=Paper=
{{Paper
|id=Vol-3434/125
|storemode=property
|title=Privacy-Constrained Location Accuracy in Cooperative Wearable Networks in Multi-Floor Buildings
|pdfUrl=https://ceur-ws.org/Vol-3434/paper5.pdf
|volume=Vol-3434
|authors=Elena Simona Lohan,Viktoriia Shubina
|dblpUrl=https://dblp.org/rec/conf/wiphal/LohanS23
}}
==Privacy-Constrained Location Accuracy in Cooperative Wearable Networks in Multi-Floor Buildings==
<pdf width="1500px">https://ceur-ws.org/Vol-3434/paper5.pdf</pdf>
<pre>
Privacy-Constrained Location Accuracy in
Cooperative Wearable Networks
in Multi-Floor Buildings
Elena Simona Lohan1 , Viktoriia Shubina1,2
1
    Tampere University, Tampere. Finland
2
    University ‘Politehnica’ of Bucharest, Bucharest, Romania


                                         Abstract
                                         This paper proposes a geometric dilution-of-precision approach to quantize the privacy-aware location
                                         errors in a cooperative wearable network with opportunistic positioning. The main hypothesis is
                                         that, a wearable inside a multi-floor building could localize itself based on cooperative pseudoranges
                                         measurements from nearby wearables, as long as the nearby wearables are heard above the sensitivity
                                         limit and as long as nearby wearables choose to disclose their own positions. A certain percentage of
                                         wearables, denoted by 𝛾, is assumed to not want to disclose their positions in order to preserve their
                                         privacy. Our paper investigates the accuracy limits under the privacy constraints with variable 𝛾 and
                                         according to various building maps and received signal strength measurements extracted from real
                                         buildings. The data (wearable positions and corresponding power maps) are synthetically generated
                                         using a floor-and-wall path-loss model with statistical parameters extracted from real-field measurements.
                                         It is found that the network is tolerant to about 30% of the wearables not disclosing their position (i.e.,
                                         opting for a full location-privacy mode).

                                         Keywords
                                         wearables, indoor localization, location privacy, Geometric Dilution of Precision (GDOP)




1. Introduction
According to the survey by Grand View Research, Inc. in [1], the size of the worldwide wearable
technology market is anticipated to reach USD 186.14 billion by the year 2030, expanding at a
compound annual growth rate (CAGR) of 14.9% over the forecast period. The rapid development
of technology, including wireless technology for location tracking and health monitoring, is
predicted to drive industry expansion over the next several years. As of now, wearables are
using smartphones as gateways to delegate heavy computations, however, in the near future,
the trend is set to change and wearable technology could have enough computational capacity
to become standalone [2].
   Given the widespread adoption of wearable devices and smartphones (serving as a gateway
for their data processing) [3], one of the most on-demand functionalities nowadays is the ability
to locate oneself within defined indoor or outdoor space [4]. When localization engines are
WIPHAL 2023: Work-in-Progress in Hardware and Software for Location Computation, June 06–08, 2023, Castellon,
Spain
$ elena-simona.lohan@tuni.fi (E. S. Lohan); viktoriia.shubina@tuni.fi (V. Shubina)
 0000-0003-1718-6924 (E. S. Lohan); 0000-0001-8178-5652 (V. Shubina)
                                       © 2023 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)
used on power-constrained devices such as wearables, it is becoming more and more important
to be able to use the signals coming from opportunistic networks to perform localization in
the absence of a Global Navigation Satellite System (GNSS) chipset or in order to decrease the
energy consumption at the wearable side. Indeed, opportunistic ad-hoc networks have been
highly studied in order to provide seamless connectivity in situations where an infrastructure
mode is not continuously available [5, 6, 7]. When various wearables found inside a certain
area, such as an indoor mall or a commuting hall, are interacting with each other and do various
measurements based on the received wireless signals, the exchange of information can be
done in a faster and lower energy-consuming way than in an infrastructure mode. One of the
convenient aspects of an opportunistic network is the possibility of a low-energy cooperative
localization through basic information exchanges between wearables, such as pseudorange
computations based on Received Signal Strengths (RSS), timing measurements, angle, or acoustic
measurements [8, 9, 10]. Hence, not only high-end wearables but also low-cost wearables could
perform cooperative self-positioning through these basic information exchanges. One of the
drawbacks of such opportunistic positioning with wearables is the inherent risk in terms of
user privacy, e.g., when the data exchange contains accurate location information of one’s
wearables. For example, for an opportunistic positioning scenario, wearable devices equipped
with GNSS modules and/or Inertial Measurement Units (IMUs) acting as Anchor Nodes (ANs)
for their nearby wearables with lower computational resources will have to disclose their
locations to nearby nodes in order to also enable the nodes in the ANs’ vicinity to self-locate
(e.g., when such nearby nodes are not equipped with GNSS/IMUs). Another scenario is when
all wearables in the system have only WiFi/BLE chipset, but no GNSS or IMUs, and thus the
process could run iteratively, where each node takes turns to act as a mobile AN for other nodes
in its vicinity, based on its previously computed position. Localization can be performed by
relying on distance measurements to neighboring wearables, acting as ANs and transmitting
their estimated location to the devices within range [11]. Such distance measurements, at their
turn, can be obtained from time, angle, or power measurements.
    RSS-based measurements are susceptible to noise, signal fluctuations, and line-of-sight (LOS)
vs. non-line-of-sight (NLOS) detection difficulties and other factors, as reported, for example,
in [12, 13, 14, 15]. Therefore, the study in [16] investigated the RSS-based cooperative localization
challenge and used Cramer–Rao lower bound (CRLB) to compare performance of the proposed
method of mitigating NLOS-related errors with the conventional approaches, showing increased
performance.
    Another metric, acknowledged by the research community is the geometric dilution of
precision (GDOP), which was originally developed to assess the precision of location estimates
in GNSS [17, 6, 18, 19]. This metric fundamentally explains how the placement of the transmitters
(i.e., the ANs in a terrestrial network or the satellites in GNSS) influences the precision of the
estimated location and quantifies the effect of the network topology on the precision of location
estimates.
    However, indoor localization systems may use various technologies, such as WiFi, Bluetooth,
ultrasonic, or infrared, for determining the position of a user or object within a building [20, 21].
When applying the GDOP concept to indoor localization, it is used to evaluate the geometry of
the infrastructure, such as access points or beacons, that provide positioning information [22].
The more evenly distributed the infrastructure, the better the geometry and the lower the GDOP
value, which in turn results in more accurate location estimates.
   Based on the literature review, one can infer that applying different metrics allows to de-
termine circumstances when the geometry may have a detrimental impact on the localization
accuracy, leading to improvements in system performance as well as its design.
   The goal of this paper is to investigate the tradeoff between location accuracy on one hand (i.e.,
how well a wearable can locate itself based on cooperative pseudoranges measurements from
nearby wearables) and the location privacy on another hand (i.e., the percentage of wearables
deciding to disclose their location, with or without a perturbation, as well as the amount of
intentional positioning errors or perturbations with which the nearby wearables are disclosing
their location). We propose a model which includes the inherent measurement errors in a
cooperative and opportunistic location-estimation algorithm, the intentional positioning errors
derived for example from various obfuscation or perturbation mechanisms with which the
nearby wearables in a multi-floor building are disclosing their position, as well as the percentage
of the wearables fully hiding their position. Our methodology is based on a GDOP approach to
quantize the privacy-constraint location errors.
   Some related work has been addressed by the authors in [23, 24]; however the mathematical
model provided here of the location accuracy based on maximum-likelihood pseudorange
estimates is new, as well as the disjoint modeling of the measurement errors, intentional
(perturbation) errors, and percentage of users hiding their positions. The GDOP concept has
been previously used in the context of indoor cooperative localization, for example in [6], but
no privacy constraints were included in [6].
   The user location privacy typically depends on three main factors: i) measurement errors
statistics, or how accurately such a location is estimated based on prior knowledge and/or
information collected from the nearby nodes, ii) intentional error statistics, i.e., if and how
accurately the nearby wearables disclose their location – we assume that the users have full
control of how and at which level of accuracy they can share own location information with other
nodes (this is computed as the percentage of users disclosing their locations), and iii) number
of wearables, namely how many wearables with similar locations are there in the area; this
affects the probability to mistake a wearable for another one in the area; this is also related to
the probability of several wearables to belong to the same user.
   Other related work to location privacy protocols and metrics [25, 26, 27, 28] or location
accuracy metrics [29, 30, 31] has been overviewed in [23, 24]. As emphasized [23], the tradeoffs
between location privacy and location accuracy are still insufficiently mapped out in the current
literature, especially in the context of opportunistic wearable scenarios. Additional surveys on
the location privacy and location accuracy tradeoffs can be found, for example, in [32, 33, 34].
   The rest of the paper is organized as follows: Section 2 focuses on the system mathematical
model that takes into account the privacy constraints and on the proposed GDOP-based metric.
Section 3 presents the simulation environment and the simulation-based results. Section 4
summarizes the findings and discusses some future research topics in the field.
Figure 1: Illustration of an indoor multi-floor scenario used in the simulation to assess location accuracy.


2. System Model and GDOP-based accuracy metric
To illustrate the considered environment, we provide a graphical example of a potential indoor
scenario for the opportunistic exchange of positioning information in Fig. 1, and in the latter
part of this section, we explain the modeling parameters used in the simulations.
   Fig. 1 shows a schematic floor plan of an indoor setting, such as a shopping mall. To offer
the context, the users are assumed to be distributed across three floors, and this setting could
be used for various location-based services, such as finding a friend, finding the nearest shop
with certain items of interests, finding the nearest exit, etc. The notion of proximity detection
may be utilized, for example, for counting passive encounters [35], to enhance the tourism
experience [36], for sociometric applications [37], etc. It can also be used to assist individuals in
navigating their surroundings. Another application of indoor positioning is the use of digital
contact tracing in public places. In such a context, proximity detection could be employed to
alert persons when they are too close to one another, assisting in maintaining of safe distances,
and in the prevention of infection spread [38]. Indoor proximity detection can be used to track
the whereabouts of valuable assets within a warehouse or factory, such as equipment, cars, or
goods. This could help in the optimization of processes, theft prevention, and maximizing the
effectiveness of equipment [39].
   Let us assume an indoor system with 𝑁𝑤 wearables. We also assume that each wearable can
perform power, time, or angle-based measurements (or a combination of those) to identify their
location in the defined indoor space. We assume also that each wearable 𝑖 = 1, . . . , 𝑁𝑤 can
hear a certain amount of neighbourhood wearables, denoted with 𝑁ℎ𝑖 . A heard wearable is a
wearable from which the received power is higher than the receiver sensitivity level 𝑃𝑅𝑚𝑖𝑛𝑖 of
the 𝑖-th wearable. An additional LOS condition can be imposed if the target measurements are
time-based or angle-based. NLOS wearables are also assumed to be ‘heard’ for power-based
measurements (but not for time or angle-based measurements). A pseudorange measurement
𝜌𝑖,𝑗 is then obtained based on the power, time, or angle measurements available at each 𝑖-th
wearable from all its heard neighbours 𝑗 with 𝑗 = 1, . . . , 𝑁ℎ𝑖 .
   The pseudorange measurement 𝜌𝑖,𝑗 is equal to the true LOS distance between 𝑖-th and 𝑗-th
wearables in the system, plus an additional measurement error, denoted here by 𝜖𝑖,𝑗 :

                     𝜌𝑖,𝑗 = ||p𝑖 − p𝑗 || + 𝜖𝑖,𝑗 , 𝑖 = 1, . . . , 𝑁𝑤 ; 𝑗 = 1, . . . , 𝑁ℎ𝑖             (1)
   In eq. (1), || · || is the Euclidean norm and p𝑖 = [𝑥𝑖 , 𝑦𝑖 , 𝑧𝑖 ] is the position vector of the 𝑖-th
wearable, having the World Geodetic System 1984 (WGS84) 3D coordinates 𝑥𝑖 , 𝑦𝑖 , and 𝑧𝑖 .
   In our simulator, we used the assumption that all measurement errors 𝜖𝑖,𝑗 are Gaussian
distributed with zero mean and 𝜎𝑚 standard deviation of error, i.e.,
                                                          2
                                            𝜖𝑖,𝑗 ∼ 𝒩 (0, 𝜎𝑚 ).                                       (2)

  In a cooperative dynamic system, each wearable can update iteratively its position estimate
based on the positions of the heard neighbours, assuming that a fraction 1 − 𝛾 of the neighbours
choose to disclose their position p̃𝑗 , but with a random intentional error as below:

                                              p̃𝑗 = p𝑗 + 𝜉𝑗                                          (3)

where p̃𝑗 is the position disclosed by the j-th wearable with a certain intentional error 𝜉𝑗 .
The intentional error is a privacy measure. In our simulator, we assumed 𝜉𝑗 to be Gaussian
distributed with zero mean and equal to 𝜎𝜖 standard deviation of error for all variables, i.e.,

                                             𝜉𝑗 ∼ 𝒩 (0, 𝜎𝜖2 ).                                       (4)

This assumption follows the model introduced in [23].To sum up, we have two categories of
wearables in our system

    • A fraction 𝛾 of wearables does not disclose at all their position (this ensures what we call
      a fully private mode)
    • A fraction 1 − 𝛾 of wearables discloses their position with an intentional positioning
      error 𝜉𝑗 ∼ 𝒩 (0, 𝜎𝜖2 )

In addition, all position estimates are assumed to suffer of some measurement errors, modeled
here via 𝜖𝑖,𝑗 ∼ 𝒩 (0, 𝜎𝑚2 ); such measurement errors are inherent in any estimation system, no

matter if the position estimates were based on RSS, Angle of Arrival (AOA), Time of Arrival
(TOA), or a combination of them.
   If we assume a maximum likelihood cooperative position estimation, e.g. similarly with [40],
the estimated updated position p  ^𝑖 is
                    p
                    ^𝑖 =
                                                    (︂                      )︂2
                                 𝑁 ℎ𝑖                    ||p −p̃ −𝜇 −𝜌 ||
                                                        − 𝑖 𝑗2𝜎 𝑖,𝑗 𝑖,𝑗
                                 ∏︁         𝑓𝑗                    𝑖,𝑗
                    𝑎𝑟𝑔 max𝑝𝑖          √︀            𝑒                    ,
                                   𝑗=1
                                          (2𝜋)𝜎𝑖,𝑗
                    𝑖 = 1, . . . , 𝑁𝑤 ; 𝑗 = 1, . . . , 𝑁ℎ𝑖                                          (5)
                                     𝑀ℎ𝑖 (︂
                                     ∑︁ ||p𝑖 − p̃𝑗 − 𝜇𝑖,𝑗 − 𝜌𝑖,𝑗 || )︂2
                    = 𝑎𝑟𝑔 min𝑝𝑖                                         ,
                                                        2𝜎𝑖,𝑗
                                    𝑗=1
                    𝑖 = 1, . . . , 𝑁𝑤 ; 𝑗 = 1, . . . , 𝑀ℎ𝑖
where 𝑓𝑗 is a 0/1 flag associated to the privacy status of each wearable (i.e., 𝑓𝑗 = 1 if the nearby
wearable choose to disclose its position and 𝑓𝑗 = 0 if the nearby wearable does not disclose its
position) and 𝑀ℎ𝑖 ≤ 𝑁ℎ𝑖 is the number of wearables in the vicinity of 𝑖-th wearable which are
heard (in terms of received power being higher than the sensitivity threshold) and choosing to
disclose their position (namely, the heard wearables flagged with 𝑓𝑗 = 1, 𝑗 = 1, . . . , 𝑁ℎ𝑖 ).
   Eq. (5) is a non-linear optimization problem which can be solved iteratively after Taylor
linearization, following, for example, the procedure in [40]:
                                                  (︂          )︂−1
                                 𝑘+1         𝑘         𝑇 −1
                               p
                               ^𝑖 = p     ^𝑖 + 𝐺𝑖 Σ𝑖 𝐺𝑖            𝐺𝑇𝑖
                                (︂                                   )︂
                             −1
                           Σ𝑖                        𝑇
                                  [𝜌𝑖,1 . . . 𝜌𝑖,𝑀ℎ ] − ||p 𝑘    𝑘
                                                          ^𝑖 − p̃𝑗 ||                             (6)

where 𝐺𝑖 ∈ R𝑀ℎ𝑖 ×3 ≜ [𝐺𝑖,1 , . . . , 𝐺𝑖,𝑀ℎ𝑖 ]𝑇 is the Taylor linearized matrix with rows 𝐺𝑖,𝑗 , 𝑗 =
1, 𝑀ℎ𝑖 from [40] equal to
                                  [︂                                           ]︂
                                       𝑥𝑖 − 𝑥˜𝑗      𝑦𝑖 − 𝑦˜𝑗      𝑧𝑖 − 𝑧˜𝑗
                         𝐺𝑖,𝑗 =                                                                  (7)
                                     ||p𝑖 − p̃j || ||p𝑖 − p̃j || ||p𝑖 − p̃j ||
and Σ𝑖 = 𝑑𝑖𝑎𝑔(𝜎𝑖,1 , . . . , 𝜎𝑖,𝑀ℎ ) ∈ R𝑀ℎ𝑖 ×𝑀ℎ𝑖 is the error covariance matrix taking into account
the measurement errors 𝜖𝑖,𝑗 coming from the cooperative pseudorange measurements. Above,
𝑘 is the iteration index in the location estimation process, 𝑘 = 1, 2, . . . . The initial point of the
estimation p ^1𝑖 can be assumed, for example, to be the true position of the 𝑖-th wearable (e.g., the
wearable is placed just at the entrance of the building and had access to accurate GNSS-based
position estimates) or it can be computed as the weighted centroid of heard wearables in range
which discloses their position:
                                               𝑀ℎ
                                               ∑︁
                                                    𝑤𝑖,𝑗 𝑓𝑗 p̃1𝑗
                                                  𝑗=1
                                          ^1𝑖 =
                                          p         𝑀ℎ
                                                                                                    (8)
                                                    ∑︁
                                                          𝑤𝑖,𝑗 𝑓𝑗
                                                    𝑗=1

with 𝑤𝑖,𝑗 = 10( 𝑃𝑅𝑖,𝑗 /10), and 𝑃𝑅𝑖,𝑗 is the RSS (in dBm) by the 𝑖-th wearable from the 𝑗-th
wearable.
  If we assume that we have uncorrelated measurement errors 𝜖𝑖,𝑗 of zero means and equal
variances 𝜎𝑖,𝑗 ≜ 𝜎𝑚 , then the accuracy of the location solution from eq. (6), measured as the
overall variance of the location error, is directly proportional to the trace of the square root
                               √︃(︂           )︂−1
geometry matrix 𝐻𝐺𝐷𝑂𝑃,𝑖 ≜            𝑇
                                   𝐺 𝑖 Σ𝑖 𝐺 𝑖      [40]. This means that

                                           (︂                  )︂
                                  2
                                 𝜎𝑎𝑙𝑙 =E        𝑡𝑟𝑎𝑐𝑒(𝐻𝐺𝐷𝑂𝑃,𝑖 ) ,                             (9)

where E(·) is the expectation operator taken with respect to all wearables in the building.
   The matrix 𝐻𝐺𝐷𝑂𝑃,𝑖 is also known as the GDOP matrix. The overall location error accuracy
becomes thus a function of both the measurement error standard deviation 𝜎𝑚 as well as of
the intentional error standard deviation 𝜎𝜉 (for clarity we assumed that all wearables have the
same standard deviation of the measurement and intentional errors), as 𝐺𝑖 matrix is a function
of 𝜎𝜉 . Moreover, the 𝐻𝐺𝐷𝑂𝑃,𝑖 can be computed either based only on LOS links from wearables
which choose to disclose their position (e.g., when the pseudorange measurements in eq. (1) are
based on timing or angle measurements which require LOS), or based on all heard wearables
which choose to disclose their position, both LOS and NLOS (e.g., this is relevant when the
pseudorange estimates are based on RSS measurements, which do not necessarily require LOS).
   Therefore, the overall location accuracy per wearable 𝑖 can be modeled via the above-
introduced GDOP-based statistics 𝜎𝑜𝑣𝑒𝑟𝑎𝑙𝑙 ≜ 𝐻𝐺𝐷𝑂𝑃,𝑖 and it will be a function of the mea-
                                                 𝑁ℎ
                                                 ∑︁
surement error 𝜎𝑚 , the number of wearables          𝑓𝑗 , which choose to disclose their position
                                                    𝑗
with some intentional error, their intentional error standard deviation 𝜎𝜉 and, possibly, of the
number of LOS links.


3. Simulation-based results
3.1. Simulator description
A Matlab-based simulator has been implemented for our studies. One building map from a
three-floor shopping center was used in our models, as shown in Fig. 2. The wearables are
assumed uniformly distributed across the 𝑁𝑓 𝑙𝑜𝑜𝑟𝑠 floors of each building and a random walk
model is assumed for each wearable. The wearables can have different heights and placements,
ranging from 5 cm above the floor (e.g., foot/shoe mounted wearable) to 1.8 m above floor
(e.g., head-mounted wearable). The following single-slope floor-and-wall path-loss model was
assumed:
              𝑃𝑅𝑖,𝑗   = 𝑃𝑇𝑗 − 10 * 𝑛𝑖,𝑗 * 𝑙𝑜𝑔10 ||p𝑖 − p𝑗 ||
                      − 𝑁𝑖𝑛𝑛𝑒𝑟𝑤𝑎𝑙𝑙𝑠𝑖,𝑗 𝐿𝑖𝑛𝑛𝑒𝑟𝑤𝑎𝑙𝑙 − 𝑁𝑜𝑢𝑡𝑒𝑟𝑤𝑎𝑙𝑙𝑠𝑖,𝑗 𝐿𝑜𝑢𝑡𝑒𝑟𝑤𝑎𝑙𝑙               (10)
                      − 𝑁𝑓 𝑙𝑜𝑜𝑟𝑠𝑖,𝑗 𝐿𝑓 𝑙 + 𝜂𝑖,𝑗

where 𝑃𝑅𝑖,𝑗 is the received signal power (in dBm) of the 𝑖-th wearable from the 𝑗-th wearable,
𝑃𝑇𝑗 is the transmit power (in dBm) of the 𝑗-th wearable, 𝑛𝑖,𝑗 is the path-loss slope coefficient
Figure 2: Illustration of the dynamic three-floor indoor simulator. The moving wearables (shown in
red circles) can be used at various body heights within one floor. Left: shopping mall; right: university
building


for the path connecting wearable 𝑖 to wearable 𝑗 (channel reciprocity condition 𝑛𝑖,𝑗 = 𝑛𝑗,𝑖 was
assumed to be respected), 𝑁𝑖𝑛𝑛𝑒𝑟𝑤𝑎𝑙𝑙𝑠𝑖,𝑗 and 𝑁𝑜𝑢𝑡𝑒𝑟𝑤𝑎𝑙𝑙𝑠𝑖,𝑗 are the numbers of inner and outer
walls,respectively, between wearable 𝑖 and wearable 𝑗 (computed based on the building map),
𝑁𝑓 𝑙𝑜𝑜𝑟𝑠𝑖,𝑗 is the number of floors between wearable 𝑖 and wearable 𝑗, 𝐿𝑖𝑛𝑛𝑒𝑟𝑤𝑎𝑙𝑙 and 𝐿𝑜𝑢𝑡𝑒𝑟𝑤𝑎𝑙𝑙
are a loss factor (in dB) per inner or outer wall, respectively, and 𝐿𝑓 𝑙 is a loss factor (in dB)
per floor (all floors were assumed to introduce equal wall losses). The term 𝜂𝑖,𝑗 models the
random shadowing effects and was assumed to follow a Gaussian distribution of 0 mean and
𝜎𝑠ℎ𝑎𝑑 standard deviation (in our simulations, 𝜎𝑠ℎ𝑎𝑑 = 4 dB, based on the measurement results
reported in [41].
   A wearable 𝑗 can be heard by another wearable 𝑖 in the building if and only if 𝑃𝑅𝑖,𝑗 ≥
𝑃𝑅𝑚𝑖𝑛𝑖 . In our simulations, the sensitivity threshold 𝑃𝑅𝑚𝑖𝑛𝑖 was set to −100dBm. Additionally,
two wearables 𝑖 and 𝑗 are in assumed to be in LOS condition to each other if and only if
𝑁𝑤𝑎𝑙𝑙𝑠𝑖,𝑗 + 𝑁𝑓 𝑙𝑜𝑜𝑟𝑠𝑖,𝑗 = 0 (and they are in a NLOS condition otherwise).
   Two arbitrary examples of the synthetically generated power map from two wearables in the
building is shown in Fig. 3.
   A random-walk mobility model [42] with a randomly distributed velocity between 0.1 and 1
m/s was used. The wearable movements were assumed to remain at the floor of their initial
position (i.e., vertical/across-floor mobility is not yet included in our model). As the building
maps are proprietary, the Matlab-based simulator is not currently provided in open access.

3.2. Simulation-based results
The simulation results are based on the in-house built simulator described in Section 3.1. A
total of 𝑁𝑤 users carrying one wearable each were assumed to be distributed uniformly across
the three floors of a simulated building. The buildings were based on real maps, collected from
a university and from a shopping mall. The information about the building walls and floors
was used in the path-loss model (see eq. (10)). All wearables are assumed to be able to hear
all other wearables in the building as long as the received power is higher than the sensitivity
Figure 3: Illustration of the synthetically generated power map (as RSS values in dBm) for two randomly
picked wearables in the building. The location of wearables acting as ’transmitters’ is shown as a large
magenta point, and the locations of the wearables acting as ’receivers’ (i.e., where RSS values are
measured) are shown in red.


threshold (in our simulations, it was set to −100 dBm). The received power values depend,
of course, on the distance between any two wearables as well as on the number of walls and
floors between any pair of wearables (see eq. (10)). The path-loss coefficient, inner and outer
walls attenuation factors, floor attenuation factors and transmit powers of each wearable were
modeled according to models extracted from real-world measurements in the two buildings
based on [41], as follows

    • A log-normal distribution for the transmit power 𝑃𝑇𝑗 of each 𝑗 wearable, 𝑗 = 1, . . . , 𝑁𝑤
    • A normal distribution for the path loss coefficient 𝑛𝑗 of each 𝑗 wearable, 𝑗 = 1, . . . , 𝑁𝑤
    • A Weibull distribution for the inner-wall 𝐿𝑖𝑛𝑛𝑒𝑟𝑤𝑎𝑙𝑙𝑠 and floor losses 𝐿𝑓 𝑙 of each 𝑗 wear-
      able, 𝑗 = 1, . . . , 𝑁𝑤
    • A Gamma distribution for the outer-wall losses 𝐿𝑜𝑢𝑡𝑒𝑟𝑤𝑎𝑙𝑙𝑠 of each 𝑗 wearable, 𝑗 =
      1, . . . , 𝑁𝑤

   Fig. 4 illustrates the histograms of the path-loss parameters used in our simulations and
based on field RSS measurements. Further details on choosing these parameters based on
measurement data can be found in [41].
   Under the assumption that a fraction 𝛾 of the wearables within a multi-floor building do
not disclose their location estimates (in order to preserve their location privacy) and that all
the other wearables form an opportunistic network for self-positioning, we have looked at the
number of heard wearables as well as at the GDOP-based positioning accuracy in different
buildings and for different 𝛾 levels. The number of heard wearables is shown in Fig. 5; the
left-hand plot compares the two buildings (university building and shopping mall) assuming
a small measurement noise standard deviation 𝜎𝑚 = 0.2 m and an intentional position error
for the wearables that disclose their position of a moderate standard deviation 𝜎𝜖 = 2 m. The
right-hand plot in Fig. 5 also shows the number of heard wearables (taken into account the
path-loss propagation and 𝛾) for three different combinations of measurement and intentional
errors standard deviations (𝜎𝑚 , 𝜎𝜖 ).
Figure 4: Distributions (histograms) of the simulation parameters in the two considered buildings.




Figure 5: The average number of heard wearables versus the percentage 𝛾 of wearables not disclosing
their position. 80 wearables uniformly distributed in the building and 7500 Monte Carlos runs. Left:
comparison for two building maps; right: comparison for various 𝜎𝑚 and 𝜎𝜉 assumptions


   As we can see from the left plot in Fig. 5, when all wearables disclose their position, the number
of average heard number of wearables by their neighbours is a bit higher in the university
building than in the shopping mall building; this can be explained if we refer to Fig. 4, where we
can see that the path-loss slopes are a bit sharper and the inner wall losses are a bit higher for
the shopping mall than for the university building, which means that signal attenuates faster
and can go faster below the −100 dBm sensitivity limit. Surprisingly enough, when only 1 − 𝛾
of the wearables disclose their position, the number of heard wearables in the two buildings are
closer to each other. As expected, this number severely decreases when 𝛾 increases. The right
plot in Fig. 5 focuses only on the shopping mall building and checks different combinations of
(𝜎𝑚 , 𝜎𝜖 ). The impact of varying (𝜎𝑚 , 𝜎𝜖 ) on the number of heard wearables is very small, as
expected.
   The average positioning accuracy per wearable is shown in Fig. 6. Again, the left-hand
plot compares the results for different buildings and the right-hand plot compares the results
Figure 6: The average location error for all wearables in the system 𝜎𝑎𝑙𝑙 versus the percentage 𝛾
of wearables not disclosing their position. 80 wearables uniformly distributed in the building. 7500
Monte Carlos runs. Left: comparison for two building maps; right: comparison for various 𝜎𝑚 and 𝜎𝜉
assumptions; shopping mall building.




Figure 7: Impact of the number of wearables within the shopping-mall building. Left: Average number
of heard wearables versus the percentage 𝛾 of wearables not disclosing their position. Right: Average
location error for all wearables in the system 𝜎𝑎𝑙𝑙 versus the percentage 𝛾 of wearables not disclosing
their position.


inside the shopping mall building, for different (𝜎𝑚 , 𝜎𝜖 ) pairs. The blue lines are independent of
𝛾 and show the GDOP-based accuracy when all wearables disclose their position. In theory,
these curves should be completely flat, but since at every Monte Carlo run we have random
placement of wearables within the building and random path-loss parameters, there are small
variations with 7500 Monte Carlo runs; these blue curves would converge to completely flat
curves for a sufficiently high number of Monte-Carlo runs. The red lines show the deterioration
in the positioning accuracy when 𝛾 increases. If we set a target of maximum 1 m accuracy
deterioration, then the network would be tolerant to maximum 30% of wearables not disclosing
their position (i.e., 𝛾 = 0.3 as a fraction or 𝛾 = 30% as a percentage; for clarity reasons, 𝛾
is given in percents in our figures). Despite the fact the the number of heard wearables was
rather independent on the (𝜎𝑚 , 𝜎𝜖 ), the positioning accuracy, as expected, is highly influenced
by the measurement and intentional errors, as seen in the right-hand plot of Fig. 6. Again, up to
𝛾 = 30% offers very little degradation in the overall positioning accuracy, but for 𝛾 > 30%,
the performance starts to deteriorate fast. We would also like to emphasize the differences
between the two situations: a limited number of devices all disclosing their position (let’s
say 𝑁𝑤 = 70 devices, 𝛾 = 0%) and the presence of some devices not willing to share their
position (let’s say 𝛾 = 30% out of 𝑁𝑤 = 100 devices not sharing the position); while the overall
performance will be the same in both cases (as only 70 cooperative devices that share their
positions would be available in both cases), our research question pertained to finding out how
much the performance is deteriorating with respect to the maximum achievable performance
(i.e., 𝑁𝑤 = 100 devices in our second example) when some of them are not disclosing the
position. Our findings show that such performance deterioration is not high as long as the
𝛾 ≤ 30%, no matter on the value of 𝑁𝑤 .
    Last but not least, the effect of the number of the wearables in the building is shown in Fig. 7,
where we compare a situation with a low number of wearables 𝑁𝑤 = 30 with a situation with
a moderate number of wearables 𝑁𝑤 = 80. The left-hand plots show the average number of
heard wearables, which, of course, decreases when 𝑁𝑤 decreases. The right-hand plot of Fig. 7
show again that the positioning accuracy starts to deteriorate significantly for 𝛾 > 30% for
both 𝑁𝑤 = 30 and 𝑁𝑤 = 80.
    To sum up, our findings show that the opportunistic network for positioning tolerates up
to 30% of wearables not disclosing their position, without a significant loss in the positioning
accuracy and for 𝛾 > 30%, the accuracy starts to deteriorate significantly.


4. Conclusions and future research topics
Privacy-aware opportunistic and collaborative positioning could rely on the hypothesis that
only a percentage 𝛾 of wearables within an indoor space are willing to disclose their positions.
After proposing a GDOP-based positioning accuracy metric, we have investigated the robustness
to such a collaborative opportunistic setup under various scenarios (building maps, number of
wearables, assumptions regarding the measurement errors in estimating the position, etc.). It
was shown that up to around 30% of the wearables can choose to keep their location undisclosed
without a significant impact on the overall system performance.
   Different random distributions of the wearables within a building as well as different mobility
models of the wearables, including across-floor mobility, are to be investigated next. Further-
more, the relationship between the percentage 𝛾 of wearables hiding their position and classical
location privacy metrics, such as entropy-based privacy of [23] or the normalized cell error of
[24] are also to be investigated.


Acknowledgments
The authors gratefully acknowledge funding from the European Union’s Horizon 2020 Research
and Innovation programme under the Marie Sklodowska Curie grant agreement No. 813278
(A-WEAR, http://www.a-wear.eu/).


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