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Fingerprinting-Assisted UWB-based Localization
Technique for Complex Indoor Environments
Sandra Djosic, Igor Stojanovic, Milica Jovanovic, Tatjana Nikolic, Goran Lj. Djordjevic
University of Nis, Faculty of Electronic Engineering, Aleksandra Medvedeva 14, 18000 Nis Serbia
Abstract
Among the numerous radio-based solutions for indoor localization, ultra-wideband (UWB) technology
is of particular interest due to its signal characteristics. The wide bandwidth of the UWB signal provides
a fine time resolution of the transmitted pulses that enables a centimetre-level ranging accuracy under
line-of-sight (LOS) conditions even in multipath intensive indoor environments. Nevertheless, it is still
a challenge to implement accurate UWB-based localization in complex multi-room indoor
environments at low cost because of a large number of static UWB anchors that may need to be
deployed in order to provide an adequate LOS coverage in every segment of the environment.
Therefore, there is a strong interest in developing UWB-based localization techniques that will provide
acceptable accuracy under partially LOS coverage conditions. In this paper, we present a novel hybrid
method that combines two conventional localization techniques, trilateration and fingerprinting, to
address the problem of cost-effective UWB-based localization in complex indoor environments. With
the proposed method, the target location is determined by a trilateration algorithm, while a
fingerprinting-based algorithm is used to provide additional distances for trilateration in cases when
there is an insufficient number of available LOS measurements. The additional distances are generated
by a non-parametric regression algorithm that relies on a fingerprint database to map all available online
range measurements (LOS as well non-LOS) to distances between the target and the set of pre-defined
reference points. To minimize human effort in fingerprint collection, the indoor environment is site-
surveyed in a room-by-room fashion with auxiliary UWB anchors temporarily placed at up to three
reference points in the surveyed room. The method is validated through an extensive indoor
measurement campaign with commercially available UWB transceivers. The experimental results show
that the proposed method achieves sub-decimetre level localization accuracy under typical real-world
conditions.
Keywords: Indoor localization, ultra-wideband, fingerprinting, trilateration, machine learning
1 Introduction
The task of an indoor localization system (ILS) is to determine and track the location of a
person or an object in a closed indoor environment. In recent years, ILSs have attracted
considerable research interest due to their potential to significantly impact everyday life in the
near future. Application areas include health, industry, disaster management, building
management, surveillance, and many more (Zafari et al., 2019; Bergeron2018). Of particular
interest are radio signal-based ILSs, e.g., Wi-Fi, Bluetooth low energy (BLE), and ultra-
wideband (UWB), because radio transceivers are built at small form factors with low power
consumption, and can be integrated into existing devices (Farid et al., 2013; Davidson & Piché,
2016; Velimirovic et al., 2012; Belmonte-Fernandez 2018). Such systems typically consist of
a set of anchor nodes (ANs), placed at fixed locations in the area of interest, and a target node
(TN) carried by the person or attached to the object that needs to be localized. The location of
the TN is estimated by a localization algorithm, which interprets some physical parameters
obtained from received radio signals (Liu et al., 2007). However, despite many localization
technologies and techniques available today, the design and deployment of radio signal-based
ILS is still a challenging task, especially in indoor environments of complex geometry
(multiple rooms, rooms of irregular shapes, doors, corridors, presence of obstacles, etc.), which
are characterized by radio signal attenuation, presence of different interfering signals, and harsh
multipath conditions (Kaemarungsi & Krishnamurthy, 2012).
Nowadays, UWB is considered the most promising radio-based ILS technology for harsh
environments and accuracy-critical applications (Alarifi et al., 2016; Ruiz & Granja, 2017;
Tiemann et al., 2015). The most important characteristic of the UWB radio technology is the
large bandwidth in comparison with prevalent narrowband systems (e.g., Wi-Fi, and BLE).
One result of the large bandwidth is that due to the inverse relation between the time of flight
(TOF) estimation error and signal bandwidth, the distance between two UWB devices can be
measured with centimetre-level accuracy, even in multipath intensive indoor environments
(Zwirello et al., 2014; Zhang et al., 2009). With accurate distance information to at least three
ANs at disposal, the location of the TN can be estimated with a sub-decimetre level accuracy
by applying standard trilateration techniques. Note that the high localization accuracy
is essential for many ILS applications such as precise target tracking, and manoeuvring of a
robot in tight spaces (e.g., when passing through a doorway). Because of large bandwidth,
UWB is also resilient to multipath interference and fading and can pass through obstacles and
penetrate walls in buildings, thus enabling non-line-of-sight (NLOS) communication and
ranging. However, high localization accuracy is attainable only under the LOS operating
conditions. With the absence of the LOS path, the transmitted signal could only reach the
receiver through penetrated, reflected, diffracted, or scattered paths, called NLOS paths.
Signals propagating in NLOS conditions are usually delayed and attenuated, which introduces
a positive bias in TOF-based ranging and can significantly degrade the performance of the
UWB localization system (Ferreira et al., 2017).
In general, there are two approaches to how UWB localization is applied in complex multi-
room indoor environments. The first one is the deployment of a sufficiently large number of
ANs in order to provide LOS paths to at least three ANs in every part of the indoor
environment. At the run-time, the localization system identifies and discards NLOS
measurements, and uses only LOS measurements for location estimation (Gururaj et al., 2017;
You et al., 2015). By using only LOS measurements, this full LOS coverage deployment
strategy ensures consistently high localization accuracy over the entire coverage area, but it
may incur a high system cost in indoor environments of complex geometry (e.g. houses or
office buildings with many rooms and/or rooms with irregular shapes). Therefore, in this paper,
our focus is on the second approach, which relies on a partial LOS coverage deployment
strategy to trade-off localization accuracy for a significant saving in system cost. With the
partial LOS coverage, a simple identify-and-discard approach of handling NLOS
measurements is not adequate because the removal of NLOS measurements may leave the
localization system with an insufficient number of distance measurements to perform spatial
localization. Instead, all available measurements (LOS as well as NLOS) should be used for
location estimation. One approach is to first identify NLOS measurements, and then employ a
suitable error mitigation technique to improve the accuracy of NLOS ranges before being used
by a localization algorithm (Khodjaev et al., 2010; García et al., 2015). The location
fingerprinting is another widely adopted data-driven technique for UWB localization under
mixed LOS/NLOS conditions, which usually involves two phases. The offline training phase
consists of building a fingerprint database with location signatures, also called fingerprints,
based on location-dependent received signal parameters (e.g., signal time-of-flight, channel
impulse response (CIR), and received signal strength (RSS)), which are collected at a number
of locations in the area of interest. Then, in the online phase, any observed fingerprint is
compared against the ones stored in the fingerprint database to infer the location of the TN.
The major advantage of the fingerprinting-based methods is that they can provide accurate
location estimations in the challenging multipath environments without requiring the existence
of LOS paths between the TN and ANs, nor an analytical characterization of the relation
between the signal parameters and the TN’s location. However, the task of building the
fingerprint database is usually very labour-intensive and time-consuming, involving substantial
human efforts in providing accurate ground truth location information for each collected
fingerprint. Moreover, the fingerprint database should be updated timely to reflect
environmental changes, which may incur a high maintenance cost.
In this paper, we propose a practical and cost-effective fingerprinting-assisted UWB-based
localization (FAUL) method, which offers high accuracy in multi-room indoor environments
with a reduced number of ANs. The primary goal of the proposed method is to provide a near
LOS localization accuracy in partially LOS covered indoor scenarios. To this end, FAUL
employs a hybrid localization scheme, which combines a trilateration algorithm with location
fingerprinting. The TN location is determined by a weighted trilateration algorithm, while a
fingerprinting-based algorithm is used to provide additional distances for trilateration in cases
when less than three TN-to-AN LOS measurements are available. FAUL distinguishes from
traditional fingerprinting-based approaches in that it uses different anchor configurations
during the offline and online phases. During the offline phase, a set of permanently-installed
ANs is temporarily extended with a set of auxiliary ANs that are strategically distributed
throughout the surveying-area to form a full LOS coverage configuration. With such a setup,
the fingerprint database is built by only taking UWB-measured TN-to-AN distances, avoiding
the need for manual labelling individual fingerprints with ground truth coordinates. In this
manner, a large indoor area can be site-surveyed automatically in a relatively short amount of
time, producing a dense fingerprint database. In the online phase, when only permanent ANs
are present, the fingerprint database is used to predict distances between TN and the points
where auxiliary ANs were placed during the offline phase. The predicted distances are then
used as additional distances for trilateration when needed.
The real-world data used in this paper were collected in a measurement campaign that was
carried out in a multi-room residential apartment. In the experiments, we used six permanent
UWB anchors distributed throughout the five rooms to explore how the FAUL localization
performance depends on fingerprint density and the number of available LOS measurements.
The results validate our overall localization strategy and demonstrate that the FAUL method
can achieve sub-decimetre level localization accuracy under typical real-world conditions
allowing significant saving in the number of deployed ANs.
The remainder of this paper is structured as follows: In Section 2, we summarize related studies
on radio signal-based indoor localization. The proposed algorithm is presented in Section 3.
We start with the localization setup, anchor deployment strategy, and an outline of the
underlying ranging protocol. Then, we present detailed descriptions of the offline training and
online localization phases of the proposed localization method. The experimental results are
presented in Section 4, and Section 5 provides conclusions.
2 Related works
The last decade has witnessed tremendous efforts at building small, medium, and large-scale
ILSs using various radio signal-based technologies, especially using Wi-Fi, and more recently
BLE and UWB (Gu et al., 2009; Liu et al., 2007). The following two general localization
strategies are commonly used for designing ILSs: i) the range-based localization, which
assumes the existence of a ranging mechanism relating distance to observed signal parameters,
and ii) the fingerprinting-based localization, which relates an observed set of signal parameters
to ones at known locations. As narrowband communication and multipath propagation make
precise ranging extremely challenging in indoor environments, most Wi-Fi ILSs follow the
fingerprinting approach, usually based on RSS signal vectors (Bahl & Padmanabhan, 2000;
Huang et al., 2019; Stella 2014). Significant research has been devoted to the online phase,
aiming to improve the localization accuracy using either deterministic or probabilistic
algorithms to match the online fingerprint with those in the fingerprint database (He & Chan,
2015). With deterministic algorithms, the TN is located at the closest fingerprint location in the
RSS space, using a suitable similarity metric for fingerprint comparison (e.g., Euclidean
distance, and cosine similarity). Deterministic methods can be implemented using a variety of
machine learning algorithms, e.g., k-nearest neighbours (kNN) (Bahl & Padmanabhan, 2000),
the support vector machine (Cai et al., 2015), and the decision trees (Banitaan et al., 2016),
with usually low computational complexity. With probabilistic algorithms, RSS values are
represented as a probability distribution, and the algorithm calculates the probability of a TN’s
location based on the online measurements and fingerprint database (Sciarrone et al., 2016;
Zhao et al., 2019). Probabilistic techniques are computationally more expensive than
deterministic techniques but provide higher accuracy and robustness to missing or incomplete
data (Bisio et al., 2013).
The main advantages of the UWB radio technology are the high temporal resolution, and the
capacity of resolving individual multipath components, which enables accurate indoor ranging.
Therefore, the UWB-based ILSs usually employ range-based localization techniques,
especially in small-scale systems where full LOS coverage can easily be attained with a small
number of deployed ANs. The range-based methods also involve two phases. In the ranging
phase, TN-to-ANs distances are estimated based on time delay information of the received
radio signal, which is typically made available by UWB hardware (DecaWave, 2018). In the
localization phase, with a sufficient number of distance estimates at disposal, a trilateration or
multilateration algorithm is used to compute the TN’s location (Yan et al., 2013). However,
reaching a high localization accuracy under predominantly NLOS conditions in complex large-
scale indoor environments requires more elaborate methods, which often involves
fingerprinting. To cope with the presence of NLOS induced ranging errors, the TN’s location
can be estimated using the conventional fingerprinting approach (Luo & Gao, 2016; Steiner &
Wittneben, 2009; Yu et al., 2011), or a fingerprinting scheme can be integrated within a range-
based technique for identifying NLOS measurements (Caso et al., 2018), and/or estimating the
NLOS ranging errors (Guvenc et al., 2007a; Guvenc et al., 2007b). Instead of RSS
measurements, UWB fingerprints typically include either range estimates (Bogdani et al.,
2016; Song et al., 2017) or multiple location-dependent features extracted from the channel
impulse response (CIR) (Dardari et al., 2009; Luo J 2016). The CIR-based UWB fingerprinting
improves localization accuracy at the expense of the increased size of the fingerprinting
database.
The main challenge in both Wi-Fi and UWB fingerprinting methods is the construction of a
fingerprinting database, which can be time and cost-prohibitive for large-scale environments if
the ground truth coordinates are determined manually. The problem is particularly severe in
the case of UWB-based localization, in which a dense fingerprint database is essential to
achieve the high expected localization accuracy. Several methods have been proposed to reduce
the site-survey effort. An approach is to reduce the number of survey points, and then apply
interpolation and extrapolation methods to recover missing fingerprint data (Talvitie et al.,
2015; Chai & Yang, 2007). Methods for fingerprint database construction by unsupervised
learning and crowdsourcing have also been proposed (Chintalapudi et al., 2010; Yang et al.,
2012). However, by trading-off the localization accuracy for survey cost, these methods are
often insufficient for applications with high accuracy requirements. In (Prorok & Martinoli,
2014), offline fingerprints are collected by a mobile robot equipped with a UWB tag. During
the training phase, fingerprints are labelled with ground truth coordinates obtained by
accurately tracking the robot position with an overhead camera system. Although this approach
allows for the fast construction of a high-density fingerprint database, its practicality is limited
by the cost of the external high-precision reference localization system.
The UWB-based localization strategy we propose in this work follows the general
fingerprinting-based approach, as it relies on the offline fingerprint measurements to improve
the localization accuracy during the online phase. One of the unique features of the proposed
method is that it offers a simple solution for improving the productivity of the training phase.
Our proposed FAUL method avoids manual labelling of the offline fingerprints with ground
truth coordinates by using a few auxiliary UWB ANs, rather than deploying a costly full-
featured external localization system as in (Prorok & Martinoli, 2014). Another unique feature
of the proposed FAUL method relates to how the fingerprint database is used in the online
phase. Different from other fingerprinting-based approaches, FAUL utilizes the fingerprint
database to predict the ranging responses of the auxiliary ANs, and then uses the predicted
ranges for trilateration whenever less than three LOS distance measurements are available. In
this study, we are also focused on investigating the accuracy implication of using auxiliary
UWB ANs for system training. To avoid biasing the results with the impact of advanced
fingerprinting-related implementation options (e.g. probabilistic fingerprinting, the use of CIR
parameters, and advanced machine learning algorithms), we chose to adopt a deterministic
kNN-based fingerprinting scheme, in which the UWB-measured distances are used as location
signatures.
3 Fingerprinting-assisted UWB-based indoor localization
3.1 Localization setup
The proposed FAUL indoor localization scheme addresses the mobile TN localization problem
in multi-room indoor environments using UWB-enabled devices. Although it can be adapted
to numerous application scenarios, in this paper we present the FAUL localization scheme
within the context of a system for real-time 2D localization of an autonomous domestic service
robot. We assume a single robot operating within a typical multi-room residential apartment.
The FAUL infrastructure includes: a) a set of anchor placeholders, b) a set of ANs, c) single
TN, and d) a location server. Anchor placeholders (APs) are installed at fixed and known
positions in the apartment, and each placeholder is assigned a unique identifier (ID) in the range
, where is the number of placeholders deployed. ANs are designed to be easily
inserted into and removed from APs. ANs do not have pre-assigned IDs, but each AN takes
over the ID of the AP in which it is inserted. The TN is attached to the robot and periodically
performs UWB ranging to all ANs. The measured distances are collected by the TN and then
sent to the location server, which executes the localization algorithm to obtain the estimated
location of the TN.
3.2 Anchor deployment
FAUL requires a specific AP deployment strategy in order to achieve acceptable localization
accuracy at minimum cost. Fig. 1 shows an exemplary deployment of APs within a five-room
apartment. There are two types of APs, represented by red-filled and white boxes. The primary
APs (red boxes) are dedicated to permanent ANs, i.e. those ANs that remain permanently
inserted into their placeholders, except in a case of failure or system reconfiguration. The
secondary APs (white boxes) are for auxiliary ANs, which are used during the offline training
phase, only.
The APs are deployed in two steps. In the first step, the user defines locations of primary APs.
FAUL requires that each point in the localization space is covered by at least three permanent
ANs. A point is covered by an AN if the successful (LOS or NLOS) ranging between the AN
and TN located at that point can be performed with a high probability. Because the UWB signal
can penetrate walls, one primary AP per room is usually sufficient to provide the required
permanent AN coverage in a typical deployment scenario. For example, point in Fig. 1 is
covered by four permanent ANs: 1, 2, 3, and 4. It is LOS-covered by ANs 1 and 2, and NLOS-
covered by ANs 3 and 4. The remaining two ANs, 5 and 6, are too far or obstructed by several
walls preventing reliable ranging with a TN located at point.
Fig. 1 The map of experimental environment. Red boxes denote primary, while white boxes denote
secondary anchor placeholders.
In the second deployment step, the user adds secondary APs in order to improve LOS coverage
to the level required for the offline training. The locations of secondary APs are chosen in a
way so that each point in the localization space is LOS-covered by at least three
primary/secondary APs. To this end, the user first divides the localization space into zones.
Typically, a zone corresponds to a room, although the rooms with irregular shapes can be
subdivided into two or more smaller zones. Then, the user adds and arranges secondary APs
so that all points in the same zone are LOS-covered by the same set of three primary/secondary
APs. The set of three APs that provide LOS coverage in a zone is referred to as LOS-set of that
zone. The LOS-sets do not have to be mutually disjoint, i.e., the same AP can provide LOS
coverage in more than one neighbouring zones. We say that a zone is -PLOS covered if among
three APs that provide LOS coverage in the zone there are primary APs (and secondary
APs). After the deployment phase, the deployment-related parameters are stored in the
configuration database. These parameters include: a) information about APs, their roles
(primary or secondary) and locations within the environment, and b) LOS-sets of all zones.
For example, each room in Fig. 1, except rooms and , constitutes a zone, whereas rooms
and are divided into two zones each. Note that only two secondary APs are sufficient to
provide LOS coverage in both zones of room . APs 7 and 8 together with primary AP 1 form
LOS-set of zone , while the same two secondary APs and primary AP 2 form LOS-set of
zone . LOS-sets of all zones are listed in the table in Fig. 1. Identifiers of primary APs in
LOS-sets are written in bold. As can be noticed, zone is the only zone with 2-PLOS coverage
in this deployment. The LOS-set of zone includes secondary APs, only. The remaining
zones are 1-PLOS covered. There is no 3-PLOS covered zone in this deployment.
3.3 Ranging protocol
The distance between two UWB radio transceivers is commonly estimated by carrying out the
alternative double-sided two-way ranging (AltDS-TWR) method (Neirynck et al., 2016). As
shown in Fig. 2, AltDS-TWR is a TOF based method, which requires exchanging of three
messages (Poll, Response, and Final) between an initiator (node ) and a responder (node ).
During the message exchange, nodes and take timestamps () of receive and send
events on the physical layer using their respective local clocks. The timestamps are then used
to calculate the time of flight, and therefore the distance between nodes and . The time of
flight () is calculated by substituting measured round-trip times (,) and
reply times (,) into the formula (1). Note that the distance is calculated by the
responder node after it receives and from the initiator node .
(1)
Fig. 2 Asymmetric double-sided two-way ranging method
In FAUL, distances between the TN and ANs are obtained through periodic ranging rounds,
where each round involves performing AltDS-TWR ranging between the TN and all ANs in
succession. During the ranging round, the TN calculates and stores distances into the distance
vector. The distance vector consists of elements, and element contains the measured
distance between the TN and th AN, that is, the AN inserted into the AP assigned with an ID
value of. If any AN is either not available or the ranging with the AN was not successful, then
the corresponding element of vector is set to . A ranging round is considered successful if,
at the end of the round, the distance vector contains at least three non-zero distance values. In
the case of the unsuccessful ranging round, the distance vector is discarded by the TN.
Otherwise, the TN sends the distance vector to the location server for further processing.
3.4 Offline training phase
FAUL requires an offline training phase for building fingerprint databases. It is assumed that
the permanent ANs are already inserted in the corresponding primary APs. Additionally, the
user should have at his/her disposal three auxiliary ANs to use during the training phase. The
fingerprints are collected zone-by-zone. Before starting surveying a zone, auxiliary ANs are
inserted into all secondary APs that are included in the LOS-set of that zone. During the zone
survey, the location server is put in an automatic fingerprint collection mode wherein the
ranging rounds are initiated periodically. The distance vectors are collected while the robot is
scanning the area of the zone (e.g. by moving in a rectangular path). The only requirement is
that the robot visits all parts of the zone. After the zone is surveyed, the auxiliary ANs are
moved to the next zone, and the process is repeated. Note that the use of auxiliary ANs during
the zone survey ensures that each collected distance vector will contain at least three LOS
measured distances, which should compensate for the lack of ground truth coordinates of the
TN’s location.
Based on each distance vector received from the TN during the training phase, the location
server creates two fingerprints for inserting into two separate fingerprint databases: the distance
database, and the zone database (Fig. 3). The fingerprints in both databases are labelled with
the zone ID and differ in the location-dependent parameter extracted from the distance vector.
The fingerprint for distance database contains a complete distance vector, i.e. it is defined as a
pair of , where is the zone ID. The fingerprint for the zone database is a pair
of , where is the 2D coarse position of the fingerprint, which is
calculated through the least square-based multilateration algorithm by using measured
distances to permanent ANs, only. The least-square multilateration algorithm finds
fingerprint’s coarse coordinates that satisfy the following minimization problem:
(2)
where is the set of indices of non-zero elements in that correspond to permanent ANs, and
is the known location of AN .
Figure 3 shows how the distance vector taken at point in zone of the apartment in Fig.
1 is processed. In Fig. 3, dots represent valid measured distances, while cross signs indicate
missing values. At point, the TN performed six successful ranging operations, i.e., four with
permanent ANs and two with auxiliary ANs temporary placed into secondary APs 7 and 8. The
complete distance vector is recorded in the distance database. The fingerprint for the zone
database is obtained by applying the multilateration procedure on distance measurements to
four permanent ANs. Note that because of NLOS paths between the TN and permanent ANs 3
and 4, the computed coarse position, , is only a rough estimate of the exact 2D coordinates of
point .
Fig. 3 Fingerprint databases construction procedure
3.5 Online localization phase
During the online localization phase, only permanent ANs are in use, while all secondary APs
are empty. The TN periodically initiates ranging rounds and sends an online distance vector to
the location server after each round. The location server estimates the TN location by using
fingerprint databases in order to improve localization accuracy.
The proposed online localization method is basically a trilateration procedure which is applied
to the measured/estimated distances to three APs in the LOS-set of the zone where the target
node is currently located. The distances for trilateration are obtained through two pre-
processing steps, as illustrated in Fig. 4. In this figure, the online distance vector comes from
the TN located somewhere in the zone of the apartment in Fig 1. In the first step (zone
identification), the zone database is used to identify the zone where the TN is currently in. In
the second step (virtual distance measurement), the LOS-set associated with the identified zone
is first retrieved from the configuration database, and then the distances to three APs in the
LOS-set are determined. The distances to permanent ANs in the LOS-set are taken directly
from the online distance vector, while the distances to secondary APs in the LOS-set are
estimated by using the distance database. Finally, with known distances to three APs at
disposal, the TN’s location is calculated by a trilateration method.
Fig. 4 Overview of the localization algorithm assuming that the online distance vector is taken in
vicinity of point in zone of the apartment in Fig. 1.
3.5.1 Zone identification
To identify the zone, the TN’s coarse position is first calculated by applying the least square-
based multilateration algorithm to all non-zero distances in the online distance vector. Then,
the TN’s coarse position is classified into one of the zones by using well-known -nearest
neighbours (kNN) classification algorithm. With this algorithm, the zone is determined by
majority voting, with the TN’s coarse position being assigned to the zone most common among
its nearest neighbours in the zone database as measured by a distance function. For
application in FAUL, we adopt and Euclidean distance function:
(3)
where, and are coarse positions of TN and fingerprint in zone
database, respectively. Note that the use of coarse positions solves the problem of missing
values that could arise if the Euclidean distance function were applied directly to distance
vectors with different subsets of zero-valued elements. Because of a limited range of UWB
signal in indoor environments, the missing values, i.e. the zero-valued entries in distance
vector, commonly appear. No matter which elements in the distance vector are missing, the
coarse position can always be calculated as long as the number of non-zero elements is greater
than or equal to three.
3.5.2 Virtual distance measurement
Let the TN be located in zone with the LOS_set. If is -PLOS covered, and,
then this algorithm step is skipped, and the measured distances to three permanent ANs in
are passed directly to the trilateration step. Otherwise, if, the missing distances for
trilateration are determined through the process of virtual distance-measurement (VDM).
Given online distance vector, the VDM procedure estimates the most likely distances that
would be measured by auxiliary ANs if they were placed in the corresponding secondary APs
in. In FAUL, the VDM is implemented as a weighted kNN-based regression scheme that
maps the online distance vector to the distances between TN and secondary APs in the.
First, the algorithm finds nearest neighbours comparing and distance vectors of every
fingerprint in the distance database labeled with the zone. For comparison, we use the
Euclidean distance function between and, by taking into account non-zero elements in
both vectors, only:
(4)
where is the set of indices for which . Note that contains measured
distances to primary ANs, only, while additionally contains distances measured by axillary
anchors placed into secondary APs from. After finding nearest distance vectors in
the distance database, the algorithm estimates the distance between TN and each secondary AP
in as a weighted sum of elements that correspond to that AP in the selected neighboring
distance vectors, adopting inverse of as weights.
3.5.3 Trilateration
In the last step of the proposed online localization procedure, distances to three APs in the
LOS-set of the identified zone are used to determine the 2D coordinates of the TN by applying
a trilateration method. The accuracy of the trilateration method depends on the accuracy with
which the three distances are measured/estimated. Obviously, the best localization accuracy
can be obtained in 3-PLOS cases, where all three input distances for trilateration are the result
of UWB ranging with permanent ANs under LOS conditions. On the other hand, localization
under 0-PLOS conditions is the least accurate because of unavoidable distance estimation
errors induced by the VDM procedure. A common characteristic of these two boundary cases
is that all three input distances have roughly the same contribution to the localization accuracy.
This assumption clearly does not hold with 2-PLOS and 1-PLOS scenarios, where the less
reliable VDM estimations are combined with highly accurate UWB measurements. As
illustrated in Fig. 5(a), in 2-PLOS case, the TN is most probably located near one of two
intersection points ( and) of two circles cantered at the permanent ANs inserted in APs 1
and 3. However, the involvement of the third, less accurately estimated distance to secondary
AP 2 in the trilateration process, with equal importance, could easily lead to displacement of
the resulting position away from the exact position. Similarly, in the 1-PLOS case, the most
probable location of the TN is a point on circle cantered at the permanent AN (Fig. 5(b)). The
presence of two less accurate distances could move the resulting location at the point that is
further away or closer to the permanent AN than it is determined by the accurate UWB
measurement.
(a) (b)
Fig. 5 Combining accurately measured distances to permanent anchors and estimated distances to
secondary anchor placeholders can introduce significant localization error in: (a) 2-PLOS, and (b) 1-
PLOS cases. Red boxes denote primary, while white boxes denote secondary anchor placeholders;
cross signs denote estimated locations.
To improve the localization accuracy in 1- and 2-PLOS cases, we adopt the weighted least-
square trilateration method, which allows each input distance to be weighted based upon its
type. The method gives higher weights to measured distances to permanent ANs, versus
estimated distances to secondary APs. In particular, the weighted least-square algorithm finds
the coordinates of the TN that satisfy the following minimization problem:
(2)
where are coordinates of APs in the LOS-set, and are
measured/estimated distances to the corresponding APs. The weights can take
only two different values: for primary, and for secondary APs, where. Note
that in 3-PLOS and 0-PLOS cases, all three weights are of the same value, thus not affecting
the trilateration result.
4 Results and discussion
This section presents an experimental evaluation of the proposed FAUL localization method.
The evaluation was carried out within the experimental testbed platform deployed within
residential apartment whose layout is shown in Fig. 1. The apartment represents a
typical complex indoor environment as it includes several rooms of different shapes and sizes.
The testbed includes eight UWB nodes: seven ANs and one TN. The hardware design of UWB
nodes is based on UWB compliant wireless transceiver DW1000 (DecaWave, 2018), which is
used for both ranging and data communication. ANs are mounted on the walls at pre-specified
positions above the floor. The TN is attached to the top of a tripod in height. We
performed two sets of experiments to evaluate FAUL localization performances. In the first set
of experiments, we examine how accurately FUAL identifies zones. The focus of the second
set of experiments is FAUL coordinate-level accuracy.
4.1 Zone identification results
Accurate zone identification is of crucial importance for the FAUL’s overall localization
accuracy. With an incorrectly identified zone, a wrong LOS-set will be selected for the final
localization, which may cause a considerable localization error. To estimate FAUL’s zone-
level accuracy, we collected distance vectors at a number of locations throughout the apartment
at roughly every. During site-surveying, the user moved the tripod across the apartment
briefly stopping for about seconds at each location to allow the system to complete single
ranging round, collect the measured distances, compute the coarse position and store the
fingerprint into the zone database. A total of fingerprints are collected, with an average
density of (fingerprints per square meter).
Fig. 6 Coarse positions of fingerprints in zone database
Figure 6 plots the coarse positions of all fingerprints in the zone database. The fingerprints
taken in different zones are shown in different colours. The oval symbols on this map represent
unmovable furniture. As can be noticed, the shape of each cluster of same-coloured dots only
roughly matches the shape of the surveyed area within the corresponding zone. In some parts
of the apartment, the dot clusters are skewed or squeezed, while in other parts are stretch and
even cross the zone boundaries. These anomalies are expected since the coarse positions are
calculated through the multilateration of all available TN-to-AN distances, most of which are
measured under NLOS conditions. However, what is important to note is the minimal
overlapping between neighbouring dot-clusters, which represents a prerequisite for accurate
zone identification. Although NLOS propagation degrades coordinate-level accuracy, it
actually useful in the context of zone identification. For example, propagation of the UWB
signal through a typical wall increases the measured distance for about (Dardari
et al., 2008), while reflections may add even a larger positive offset. The positive ranging
offsets make fingerprints on opposite sides of a wall to appear further than they actually are,
leading to a clear separation of fingerprint clusters from adjacent rooms.
Fig. 7 Zone-level accuracy with varying fingerprint density
In order to estimate FAUL’s zone-level accuracy, we randomly select a fraction of the collected
fingerprints for validation and leave the rest in the zone database. By varying the percent of the
collected fingerprints selected for validation, we are able to investigate the influence of the
fingerprint density on the zone-level accuracy. For each validation fingerprint, the zone is
identified using the kNN classification algorithm with. The zone-level accuracy results
are shown in Fig. 7. With a fingerprint density of , zone identification is correct 99.7%
of the time. As expected, the zone-level accuracy decreases with the decrease of fingerprint
density, but it is still above even with the fingerprint density of only. These
results point out that the UWB technology could be an effective solution for floor, room, and
zone identification in complex indoor environments.
4.2 Localization results
The second experiment was carried out in a part of the zone in room of the apartment in
Fig. 1 by collecting distance vectors at a grid of reference points evenly spaced at
apart, as depicted by grey dots in Fig. 8. The survey was carried out with ANs inserted
into all three APs in the LOS_set of zone. At each grid point, ten ranging rounds were
performed, each producing a distance vector containing eight non-zero distances: three to
anchor nodes in the zone (AP 6, 15, and 16) and remaining five to permanent ANs in other
rooms (AP 1,..., 5). Fingerprint for distance database is generated by averaging distance vectors
obtained in the first five ranging rounds. The remaining five distance vectors are also averaged
and the resulting vector is saved into the test database that is used for validation. Ground truth
coordinates of the grid points were manually measured with millimetre level of accuracy and
also recorded. Note that the ground truth information is used only for the evaluation of ranging
and localization errors, and is not supplied to FAUL.
Fig. 8 Measurement grid points for localization accuracy test
We use measured data to analyse FAUL localization performances in four deployment
scenarios: 3-, 2-, 1- and 0-PLOS. The content of the test database is used as a test case for 3-
PLOS scenario. Test cases for the remaining three deployment scenarios are obtained by
modifying the initial test database. To emulate the 2-PLOS scenario, we annul measured
distances to AP 15 in all distance vectors in the test database. With this modification, before
the trilateration step, FAUL will apply VDM to estimate the missing distance to AP 15. For the
1-PLOS test case, in addition to AP 15, distances to AP 16 are also annulled. Finally, the 0-
PLOS test case is created by annulling measured distances to all three APs in zone. We also
tested FAUL performances under different fingerprint densities. We start the evaluation with
the distance database containing the full set of fingerprints, which corresponds to a
fingerprint density of. We then repeated the evaluation using random subsets
comprising, , , and of the full set.
4.2.1 VDM accuracy
The first set of results corresponds to the accuracy of the VDM procedure. For each distance
vector in the test database, VDM error, , was evaluated as the absolute difference between
the actual distance from the corresponding grid point to the AP 6 and the distance to the same
AP as estimated by VDM. The test is repeated for three deployment scenarios (2-, 1-, and 0-
PLOS) and five fingerprint densities. The magnitude and uncertainty of VDM errors are
quantified by Mean Distance Error (MDE), and Root Mean Square Error (RMSE) of. The
results are reported in Table 1. The first row in this table corresponds to UWB ranging with
AN inserted into AP 6 under LOS conditions. The obtained MDE and RMSE values of
and, respectively confirm high ranging accuracy and precision of DW1000
transceiver. As can be noticed in Table 1, at higher fingerprint densities, the estimation error
of VDM is close to that of UWB LOS distance measurement. For example, while estimating
the distance to AP 6 with two ANs inserted in APs 15 and 16 (2-PLOS case), and fingerprint
density of , VDM introduces additional MDE of only compared with the
direct UWB ranging. Even without ANs in zone (0-PLOS case), the MDE of VDM is only
larger than that of UWB ranging. As expected, the VDM accuracy decreases with the
decrease of fingerprint density. As can be seen, under the 0-PLOS condition, a fingerprint
density larger than is required to keep the MDE of VDM smaller than.
However, with at least one AN in the zone (1-PLOS case), a sub-decimetre average
estimation error of VDM is obtained with fingerprint density of only.
Figure 9 shows the Cumulative Distribution Functions (CDFs) of for different fingerprint
densities. The results indicate that for the fingerprint density of VDM attains sub-
decimetre accuracy in more than of the cases in all deployment scenarios. However, when
a relatively sparse distance database with a density of is used, the VDM error is
larger and ranges from more than (in the 2-PLOS scenario) to more than (in the
0-PLOS scenario) in 20% of the cases.
Table 1 VDM error (in cm) for different number of LOS anchor nodes and fingerprint density
Deployment
scenario
Fingerprint density (f/m2)
100
50
25
12.5
6.25
MDE
RMSE
MDE
RMSE
MDE
RMSE
MDE
RMSE
MDE
RMSE
UWB LOS
2.80 / 3.49
VDM 2-PLOS
3.52
4.44
4.80
6.52
6.64
8.79
8.03
10.48
11.04
14.47
VDM 1-PLOS
4.42
5.85
7.00
9.46
9.07
12.15
10.32
13.64
13.45
17.74
VDM 0-PLOS
5.20
6.99
7.80
10.47
10.18
13.37
11.32
14.87
14.04
18.05
(a)
(b)
(c)
(d)
(e)
Fig. 9 CDF of the distance errors for VDM procedure when using distance database of density: a)
; b) ; c) ; d) , and e)
4.2.2 Coordinate-level accuracy
The second set of localization results illustrates the FAUL coordinate-level accuracy for
different deployment scenarios and fingerprint densities. The coordinate-level accuracy is
evaluated through the localization error, , which is defined as the Euclidian distance
between the actual position of a grid point and the position determined by the FAUL method.
The weight parameters for the trilateration procedure are set to , and . Table 2
reports the MDE and RMSE of for 3-, 2-, 1-, and 0-PLOS deployment scenarios under
different fingerprint densities. The distribution of the localization error is described by CDFs
shown in Fig. 10.
Table 2 Localization error (in cm) for different number of LOS anchor nodes and fingerprint densities
Deployment
scenario
Fingerprint density (f/m2)
100
50
25
12.5
6.25
MDE
RMSE
MDE
RMSE
MDE
RMSE
MDE
RMSE
MDE
RMSE
3-PLOS
4.71/5.64
2-PLOS
5.00
5.92
5.12
6.09
5.22
6.23
5.31
6.41
5.31
6.36
1-PLOS
5.74
6.78
7.18
9.71
9.04
11.16
10.3
12.74
12.8
15.87
0-PLOS
6.31
7.54
9.07
11.16
12.3
14.80
14.6
16.99
19.8
23.36
(a)
(b)
(c)
(d)
(e)
Fig. 10 CDF of localization errors for FAUL method when using distance database of density: a)
; b) ; c) ; d) , and e)
As expected, the best localization performances are attained in 3-PLOS scenario, where all
three distances for trilateration are the result of accurate LOS UWB ranging. In particular, the
MDE of is achieved, with exceeding the localization error of in less than
of cases. In the remaining three deployment scenarios, FAUL relies on VDM to estimate
distances to missing ANs, which inevitably increases the localization error. The accuracy of
the final result depends on both the number of available LOS UWB-measured distances, and
on how accurately VDM predicts the missing distances. It is important to observe that the
localization accuracy in the 2-PLOS case is very close to that obtained in the 3-PLOS case, and
only slightly drops with the decrease of the fingerprint density. The near-LOS accuracy in the
2-PLOS case is because of the adopted weighted trilateration method, in which LOS UWB-
measured distances have a larger impact on the final location estimates than those obtained by
VDM. In fact, in the 2-PLOS case, the only role of single VDM distance is the selection
between two alternative locations determined by the remaining two LOS UWB-measured
distances.
In the 1-PLOS case, single LOS UWB-measured distance cannot fully compensate for the
lower accuracy of two VDM distances, which leads to increased localization error. With a high
fingerprint density of, the MDE is only larger than in the 3-PLOS case.
However, when the distance database with a density of is used for VDM
estimations, FAUL produces localization error that is larger than in 50% of cases.
In the 0-PLOS deployment scenario, FAUL relies solely on VDM distances to determine the
TN’s location. Nevertheless, FAUL can attain relatively high coordinate-level accuracy even
without LOS UWB-measured distances provided that the distance database of high fingerprint
density is available. However, as the fingerprint density decreases, the localization error
increases more rapidly than in the 1-PLOS scenario. For example, in the 0-PLOS case, the
MDE with the fingerprint density of is times larger than with a density
of. Under the same conditions, the MDE in the 1-PLOS case rises 1.57 times.
4.2.3 Impact of training data inaccuracy
In FAUL, the ground truth coordinates of grid points are not recorded during the offline
fingerprint collection phase. Instead, the offline fingerprints include distances obtained by
UWB ranging with auxiliary ANs that are temporarily placed into APs from the LOS_set of
the surveyed room. Thus, the fingerprint collection procedure can be performed automatically
by the localization system, which greatly reduces the site-surveying effort. However, with this
approach, UWB ranging errors are built in into the training data, which may lower the FAUL
overall localization performance. To quantify the localization error induced by using auxiliary
ANs during the offline phase, we repeat the coordinate-level accuracy analysis, but with the
use of exact distances between grid points and auxiliary ANs instead of UWB measured
distances.
Table 3 shows the differences in MDE and RMSE (i.e., ∆MDE, and ∆RMSE) of FAUL method
when the distances to auxiliary ANs in offline location fingerprints are obtained by UWB
ranging, and when the exact distances to auxiliary ANs are used. As expected, all ∆MDE and
∆RMSE values are positive, which indicates that the elimination of UWB ranging errors from
training data improves the coordinate-level localization accuracy. However, the differences are
rather small and do not exceed in all analysed deployment scenarios under different
fingerprint densities. As can also be observed, the additional localization error due to the use
of auxiliary ANs is larger with denser than with a sparse fingerprint database. At first glance,
this observation may seem contradictory, but it can be explained by the fact that FAUL
localization accuracy is influenced by both the accuracy of training data, and fingerprint
density. When the fingerprint density is high, the UWB ranging inaccuracy represents the
dominant source of localization errors. On the other hand, when a sparse fingerprint database
is used, the removal of UWB ranging errors from training data cannot improve FAUL
localization accuracy significantly, because of relatively larger localization error due to low
fingerprint density.
Table 3 Localization error (in cm) induced by using auxiliary ANs during fingerprint collection
Deployment
scenario
Fingerprint density (f/m2)
100
50
25
12.5
∆MDE
∆RMSE
∆MDE
∆RMSE
∆MDE
∆RMSE
∆MDE
∆RMSE
3-PLOS
0/0
2-PLOS
0.05
0.08
0.06
0.11
0.05
0.09
0.04
0.10
1-PLOS
0.95
1.06
0.77
1.83
0.62
0.74
0.38
0.44
0-PLOS
1.68
1.64
1.16
0.94
0.89
0.82
0.56
0.40
4.2.4 Comparison with conventional fingerprinting approach
In order to gain insight into how the accuracy of FAUL is compared to the conventional kNN-
based fingerprinting localization scheme (C-kNN), we applied the weighted kNN algorithm on
the same test database that is used in the previous experiments. The C-kNN scheme requires
that offline fingerprints be labelled with the ground truth coordinates. We analysed two C-kNN
variants. In the first variant (C-kNN-E), fingerprints are labelled with the exact ground truth
locations, obtained by manually measuring coordinates of the grid points in the zone (Fig.
8). In the second variant (C-kNN-A), the fingerprints are labelled with approximate estimations
of grid point coordinates obtained by applying the trilateration algorithm to the UWB-measured
distances to three LOS ANs in room . In the online phase, both C-kNN algorithms compare
the online fingerprint against those in the database and estimate the TN’s location by averaging
the ground truth coordinates of most similar offline fingerprints.
Table 4 Comparison of FAUL and conventional kNN-based fingerprinting scheme in terms of MDE
(in cm) for different number of LOS ANs and fingerprint densities
Deployment
scenario
Fingerprint density (f/m2)
100
50
25
12.5
FAUL
C-kNN-E
C-kNN-A
FAUL
C-kNN-E
C-kNN-A
FAUL
C-kNN-E
C-kNN-A
FAUL
C-kNN-E
C-kNN-A
3-PLOS
4.71
3.45
5.53
4.71
6.49
7.90
4.71
9.62
10.85
4.71
12.04
12.80
2-PLOS
5.00
4.05
6.06
5.12
7.54
8.83
5.22
11.02
12.04
5.31
13.62
14.30
1-PLOS
5.74
4.88
6.71
7.18
8.73
10.00
9.04
12.73
13.72
10.3
14.97
15.66
0-PLOS
6.31
6.49
8.05
9.07
11.14
12.24
12.3
15.33
16.20
14.6
18.38
19.06
Table 4 reports the coordinate-level accuracy results, in terms of MDE, for three competitive
localization schemes. Note that the MDE data for the FAUL method are copied from Table 2.
As we observe, despite using exact ground truth coordinates, C-kNN-E produces smaller
localization errors than the FAUL method only if a very high-density fingerprint database is
used. It should be noted that the manual construction of the fingerprint database with a density
of could take an enormous amount of time, even if the surveying area is relatively
small. With the decrease of fingerprint density, the localization error of C-kNN schemes
increases faster than that of FAUL. In the full LOS coverage scenario (3-LOS), the localization
error of C-kNN-E increase from to if the density of the fingerprint database
is reduced from to. As the FAUL method does not use the fingerprint
database in the 3-LOS scenario, its accuracy is not affected by fingerprint density. In the 2-
PLOS scenario, the accuracy difference between FAUL and C-kNN-E follows a similar trend.
The accuracy advantage of FAUL is also evident in the remaining two partially LOS coverage
scenarios, although to a lesser extent. The performance advantage in a range of of C-
kNN-E over C-kNN-A is due to approximate ground truth coordinates used in C-kNN-A. It is
important to observe that the FAUL method achieves consistently lower localization error than
C-kNN-A, including the fingerprint density of, even though both methods suffer for
UWB ranging errors during the offline phase. This can be contributed to the fact that FAUL
implements a more elaborate online localization algorithm, which favours LOS over NLOS
measurements and uses the fingerprint database only when necessary to generate additional
distances for trilateration.
4.3 Discussion
An important feature of the FAUL method is that the localization system can be partially
reconfigured without interrupting the online operation. In particular, during the online phase,
the user can insert one or more auxiliary ANs into a subset of secondary APs, or move auxiliary
ANs from one to another subset of secondary APs, without the need to explicitly notify the
location server about the changes. All distances measured between the TN and the auxiliary
ANs will be present in the online distance vector at the positions reserved for corresponding
secondary APs, and therefore they can be directly used for trilateration instead of VDM
estimates. In this way, the user can easily extend the minimum system configuration
(comprising permanent ANs, only) with additional ANs if there is a need to improve the
localization accuracy in some critical parts of the environment. Another benefit of
reconfiguration flexibility is the ability to seamlessly upgrade the distance database during the
online phase. Instead of repeating the offline training, the user can occasionally move auxiliary
ANs from zone to zone during the online phase. Each time the location server receives a
distance vector containing UWB-measured distances to all three APs in the LOS_set of the
identified zone, it can create and insert a new fingerprint in the distance database by employing
a suitable database updating scheme.
Although the FAUL is primarily intended for low-cost large-scale indoor deployments, it can
also be adapted to other application scenarios. An interesting use case of FAUL is the high-
accuracy fault-tolerant localization system, which relies on the full LOS coverage to achieve
the maximum possible localization performance while providing the robustness against the AN
failures. In this setup, the location server, as a background activity, continuously builds and
updates the distance database with each distance vector received during the online operation.
With three ANs deployed in every zone, the location system will not have to use the VDM
procedure and distance database, as long as all ANs are operational. However, after any AN
stops responding, either due to malfunctioning or depleted battery, the availability of the
distance database will allow the location server to use the VDM procedure for estimating the
missing distance. In this way, the localization system will be able to tolerate multiple faults
with localization performance degrading gracefully as ANs fail, provided that each point in the
localization space is still (LOS or NLOS) covered by at least three operational ANs.
5 Conclusions
In this paper, we have presented Fingerprinting-Assisted UWB-based Localization (FAUL)
method, a novel approach of improving the accuracy of the UWB localization system in
complex indoor environments with a limited number of deployed anchors. FAUL combines
fingerprinting and weighted trilateration techniques to reduce the localization error in situations
when there are an insufficient number of line-of-sight (LOS) range measurements required for
spatial localization. The key aspect of the proposed method is that the fingerprints are not
labelled with their ground truth locations, as usual in most existing fingerprint-based
approaches, but with distances to the set of pre-defined reference points distributed throughout
the indoor environment. This localization approach favours LOS measurements and uses the
fingerprinting database to predict distances to reference points only when necessary. Besides,
FAUL considerably reduces the time and labour cost of building high-density fingerprint
database during the offline training phase by using auxiliary anchors for distance measurement
between the target node and the reference points. We have implemented FAUL in a typical
five-room residential apartment intending to analyse the localization error in deployment
scenarios when 3, 2, 1, and 0 LOS range measurements are available. Experiments show that
FAUL attains approximately the same localization accuracy in the 2-LOS case as in 3-LOS
case even with a low-density fingerprint database. In 1- and 0-LOS cases, the accuracy drops
but it still can be maintained at sub-decimetre level, provided a fingerprint database of
sufficient density (more than 50 fingerprints per meter squared) is available. One of our
findings is that the UWB is very effective in room-identification, achieving the room-level
localization accuracy of over 95% even with a relatively sparse fingerprint database. These
results make FAUL an attractive approach for reducing system cost of UWB localization in
indoor scenarios of complex geometry with an acceptable penalty in localization accuracy.
Acknowledgment
This work was supported by Ministry of Education, Science and Technological Development
of the Republic of Serbia.
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