝑡).
Afterward, we calculate the corresponding amplitudes a ^ of all determined signal echos and
subtract them from the overall received signal. This is calculated iteratively until either one
of the calculated signal echo amplitudes a ^ falls below a self-set amplitude-threshold 𝑎𝑡 . We
modified the code so that also the number of detectable MPCs is limited to 𝐼𝑡 . Then the set of
estimated MPCs with delay 𝜏^ and amplitude a ^ form our measured CIR ℎ𝑚𝑒𝑎𝑠 (𝑡) as shown in (1).
In prior work, we elaborated that a larger bandwidth decreases the minimum delay difference
Δ𝜏 between two MPCs required for successful MPC detection with the given algorithm. In
our case with bandwidth 𝐵𝑎 = 1.5 GHz, we determined a minimum distance of Δ𝜏 = 0.78 ns.
Furthermore, this minimum distance is used for defining the bin width for conversion of the
CIR-vectors Δ𝑏𝑖𝑛 = Δ𝜏 = 0.78 ns. In Algorithm 1, we convert the estimated CIR ℎ𝑚𝑒𝑎𝑠 (𝑡) to
the measured CIR-vector h𝑚𝑒𝑎𝑠 . An exemplary comparison for MPC detection of an assembled
received signal with the modeled CIR including the resulting CIR-vectors is shown in Figure 7.
In this section, we focus on (pre-)processing of the measurement and extracting the MPC
estimations from it. In the following section, we evaluate the localization system.
4. Accuracy and Ambiguity of SALOS
After introducing the single tools of SALOS, our proposed localization system, we will now
evaluate the accuracy of the system. Additionally, one of the main aims of SALOS is to reduce
the demand for external information to ensure unambiguity of the mapping from CIR-vector
h𝑃𝑇 to position 𝑃𝑇 . In the first part of this section, we describe our evaluation setup with our
general algorithmic order. Then, we will present the results.
Figure 7: Example of comparison for measured h𝑚𝑒𝑎𝑠 and modeled h𝑚𝑜𝑑 for a position estimation.
4.1. Measurement Setup with Optimal Anchor Positioning
Figure 8: Grid of the evaluation setup.
For the evaluation of SALOS, a suitable test environment must be selected. In order to validate
the algorithm of the system, this environment should be clearly assigned to the simulated
multipath propagation. On the one hand, the success of the system evaluation depends on a
small and distinct number of reflectors and therefore reflections. However, a small number of
reflectors reduces the ability to characterize the paths and thus the tag positions at suboptimal
places. Also, the choice of reflector material significantly affects the reflected signal energy of
the echoes and thus the received signal. While perfect reflectors do not exist in all environments,
this optimizations enables the evaluation focus on the system itself independent from bad
reflection behavior. The knowledge gained in the chosen optimal scenario is taken into account
when installing the system in a more complex scenario in the future.
For performance evaluation, we choose an advantageous setup. we set up an outdoor mea-
surement grid sketched in Figure 8. The environment includes two metal garage doors (red lines)
and the ground as reflectors resulting in three reflecting surfaces for the multipath propagation.
The grid consists of 48 grid points with a distance of 0.5 m to the walls and a spacing of 0.7 m
between the single points. One grid point is the position of the anchor 𝑃𝐴 , the remaining 47
points are tag positions {𝑃𝑇 }. The anchor and tag are placed at a fixed height of 1.5 m.
Figure 9: Block diagram of SALOS.
Figure 9 depicts the block diagram of SALOS. According to 2.1 and 2.3, we modeled the
multipath propagation in this environment and determined the optimal anchor position at
𝑃𝐴 = [2.6, 1.9] m with an effective length of 𝑙𝑒 = 33 · Δ𝑏𝑖𝑛 = 25.74 ns. Based on this optimal
anchor position, we converted the modeled CIRs {ℎ𝑚𝑜𝑑 (𝑡)} for all 47 tag positions into CIR-
vectors h𝑚𝑜𝑑 . The tag is placed at {𝑃𝑇 }. At every position, we record 𝑀 = 100 received
signals for each transmission band 𝐵𝑇,1 , 𝐵𝑇,2 and 𝐵𝑇,3 with Qorvo’s Decawave DW1000. The
radio settings of the DW1000 are found in Table 1. Each set of measurements is processed and
assembled to construct 𝑦𝑎 (𝑡) as described in Section 3.1. Afterward, we estimate the MPCs with
Algorithm 3 and convert the resulting CIR estimate ℎ𝑚𝑒𝑎𝑠 (𝑡) to the CIR-vector h𝑚𝑒𝑎𝑠 . For this,
we set the amplitude threshold of the MPC detection algorithm empirically to 𝑎𝑡 = 0.1 of the
maximum amplitude of the individual received signal.
We apply the similarity metrics of Section 2.4 to calculate the difference between one mea-
surement CIR-vector h𝑚𝑒𝑎𝑠 with the modeled CIR-vectors of all positions {h𝑚𝑜𝑑 }. For position
estimation, we finally compare the results of the similarity metrics among themselves. We
define the minimum difference of metric results to indicate the most probable tag position 𝑃^𝑇:
^ 𝑇 = arg min 𝑑(h𝑚𝑒𝑎𝑠 , h𝑚𝑜𝑑 ).
𝑃 (7)
{𝑃𝑇 }
4.2. Evaluation of Accuracy and Ambiguity of SALOS
To evaluate the accuracy, we define two evaluation cases for position estimation. In the first
case, we take the CIR-vectors of all 47 positions and determine the position 𝑃
^ 𝑇 as described
above based on the similarity metric. In the second case, we perform a pre-selection for the
modeled CIR-vectors before comparing them with our measured CIR-vector. The selected
vectors have a similar distance to the anchor as the measurement. This selection removes
improbable tag positions before estimation which is increasing the accuracy and reduces the
overall processing time of SALOS. All CIR-vectors with a distance 𝑑0 ± Δ𝑑, where 𝑑0 is the
distance of the measurement determined by the TWR, are included in this selection. Due to the
standard deviation of the TWR, we define Δ𝑑 = 0.2 m.
Even though a correct position is estimated for one measurement, Eq. 7 may result in a set of
positions with an identical output of the similarity metric leading to ambiguities for the position
estimation. So, for both approaches, we determined the number of correct position estimations,
as well as the number of correct and unambiguous position estimations.
Figure 10: Results of the Evaluation
a) Unambiguous and ambiguous correct position estimations - for all 47 positions and for pre-selected
positions with similar distance 𝑑0 ± Δ𝑑.
b) Ambiguity of position estimations for sliding window metric with pre-selected positions.
Figure 10 a) depicts the localization results for both approaches. The accuracy of SALOS is
depending on the choice of the similarity metric. For the first approach considering all modeled
CIR-vectors for position estimation, the sliding window results in the highest localization
accuracy of 53%. Also, our self-developed advanced ℓ1-norm, achieves a suitable accuracy of
51%, while the ℓ1-norm results in an accuracy of 49%. The second approach, that only considers
a pre-selected set for position estimation increases, as expected, the accuracy of all metrics
drastically. The best result is achieved with the ℓ1 sliding window metric and an accuracy of
70%.
Measurement inaccuracies lead to a shifting of the MPCs to the CIR-vectors, even though
these MPCs are detected correctly. The similarity metric needs to handle these mistakes to result
in correct position estimation. While the ℓ1-norm is prone to these mistakes, our advanced
ℓ1-norm performs better.
Also, the number of unambiguous position estimations is shown in Figure 10 a) for all metrics
in both approaches. Here, again, the sliding window metric results in the highest number of
correct unambiguous position estimations. The pre-selection approach maximizes this number
with 55%. Our advanced ℓ1-norm performs suboptimal (16% for the first and 40% for the
pre-selection approach). It needs to be improved in the future.
Figure 10 b) shows the ambiguity of single position estimations. It depicts the number of
estimates for the sliding window in the pre-selection approach. The value displayed is the
number of correct position estimations divided by the number of all position estimations for the
exact position. E.g. 0.5 = 1/2 results in a correct estimate, but with another incorrect estimate
forming the set of estimates.
We see that on the right-hand side of the setup (without reflecting surface) as well as for
positions quite close to the reflectors some positions are not estimated correctly. Positions close
to the reflectors lead to reflection paths with similar path lengths to the LOS with 𝑑0 , which
increases the difficulty of the MPC detection algorithm.
Although some positions are confused, no structured regularities for the ambiguities emerge.
We introduce the assessment of ambiguity 𝐴𝑎𝑚𝑏 to quantify the capability of similarity metrics to
decrease the demand for external information. 𝐴𝑎𝑚𝑏 results from calculating the average of all
(partly) correct estimate results. From Figure 10 b) follows: 𝐴𝑎𝑚𝑏 = (26 · 1 + 7 · 0.5)/33 = 0.89.
Table 2 lists the position estimation accuracy as well as 𝐴𝑎𝑚𝑏 for all six given setups.
Table 2
Assessment of ambiguity 𝐴𝑎𝑚𝑏 for all metrics.
Setup accuracy 𝐴𝑎𝑚𝑏
ℓ1-norm - all positions 49% 0.67
ℓ1-norm - pre-selected positions 60% 0.80
advanced ℓ1-norm - all positions 51% 0.61
advanced ℓ1-norm - pre-selected positions 66% 0.77
ℓ1 sliding window - all positions 53% 0.85
ℓ1 sliding window - pre-selected positions 70% 0.89
The assessment of ambiguity 𝐴𝑎𝑚𝑏 is independent of the localization accuracy. It is increased
by pre-selecting positions for position estimation. For SALOS, the ℓ1 sliding window metric
maximizes 𝐴𝑎𝑚𝑏 with 0.85 and the localization accuracy of 53% for all positions and respectively
to 0.89 and the localization accuracy of 70% for pre-selected positions.
5. Conclusion and Future Work
In this paper, we introduced SALOS a single anchor localization system based on COTS hardware.
We combined our previous theoretical and basic results into a complete solution. For a setup of
47 grid points, we achieved 70% of correct position estimations based on our measurements
in the best case. The advantage of SALOS compared to other solutions is that we modeled the
environment and the expected CIRs. We solely used the measurements of the UWB signals
and estimated the position based on filter and processing algorithms without the need for
fingerprints or additional external information or filters.
In the future, we will implement SALOS as online real live localization system and extend
the solution to adjust for a dynamic multipath environment. For this, we will choose a more
complex indoor environment including also suboptimal reflectors. Based on the setup and the
results of the optimally chosen measurement setup of this work, we will make a statement
about the position accuracy of the system to compare it with other localization approaches, like
UWB systems with two and more anchors.
Acknowledgements
This publication results from research of Center of Excellence CoSA at the Technische Hochschule
Lübeck and is funded by the Federal Ministry of Economic Affairs and Energy of the Federal
Republic of Germany (Id 03SX467B, Project EXTENSE, Project Management Agency: Jülich PTJ).
Horst Hellbrück is an adjunct professor at the Institute of Telematics of University of Lübeck.
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