#  A Collaborative Approach Using Neural Networks for BLE-RSS Lateration-Based
Indoor Positioning

Pavel Pascacio1,2, Joaquín Torres-Sospedra3, Sven Casteleyn1 and Elena Simona
Lohan2 Corresponding Author: J. Torres-Sospedra (info@jtorr.es)This work was
supported by the European Union’s Horizon 2020 Research and Innovation
programme under the Marie Sklodowska Curie grant agreements No. $813278$
(A-WEAR: A network for dynamic wearable applications with privacy constraints,
http://www.a-wear.eu/) and No. $101023072$ (ORIENTATE: Low-cost Reliable
Indoor Positioning in Smart Factories, http://orientate.dsi.uminho.pt).
1Institute of New Imaging Technologies, Universitat Jaume I, Castellón, Spain
2Electrical Engineering Unit, Tampere University, Tampere, Finland  3Algoritmi
Research Centre, Universidade do Minho, Guimarães, Portugal

###### Abstract

In daily life, mobile and wearable devices with high computing power, together
with anchors deployed in indoor environments, form a common solution for the
increasing demands for indoor location-based services. Within the technologies
and methods currently in use for indoor localization, the approaches that rely
on Bluetooth Low Energy (BLE) anchors, Received Signal Strength (RSS), and
lateration are among the most popular, mainly because of their cheap and easy
deployment and accessible infrastructure by a variety of devices.
Nevertheless, such BLE- and RSS-based indoor positioning systems are prone to
inaccuracies, mostly due to signal fluctuations, poor quantity of anchors
deployed in the environment, and/or inappropriate anchor distributions, as
well as mobile device hardware variability. In this paper, we address these
issues by using a collaborative indoor positioning approach, which exploits
neighboring devices as additional anchors in an extended positioning network.
The collaborating devices’ information (i.e., estimated positions and BLE-RSS)
is processed using a multilayer perceptron (MLP) neural network by taking into
account the device specificity in order to estimate the relative distances.
After this, the lateration is applied to collaboratively estimate the device
position. Finally, the stand-alone and collaborative position estimates are
combined, providing the final position estimate for each device. The
experimental results demonstrate that the proposed collaborative approach
outperforms the stand-alone lateration method in terms of positioning
accuracy.

###### Index Terms:

Collaborative Indoor Positioning, Multilayer Perceptron, Received Signal
Strength, Bluetooth Low Energy

ANN

    Artificial Neural Network
BS

    base Station
BLE

    Bluetooth Low Energy
CDF

    Cumulative distribution Function
CIPS

    Collaborative Indoor Positioning System
CRLB

    Cramér Rao Lower Bound
ECDF

    Empirical Cumulative Distribution Function
GDOP

    Geometric Dilution of Precision
GNSS

    Global Navigation Satellite System
GT

    Ground-Truth
IPS

    Indoor Positioning System
LBS

    location-based service
LDPL

    Logarithm Distance Path Loss
LSTM

    Long Short-Term Memory
LOS

    Line-of-sight
MAD

    Median Absolute Deviation
MLP

    Multilayer Perceptron
MSE

    Mean Square Error
NLOS

    Non-line-of-sight
PCA

    Principal Component Analysis
RF

    Radio Frequency
RMSE

    Root Mean Square Error
RSS

    Received Signal Strength
RSSI

    Received Signal Strength Indicator
SISO

    Single Input Single Output
ToF

    Time of Flight
TWR

    Two-way Ranging
UWB

    Ultra-wide band

##  I Introduction

Nowadays, there is a growing demand for indoor location-based services which
are able to ubiquitously and accurately provide a user’s position relative to
the surrounding environment in an inexpensive manner [1]. Examples of LBS
include navigation and location-aware and tracking services [2, 3, 4]. To this
end, the pervasiveness of mobile and wearable devices with high computing
power, together with growing deployment of anchors in indoor environments,
play an important role. Among the large variety of technologies and methods
used, solutions relying on Bluetooth Low Energy (BLE) and Received Signal
Strength (RSS) are very popular, as they provide a cheap and easy deployment
[5, 6, 7, 8].

Although the feasibility of using BLE–RSS anchors/devices for proximity
detection applications has been demonstrated [9, 10], their implementation for
accurate positioning applications is still an open issue. Due to their
relatively straightforward implementation, lateration algorithms are one of
the most explored solutions to enhance positioning accuracy. Unfortunately,
they suffer from accuracy degradation mainly due to four factors:

  1. 1.

Anchor deployment: a low quantity of anchors deployed in the environment
and/or the inappropriate anchor distribution increase not only the chance of
Non-line-of-sight (NLOS) conditions but also the locations inside the
operational area with insufficient anchor coverage for reliable lateration,
reducing the overall positioning accuracy dramatically.

  2. 2.

Unstable BLE signal strength: RSS of Radio Frequency (RF) signals are prone to
fluctuate due to environmental conditions (geometries, temperature, crowded
environments), building materials and presence of obstacles or people between
transmitter and receptor devices (NLOS conditions) [11, 12, 13]. Such dynamic
fluctuations are often difficult to predict and compensate for, and cause
position estimation errors when used for positioning. In fact, the BLE signal
propagation in indoor environments has not been properly modeled yet in order
to estimate the relative distance between transmitter and receiver using
smartphones.

  3. 3.

Hardware heterogeneity: the RSS signature depends on the transmitters and
receivers involved [14]. The diversity of devices involved in localization –
both anchors and smartphones – comes with variability in the hardware-specific
parameters, such as antenna gains, and thus in the BLE received signal
strength [15, 13]. Furthermore, the transmission power and transmission period
preset in each device – either by the device owner or manufacturer – presents
variations due to tolerance in the design of antennas or in the RF circuit
components, even in similar devices.

  4. 4.

Software limitations: the energy-saving modes and execution task priorities
prescribed by the mobile devices’ operating systems may alter the
transmission/reception period of BLE signals, rendering these devices non-
deterministic for the BLE broadcasting.

In this article, we aim to enhance the positioning accuracy of the stand-alone
lateration method applied to an adverse indoor scenario that copes with the
first, second, and third issues mentioned above, namely the lack of sufficient
beacons or problematic beacon distribution with the associated presence of
large NLOS areas, the lack of appropriate signal propagation models to deal
with fluctuating signal strength in unpredictable indoor conditions, and the
heterogeneity among mobile devices typically present in any scenario. We do so
by proposing a collaborative indoor position system which exploits the
neighboring mobile devices as additional anchors in an extended, ad-hoc
positioning network. The collaborating devices’ information (i.e., their
stand-alone estimated position and BLE–RSS) is exchanged and processed using a
neural network model (rather than the traditional path-loss models) to
estimate relative distances, after which lateration is applied to estimate the
device’s collaborative position. Unlike the path-loss models, which estimate
the distance primarily based on signal attenuation formulas, the neural
network model aims to relate the distance to RSS patterns, pairwise device
position, identification of devices (transmitter and receiver), and variation
of RSS measurements due to the devices’ hardware heterogeneity. The
collaborative algorithm takes mobile device variations into account by
considering, for each device, a BLE reference measurement at one meter.
Finally, a midpoint line algorithm is used to combine the collaborative and
the non-collaborative position estimates to provide the final position
estimates of each collaborative device. The key contributions of this paper
are summarized as follows:

  * •

We present a collaborative indoor position approach using Multilayer
Perceptron (MLP) Artificial Neural Network (ANN) to enhance BLE–RSS
lateration-based indoor positioning.

  * •

We present a MLP ANN model to estimate relative distances between
collaborative devices in order to provide a most reliable distance estimation.
The MLP model provides a better modeling of the NLOS and Line-of-sight (LOS)
conditions of the environment with respect to path-loss-based models, as well
as, the characteristic inherent of each receiving device. Additionally, the
proposed model avoids setting the parameters needed in path-loss-based models.

  * •

We experimentally demonstrate, using a scenario with a poor quantity and
inappropriate distribution of anchors, and rich NLOS conditions, that our
collaborative approach outperforms the stand-alone lateration approach with
respect to positioning accuracy in such conditions.

##  II Related Work

The design of reliable Indoor Positioning System (IPS), which provide a
balance between position accuracy and low-cost and easy deployment, is one of
the main concerns in the design of location-based services (LBSs) [1]. To meet
this concern, diverse solutions have been proposed. In this section, we focus
on those fields relevant for this work, namely lateration, artificial neural
network, and collaborative IPS.

###  II-A Lateration

Lateration approaches estimated the target position by considering the
distance between the target and multiple reference anchors (minimum
three)[16]. The distance is the result of the conversion of RSS measured
between reference anchors and target [16, 17]. Free space path, two-ray
ground, and logarithmic path-loss are some of the most used models to convert
RSS into distance [18, 19, 20].

In the context of indoor positioning, it has been shown in literature that
having more (even redundant) anchors yield better positioning accuracy
–independent of the lateration approach used– and least-square lateration
performs better than traditional lateration. For example, [16] proposed an
RSS-based lateration algorithm, which was implemented using a least-squares
method and required redundant anchors deployment. The distances between
anchors and target were estimated with the Logarithm Distance Path Loss (LDPL)
model, whose parameters were computed statistically. The experiments were
conducted in a $6\text{\times}6\text{\,}\mathrm{m}$ area, considering 196
measurement points collected with a single device in complete LOS. The authors
conclude that adding least-squares to lateration reduces the error by $67.6\%$
to $2.8\text{\,}\mathrm{m}$, and including redundant anchors reduces the error
to $1.35\text{\,}\mathrm{m}$. [17] also proposed a least-square lateration
approach and performed an accuracy error analysis using simulated
environments. The analysis included the level of Gaussian noise, number of
anchors, and size of the area. The results were compared with a traditional
lateration, concluding that increasing the density of anchors deployed
improves positioning accuracy. The proposed method significantly improved
lateration in scenarios with a strong noise component (high Gaussian noise,
$\sigma=5$), reducing the error from
$4.5\text{\,}\mathrm{m}1.9\text{\,}\mathrm{m}$,
$5.9\text{\,}\mathrm{m}3.9\text{\,}\mathrm{m}$ and
$18\text{\,}\mathrm{m}7.5\text{\,}\mathrm{m}$ for
$6\text{\times}6\text{\,}\mathrm{m}$, $12\text{\times}12\text{\,}\mathrm{m}$
and $24\text{\times}24\text{\,}\mathrm{m}$ test areas respectively.

In line with literature, our method uses least-square-based method for
lateration. Moreover, our approach aims to increase the amount of anchors, yet
in contrast to previous works that deploy additional fixed anchors in the
environment, we dynamically extend the positioning network using the devices
of the users in a collaborative setting.

###  II-B Artificial neural network

Artificial Neural Networks (ANNs) are commonly used to self-learn the
relationship between data provided to resolve complex problems [21].
Specifically, in indoor positioning they are used to provide robustness
against noise and interference that affect the positioning accuracy [22]. For
example, [21] presented a path-loss model based on Multilayer Perceptron (MLP)
neural networks for wireless communication networks. For that purpose they
considered several models using input vectors with fifteen features of the
environment. The authors conclude that the introduction of environment
features in the MLP model input and adding two hidden layers (with 5 and 10
neurons) provide an accurate and efficient path-loss prediction. On the other
hand, [23] proposed an indoor localization approach based on Wi-Fi
fingerprinting and Long Short-Term Memory (LSTM) neural networks for position
estimation. The experiments were carried out in
$54\text{\times}32\text{\,}\mathrm{m}$ test L-shape area with ad-hoc Wi-Fi
anchors deployed and a single smartphone to scan the signals. The LSTM model
consist of $42$ input features, $2$ outputs, $300$ neurons, learning rate
$\lambda=0.2$, drop error, and $250$ epochs. The results reported an average
error of around 1 $\mathrm{m}$.

In contrast to related work, our MLP architecture is intended for use with
heterogeneous mobile devices to estimate the relative distance between
neighboring devices in a collaborative approach. To this end, our MLP
architecture exploits the usual short distance between neighboring devices to
reduce the dimensionality of features and, consequently, obtain a lightweight
neural network architecture that is feasible to implement on mobile devices.
Specifically, the MLP architecture relates the distance to four main elements
of BLE-RSS collaborative approaches. The elements used for the features of the
architecture are the RSS patterns, pairwise device position, identification of
devices (transmitter and receiver), and variation of RSS measurements due to
devices’ hardware heterogeneity.

###  II-C Collaborative indoor positioning systems

Collaborative IPSs aim to enhance positioning of devices/users by using
wireless communication technologies, both for relative distance estimation and
information exchange between them [24]. Within the collaborative IPSs, those
relying on BLE-RSS for the non-collaborative and collaborative phase, as our
approach, are scarce (for a comprehensive overview of collaborative IPSs, we
refer to our recent systematic literature review [24]). One of the most
representative ones is proposed by [20], which presented a collaborative IPS
based on inertial sensing, adaptive multi-lateration, and a mobile
encountering approach. All these sources of data were combined using a
particle-filter model to locate a target.

The author conclude that the accuracy improvements are approximately $28.19\%$
in LOS and $19.99\%$ in NLOS when using adaptive ranging device-specific
parameter with respect to the none adaptive approach.

In contrast to what has been done in the literature, we do not rely on the
LDPL model to estimate the relative distance between a receiver (RX) and a
transmitter (TX). Instead, we use a neural network to process the RSS value
depending on the transmitter and receiver location and receiver calibration.

###  II-D Overall summary

From the above-mentioned systems, we can summarize that the lateration methods
considerably decrease the positioning accuracy as the density of anchors in
the area decreases and the noise signal increases. ANNs can mitigate the
effect of the environment on the position and distance estimation, as well as
reduce the accuracy error. Additionally, the implementation of collaborative
approaches can help to reduce the positioning error of individual estimations.
To the best of our knowledge, this is the first BLE–RSS indoor positioning
system that implements a collaborative approach based on ANNs.

##  III System Overview

Under simulations or in ideal testbed conditions, i.e. scenarios featuring a
rich amount and well distributed anchors in the environment and LOS
conditions, RSS-based lateration approaches have provided high accuracy with
positioning errors within the range of
$0.8\text{\,}\mathrm{m}1.3\text{\,}\mathrm{m}$ [16, 17]. Nevertheless, in real
environments (e.g., offices, stores, libraries) the positioning accuracy
decreases dramatically. Real environments are characterized by large NLOS
areas and anchor deployments that may not be exclusively designed for
positioning tasks. In addition, each environment requires a dedicated modeling
of the RF signal propagation to compensate for environment-specific conditions
and accurately convert RSS into distance.

In this work, we propose a collaborative IPS using ANNs to enhance BLE–RSS
lateration-based methods. Our approach tackles three main sources of
positioning inaccuracy: mitigating the inaccuracy due to NLOS areas and
inadequate deployment of anchors; reducing the impact of a inappropriate
signal propagation modeling; and minimizing the impact of device
heterogeneity. Potential application scenarios of our approach is indoor
positioning in buildings with a poor infrastructure deployment, but with a
moderate amount of mobile devices (people) inside and where the latency for
users/devices positioning is moderate (e.g., tracking library assistants in
libraries, patients in hospitals, personnel in government offices, among
others).

Our collaborative approach is divided in three phases which are described in
this section. The first phase is devoted to registering devices used in the
collaborative approach, the second phase consists of the stand-alone (non-
collaborative) lateration algorithm for position estimation of each
device/user, and the last phase is devoted to collaboratively enhance the
position of the target device/user.

###  III-A Registering a device for collaborative positioning

The registration procedure aims to identify a mobile device and record an RSS
reference value, to be used in the collaborative algorithm. To this end, a
fixed reference anchor $(BX)$ emitting BLE advertisements is placed at an
entry point to the environment. Each new user is then asked to position
himself at 1 meter from the anchor (marked on the floor) in LOS, and measure
and record the RSS value (i.e., $RSS^{1m}_{RX}(BX)$). This lightweight
calibration procedure is performed only once for each (new) device. To ease
this procedure, the calibration could be integrated with the electronic
locking system of the main doors, calibrating the device every time the user’s
smartphone is used to unlock a door.

###  III-B Stand-alone phase

The stand-alone phase is devoted to estimating each initial individual
device/user’s position considering the RSS and the Ground-Truth (GT)
coordinates of BLE anchors deployed in the environment. For reference, in this
article this position estimation is performed using a lateration method based
on the LDPL model, a minimization problem, and the Levenberg-Marquardt
algorithm for weighted nonlinear least-squares to solve the minimization
problem.

The LDPL model expresses the relation between RSS and distance, as described
by Eq. (1) [25]:

$RSS^{d}_{RX}(TX)=RSS^{1m}_{RX}(BX)-10\>\eta\>log\left(\frac{d}{d_{0}}\right)\textbf{}$
(1)

Where $RSS^{d}_{RX}(TX)$ is the RSS measured at a distance $d$ between
transmitter ($TX$), which can be a BLE beacon or a smartphone, and receiver
($RX$); $RSS^{1m}_{RX}(BX)$ is the RSS measured at $1\text{\,}\mathrm{m}$; and
$\eta$ is the path-loss attenuation factor.

Mathematically, the lateration approach is expressed by Eq. (2) as a
minimization of the sum of squared errors between the measured distances
($d_{m}$) and hypothetical ones ($g_{m}(\b{x})$), based on the unknown target
position, $g_{m}(\b{x})$, which is denoted by Eq. (3) [26].

$\min_{\b{x}}\displaystyle\sum_{m=1}^{M}\left(g_{m}(\b{x})-d_{m}\right)^{2}$
(2)
$g_{m}(\b{x})\triangleq\sqrt{\left(x-bx_{m}\right)^{2}-\left(y-by_{m}\right)^{2}}$
(3)

Where, $m=\\{1,2...M\\}$ are the number of BLE anchors deployed;
$\b{x}=\\{x,y\\}$ are the device/user’s unknown coordinates; and
$\\{bx_{m},by_{m}\\}$ the GT coordinates of BLE anchors.

Algorithm 1 shows the pseudo-code for the stand-alone lateration approach,
whose workflow is summarized as follows:

  * •

1st step: Collect the RSS from BLE anchors ($RSS^{d}_{RX}(TX)$) within a time
window ($tw$) of $60\text{\,}\mathrm{s}$, by discarding those not belonging to
the deployed scenario (input data for Algorithm 1);

  * •

2nd step: Group the RSS readings by anchor removing the outlier values. We
consider the values falling out of 25 and 75 percentiles (lines 1–2 in
Algorithm 1) as outliers;

  * •

3rd step: Apply the average operator to the RSS values of each anchor, in
order to get one averaged RSS value per anchor (line 3 in Algorithm 1);

  * •

4rd step: Select ”strong reference BLE anchors”, defined as the anchors with
averaged RSS equal or greater than a predefined threshold (lines 4–8 in
Algorithm 1);

  * •

5th step: Estimate the relative distances of selected reference BLE anchors to
the device/user’s target position, by using the LDPL model, which is expressed
by eq.(1), and their RSS values (line 9 in Algorithm 1);

  * •

6th step: Estimate the device/user’s position, $\hat{\textbf{P}}^{Lat1}$,
using the Levenberg-Marquardt Weighted Least Squares (L-MWLS) lateration
method to fit the Euclidean Distance model. Henceforth, $Lat1$ will refer to
the L-MWLS lateration method. The input data to fit the model are the
distances estimated in the 5th step, the weights and the GT of the BLE
anchors. The weight value for every BLE anchor is computed as the inverse of
its distance square with respect to the device/user;

  * •

7th step: Share the estimated position,
$\hat{\textbf{P}}^{Lat1}(RX)=[\hat{P}^{Lat1}_{x}(RX),\hat{P}^{Lat1}_{y}(RX)]$.

We set the $threshold$ value to $-83\text{\,}\mathrm{dBm}$ and the path-loss
attenuation factor to $\eta=2.1$, as we previously used in [27] and which are
in phase to values in literature [16]. Each device involved in the
collaborative positioning model will have its own value for
$RSS^{1m}_{RX}(BX)$ calculated from the data collected in the device
registration phase (see Table II).

Algorithm 1 Stand-alone Lateration

0: Deployed anchors information collected within a time window $tw$:
$RSS^{d}_{RX}(TX)$ values and GT

0: LDPL: $\eta=2.1$ and $RSS^{1m}_{RX}(BX)$

0: $threshold$

0: Estimated device/user position $\hat{\textbf{P}}^{Lat1}(RX)$

1: Group the $RSS^{d}_{RX}(TX)$ values by beacon

2: Remove $RSS^{d}_{RX}(TX)$ outliers values of each group

3: Average $RSS^{d}_{RX}(TX)$ values of each group :
$\overline{RSS^{d}_{RX}(TX)}$

4: for $i\leftarrow$ 1 to number of $\overline{SS^{d}_{RX}(TX)}(i)$ do

5: if ($\overline{SS^{d}_{RX}(TX)}(i)\geq treshold$) then

6: Include $i$-th anchors to reference anchors set ($ref_{anchorset}$)

7: end if

8: end for

9: Estimate the distances between anchors of $ref_{anchorset}$ and the
device/user position using Eq.1, $\eta$ and $RSS^{1m}_{RX}(BX)$

10: Estimate the device/user position ($\hat{\textbf{P}}^{Lat1}(RX)$) using
the Levenberg-Marquardt Weighted Least Squares method

11: Share the estimated device/user position
($\hat{\textbf{P}}^{Lat1}(RX)=[\hat{P}^{Lat1}_{x}(RX),\hat{P}^{Lat1}_{y}(RX)]$)

###  III-C Collaborative phase

The collaborative phase uses the neighboring mobile devices’ information,
which include the measured BLE-RSSs, the estimated positions for the receiver
and transmitter devices, and the RSS at $1\text{\,}\mathrm{m}$ of the receiver
to collaboratively estimate the device/user’s position, and ultimately provide
the final position estimate based on the combined collaborative and stand-
alone estimates, aiming to improve the latter. Each device/user, which
exchanges information and collaborates with others, acts as an additional
anchor, creating an extended ad-hoc positioning network, hereby improving the
coverage of the original anchor network.

The collaborative phase relies on four main elements: 1) information exchanged
between devices; 2) estimation of relative distances using a Multilayer
Perceptron (MLP) neural network; 3) a lateration algorithm to collaboratively
estimate the target device/user’s position; and 4) a method to combine the
stand-alone and collaborative position estimations.

####  III-C1 Information exchanged between devices/users

Currently, the operating systems of mobile and wearable devices permit
broadcasting BLE advertisements. This feature allows them to act as BLE
anchors and share information, enabling the development of collaborative
positioning systems [28]. The information used in our collaborative
positioning system includes: the RSS received at receiver from transmitter
($RSS_{RX}(TX)$), the RSS at $1\text{\,}\mathrm{m}$ ($RSS^{1m}_{RX}(BX)$) of
the receiver obtained after registering the device and the position of each
collaborative device/user estimated by the stand-alone lateration
($\hat{P}_{x}^{Lat_{1}}(TX)$,$\hat{P}_{y}^{Lat_{1}}(TX)$,$\hat{P}_{x}^{Lat_{1}}(RX)$,$\hat{P}_{y}^{Lat_{1}}(RX)$).

All these collected data are used as inputs for the neural network presented
in next subsection and the collaborative algorithm presented in Algorithm 2.

####  III-C2  Multilayer Perceptron (MLP) neural network and relative
distances

The MLP neural network model’s architecture used to estimated the relative
distances is presented in Figure 1. Its architecture consists of 6 input
layers, 1 hidden layer with 3 neurons, and one output layer. The activation
function used is the hyperbolic tangent. In the training, the scaled conjugate
gradient back propagation was used as training function and $50$ epochs were
considered. Further information about the selection of hyperparameters of the
MLP neural network is provided in Section IV. The 6 inputs that feed the MLP
neural network model correspond to the exchanged information between each pair
(target device–neighbor device) and the output is the estimated distance of
that specific pair. The input are: the $RSS_{RX}(TX)$, which corresponds to
the RSS of the BLE advertisement sent by the transmitter $TX$ and measured at
the receiver $RX$; the $x$ and $y$ coordinates of the transmitter (neighbor
device/user) position estimated by the stand-alone lateration algorithm
($\hat{P}_{x}^{Lat_{1}}(TX)$,$\hat{P}_{y}^{Lat_{1}}(TX)$); and the $x$ and $y$
coordinates of the receiver (target device/user) position estimated by the
stand-alone lateration algorithm
($\hat{P}_{x}^{Lat_{1}}(RX)$,$\hat{P}_{y}^{Lat_{1}}(RX)$).

Finally, the $RSS^{1m}_{RX}(BX)$ is the RSS value measured at
$1\text{\,}\mathrm{m}$ of distance between transmitter and receiver assigned
at each mobile device by phase one (see Table II).

Figure 1: MLP neural network model architecture. Used to estimate relative
pairwise distance between target and neighboring devices/users.

####  III-C3 Collaborative lateration algorithm

The lateration algorithm used in the collaborative phase is the same algorithm
used in the stand-alone phase (see Section III-B). The main two differences
are within the data used to perform the lateration.

  * •

First, rather than fixed BLE beacons in the environment with well-known
position, the anchors considered in the collaborative lateration algorithm are
the neighboring devices/users, of which only the position estimated by the
stand-alone lateration is known.

  * •

Second, the relative distances between the target device/user and the
neighboring devices/users is computed using a MLP neural network model instead
of the LDPL model.

####  III-C4 Combining stand-alone and collaborative estimated positions

Once the position of the target device is collaboratively estimated using
neighbor devices/users as anchors, it is combined with the stand-alone
estimation to come to a final estimated position. In this article, we used a
midpoint line algorithm, as described in Eq. (4).

$\displaystyle\hat{\hat{P}}_{x}(RX)$
$\displaystyle=\frac{\hat{P}^{lat_{1}}_{x}(RX)+\hat{P}^{lat_{2}}_{x}(RX)}{2}$
(4) $\displaystyle\hat{\hat{P}}_{y}(RX)$
$\displaystyle=\frac{\hat{P}^{lat_{1}}_{y}(RX)+\hat{P}^{lat_{2}}_{y}(RX)}{2}$
(5)

Where $\hat{\hat{\textbf{P}}}=[\hat{\hat{P}}_{x}(RX)$,
$\hat{\hat{P}}_{y}(RX)]$ represents the final estimated position, with $x$ and
$y$ coordinates, of device/user $RX$, with $RX=\\{1,2....N\\}$ and $N$ the
number of devices. $\hat{P}^{lat_{2}}_{x}(RX)$ and $\hat{P}^{lat_{2}}_{y}(RX)$
are the position estimated, $x$ and $y$ coordinates, with the collaborative
lateration and $\hat{P}^{lat_{1}}_{x}(RX)$ and $\hat{P}^{lat_{1}}_{y}(RX)$ are
the position estimated, $x$ and $y$ coordinates, with the stand-alone
lateration, both for device/user $RX$.

####  III-C5 Full collaborative workflow

Finally, algorithm 2 shows the pseudo-code for the collaborative positioning
algorithm. The algorithm inputs are the shared information exchange by each
collaborative device/user within a time window ($wt$) of
$60\text{\,}\mathrm{s}$ and correspond to the RSS transmitted by each
collaborative device/user ($RSS_{RX}(TX)$), position of each collaborative
device/user estimated by the stand-alone lateration
($\hat{P}_{x}^{Lat_{1}}(TX)$,$\hat{P}_{y}^{Lat_{1}}(TX)$,$\hat{P}_{x}^{Lat_{1}}(RX)$,$\hat{P}_{y}^{Lat_{1}}(RX)$),
and the RSS at $1\text{\,}\mathrm{m}$ ($RSS^{1m}_{RX}(BX)$). The algorithm
workflow is summarized as follows:

  * •

1nd step: Group the RSS readings by device and remove outlier values. We
consider those values falling out of 25 and 75 percentiles (lines 1–2 in
Algorithm 2) as outliers;

  * •

2rd step: Apply the average to the RSS values of each device/user, getting one
averaged RSS value per device/user (line 3 in Algorithm 2);

  * •

3th step: Estimate the relative distances of neighboring devices/users to the
target device/user, using the MLP model, which structure is depicted in Figure
1. The inputs of ANN model are:$RSS_{RX}(TX)$,
($\hat{P}_{x}^{Lat_{1}}(TX)$,$\hat{P}_{y}^{Lat_{1}}(TX)$,$\hat{P}_{x}^{Lat_{1}}(RX)$,$\hat{P}_{y}^{Lat_{1}}(RX)$),
$RSS^{1m}_{RX}(BX)$ and (input values in Algorithm 2);

  * •

4th step: Estimate the device/user’s position ($\hat{\textbf{P}}^{Lat2}(RX)$)
using the Levenberg-Marquardt Weighted Least Squares (L-MWLS) lateration
method to fit the Euclidean Distance model. The input data to fit the model
are the relative distances estimated by the MLP neural network model (step 3),
the weights and the estimated positions ($\hat{\textbf{P}}^{Lat1}$) of the
neighboring devices/users. As in the stand-alone algorithm, the weight value
for every BLE anchor is computed as the inverse of its distance square with
respect to the device/user;

  * •

5th step: Compute the final estimated device/user’s position
($\hat{\hat{\textbf{P}}}(RX)$) based in the formula expressed in eq.(4), using
the estimated standalone position $\hat{\textbf{P}}^{lat_{1}}(RX)$ and
collaborative estimated position $\hat{\textbf{P}}^{lat_{2}}(RX)$, where
$(RX)$ is the identifier of the device/user to estimate its position.

Algorithm 2 Collaborative module

0: Collaborative devices information collected within a time window $tw$:
$RSS_{RX}(TX)$,
$\hat{P}_{x}^{Lat_{1}}(TX)$,$\hat{P}_{y}^{Lat_{1}}(TX)$,$\hat{P}_{x}^{Lat_{1}}(RX)$,$\hat{P}_{y}^{Lat_{1}}(RX)$,
and $RSS^{1m}_{RX}(BX)$

0: Improved estimated device/user position ($\hat{\hat{\textbf{P}}}_{dev}(n)$)

1: Group the $RSS_{RX}(TX)$ values by device

2: Remove $RSS_{RX}(TX)$ outliers values of each group

3: Average $RSS_{RX}(TX)$ values of each group: $\overline{RSS_{dev}}(i)$

4: Estimate the relative distance between the target device and the near
collaborative devices using the trained ANN model

5: Estimate the device/user’s position ($\hat{\textbf{P}}^{Lat_{2}}(RX)$)
using the Levenberg-Marquardt Weighted Least Squares (L-MWLS) Lateration
method

6: Compute the final estimated device/user’s position
($\hat{\hat{\textbf{P}}}(RX)$) using the midpoint line algorithm of eq.(4)

TABLE I: Position of the anchors, BLE beacons and collaborative devices in the 7 configurations | BLE anchors |  | Config. 1 |  | Config. 2 |  | Config. 3 |  | Config. 4 |  | Config. 5 |  | Config. 6 |  | Config. 7
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
$n$ | x | y |  | x | y |  | x | y |  | x | y |  | x | y |  | x | y |  | x | y |  | x | y
1 | 0 | 0 |  | 5.05 | 3.7 |  | 1.33 | 6.1 |  | 6.93 | 1.3 |  | 7.75 | 6.1 |  | 2.05 | 9.7 |  | 2.05 | 9.7 |  | 2.05 | 9.7
2 | 0 | 10.68 |  | 6.55 | 4.55 |  | 4.49 | 3.05 |  | 9.93 | 1.3 |  | 11.75 | 2.75 |  | 3.6 | 3.3 |  | 8.7 | 6.4 |  | 14.66 | 6.45
3 | 3.78 | 6.51 |  | 8.05 | 0.7 |  | 7.66 | 0.1 |  | 12.93 | 1.3 |  | 12.75 | 0.1 |  | 16.45 | 2.5 |  | 16.45 | 2.5 |  | 16.45 | 2.5
4 | 6.68 | 10.64 |  | 5.05 | 0.7 |  | 1.33 | 0.1 |  | 9.03 | 0.1 |  | 7.75 | 0.1 |  | 2.05 | 2.5 |  | 2.05 | 2.5 |  | 2.05 | 2.5
5 | 9.2 | 3.7 |  | 8.05 | 3.7 |  | 7.66 | 6.1 |  | 9.03 | 3.7 |  | 12.75 | 6.1 |  | 16.45 | 9.7 |  | 16.45 | 9.7 |  | 16.4 | 9.7
6 | 14.2 | 6.05 |  | - | - |  | - | - |  | - | - |  | - | - |  | - | - |  | - | - |  | - | -
7 | 16.65 | 10.65 |  | - | - |  | - | - |  | - | - |  | - | - |  | - | - |  | - | - |  | - | -

##  IV Experiments and Results

###  IV-A Objectives and Experimental setup

The principal goal of our experiments is to assess the feasibility and
benefits of our collaborative approach with respect to a traditional BLE-RSS
lateration baseline to mitigate inadequate deployment of BLE anchors and
increased NLOS conditions. Specifically, we evaluate and compare the
positioning accuracy of both in a realistic environment.

We performed the experiments in a real office scenario. The office covers an
approximate area of $10.8\text{\times}16.7\text{\,}\mathrm{m}$ and contains
seven deployed BLE beacons (anchors), with a transmission power and period of
$-4\text{\,}\mathrm{dBm}$ and $250\text{\,}\mathrm{ms}$ respectively. Figure 2
shows the complete scenario through a 3D representation, which allows us to
illustrate the complexity of the environment. The NLOS conditions are mainly
created by the furniture, which includes chairs, desks, desktop computers,
bookshelves, and the concrete metal-reinforced pillars.

Figure 2: 3D Office Scenario representation

In this office scenario, a comprehensive data collection was conducted. First,
the five collaborative devices were registered during the registration phase
(see Section III-A) and their $RSS^{1m}_{RX}$ was measured using a fixed BLE
beacon from the environment. Table II summarizes the five devices that were
used in the experiment, and their corresponding $RSS^{1m}_{RX}$ value, which
depend on the smartphone model and range from
$-78.79\text{\,}\mathrm{dBm}-62.39\text{\,}\mathrm{dBm}$.

TABLE II: $RSS^{1m}_{RX}(BX)$ values by device $RX$ | Device |  $RSS^{1m}_{RX}(BX)$ values ($\mathrm{dBm}$)
---|---|---
1 | Galaxy S8 | -68.88
2 | Lenovo Yoga Book | -74.75
3 | Galaxy A7 Duos | -62.39
4 | Galaxy S6 | -62.99
5 | Galaxy A5 | -78.79

Then, seven different collaborative distributions (called configurations in
this paper) made up of these five devices were considered. In each
configuration, the five devices simultaneously broadcast and save the
information of surrounding devices, including the BLE anchors, for 2 hours.
Devices broadcast every 100 ms in accordance with the low latency mode
supported by Android devices [29]. However, as mobile devices are not ad-hoc
positioning devices, the broadcast period is affected mainly by the priority
of executing tasks and power saving modes implemented by operating systems.
The data collection for each configuration was performed independently, at a
different time. As already mentioned, for the lateration approach based on the
Logarithm Distance Path Loss (LDPL), the path-loss factor was determined to be
$\eta=2.1$ for all the five devices. Figure 3 and Figure 4 show the
distribution of the devices in each configuration and the BLE anchors in the
scenario, and Table I summarizes the GT coordinates of them.

Figure 3: Distribution of the configuration 2, 3, 6, and 7 used in the training & validation and distribution of the BLE anchors Figure 4: Distribution of the configuration 1, 4, and 5 used in the testing and distribution of the BLE anchors (a) MLP1 | (b) MLP2 | (c) MLP3 | (d) MLP4
---|---|---|---
Figure 5: Target vs Predicted distances from the test dataset estimated with
MLP1–MLP4 architectures

The data collected in the seven configurations were split into two datasets,
where the devices cover different areas, and the distances among devices, and
between devices and anchors, varies. Each dataset is used for different
purposes: configurations 2, 3, 6, and 7 (see Fig. 3) were used to train the
model and configurations 1, 4, and 5 (see Fig. 4) were used for evaluation. In
order to tune the MLP neural network, the first dataset was randomly split
into training ($70\%$) and validation ($30\%$) with $968798$ and $242199$
samples respectively. The testing dataset contains $936103$ samples and it was
used to test the MLP ANN for relative distances, and implement the BLE-RSS
lateration baseline and collaborative approach.

The selected scenario is challenging and covers an area with low Geometric
Dilution of Precision (GDOP) and strong heterogeneous NLOS conditions
(diversity in obstacles): only 7 BLE beacons provide positioning, and there is
device diversity in the collaborative phase. The proposed collaborative model
targets dynamically extending the anchor coverage by using the collaborative
user’s devices, replacing the traditional LDPL model with a MLP ANN that
processes the RSS considering the receiver and emitter location and the
calibration of RSS (at $1\text{\,}\mathrm{m}$) to minimise the device
diversity effect.

###  IV-B Multilayer Perceptron (MLP) neural network tuning

We tested four Multilayer Perceptron (MLP) neural network architectures in
order to determine the best architecture and set of hyperparameters of our
model. As hyperparameters, we considered different numbers of hidden layers (1
and 2) and neurons, as well as two types of activation functions, the
Hyperbolic tangent sigmoid (tansig) and Log-sigmoid (logsig). Table III
summarizes the hyperparameters configured in the proposed architectures.

TABLE III: Tested MLP architectures and hyper parameters Parameters | MLP1 | MLP2 | MLP3 | MLP4
---|---|---|---|---
No. Input layers | 6 | 6 | 6 | 6
No. Hidden layers (HLs) | 1 | 1 | 2 | 2
No. Output Layer | 1 | 1 | 1 | 1
No. Neurons HL1 | 3 | 3 | 6 | 12
No. Neurons HL2 | - | - | 3 | 6
Training function | trainscg
Activation function | tansig | logsic | tansig | tansig
Performance Function | Mean Square error

Before presenting the main positioning results of the proposed collaborative
approach and the lateration baseline, we present the results of evaluating the
four proposed MLP architectures with the training dataset in order to
determine which of them provides a more accurate estimation of relative
distances. Figure 5 shows the density scatter plots of the real distance
against estimated distance by each MLP neural network architecture. Also, the
Root Mean Square Error (RMSE) and correlation coefficient (R) values are
indicated in each of them.

From those values and density scatter plots, we can notice that the Multilayer
Perceptron (MLP) architectures with one hidden layer (MLP1 and MLP2) present a
RMSE lower than the architectures with two hidden layers (MLP3 and MLP4), as
well as a greater correlation coefficient ($0.74$ and $0.69$ for MLP1 and MLP2
respectively). Therefore, architectures with a single hidden layer are able to
estimate the distance more accurately. In specific, MLP1, which use an
hyperbolic tangent sigmoid activation function (tansig), presents a higher
density of predicted values closer to the real values in comparison with the
MLP2, which use a Log-sigmoid activation function, as can be observed in the
density scatter plots of Figure 5 (a) and (b). Additionally, we notice that
the density increases for the range between
$3\text{\,}\mathrm{m}6\text{\,}\mathrm{m}$ and around $15\text{\,}\mathrm{m}$.
The results of high density values around the short distance demonstrate the
potential of the MLP architecture to improve the accuracy of position
estimations in collaborative IPS in scenarios with a high density of
collaborating mobile devices (i.e., when the distance between neighboring
devices is short).

As a result of assessing different MLP architectures, the MLP1 with one hidden
layer (3 neurons), a scaled conjugate gradient backpropagation training
function, and a hyperbolic tangent sigmoid activation function was selected to
estimate relative distances with BLE–RSS data.

###  IV-C Results of the collaborative model

Table IV presents the main results of the lateration baseline and our
collaborative approach using various evaluation metrics (i.e., RMSE, mean,
median, 70th and 90th percentile), and also indicates the relative difference
between them.

TABLE IV: Main results metrics provided by the Lateration baseline and our proposed collaborative approach | Lateration baseline |  | Collaborative approach
---|---|---|---
Eval. metric | Error (m) |  | Error (m) | Diff.
RMSE | $5.76$ |  | $5.22$ |  $\downarrow$ 9.37%
Mean | $5.36$ |  | $4.55$ |  $\downarrow$ 15.11%
Median | $5.54$ |  | $4.84$ |  $\downarrow$ 12.63%
$75^{th}$ percentile | $7.08$ |  | $6.68$ |  $\downarrow$ 5.64%
$90^{th}$ percentile | $8.08$ |  | $8.08$ |  $0$%

As reported in Table IV, our collaborative approach outperforms the lateration
baseline in four of the five evaluation metrics, with a maximum of $15.11\%$
of difference for the “mean” metric.

Figure 6 introduces the Empirical Cumulative Distribution Function (ECDF) of
the lateration baseline (black dotted line) and our proposed approach (red
line). For the first 40% of cases, our collaborative model significantly
outperforms the baseline, for the next $50\%$ of cases, the improvement is
moderate, being quite close for the last $10\%$ of cases.

It should be noted that the positioning accuracy of the lateration baseline
was significantly degraded, compared to BLE-RSS approaches reported in the
literature ($2\text{\,}\mathrm{m}3\text{\,}\mathrm{m}$ error [27, 30]), due to
the adverse test scenario conditions, namely poor quantity and inappropriate
distribution of anchors, unstable signal strength and hardware heterogeneity.
However, the magnitude of the errors is in line with scenarios that consider
the low-density anchor deployment issue. For example, [17] reported a mean
error accuracy of $7.5\text{\,}\mathrm{m}$ in their lateration algorithm,
which was tested on a $24\text{\times}24\text{\,}\mathrm{m}$ area with 8
anchors.

Figure 6: Empirical CDF provided by the Lateration baseline and our
Collaborative approach

Figure 7 provides a more detail representation of the individual positioning
errors of the laterations used in the stand-alone phase and the collaborative
phase.

Figure 7: Comparison of individual errors provide by the Lateration baseline
and our Collaborative lateration approach

From the scatter plot, we can deduce that the lateration used in the
calibration phase is providing better positioning results than the one based
on the few beacons deployed in the environment. However, for a few cases the
behavior is just the contrary as the accuracy is a few meters worse than the
baseline. Nevertheless, the strongest feature of the proposed collaborative
model is the combination of the lateration results from both phases, providing
an ensembled output. According to the ensemble theory, the combination of
estimators improves the accuracy of any of the individuals involved.

##  V Conclusion and Future Work

In this paper, we presented a collaborative indoor positioning system using
Multilayer Perceptron (MLP) Artificial Neural Networks (ANNs) to enhance the
accuracy of the models based on BLE and RSS lateration, in typical adverse
conditions, namely poor quantity and inappropriate distribution of anchors,
unstable signal strength and hardware heterogeneity. The proposed approach is
divided in three phases. The first phase is devoted to registering devices
used in the collaborative approach and establishing an RSS baseline
measurement at $1\text{\,}\mathrm{m}$, the second phase consists of the stand-
alone (non-collaborative) lateration algorithm for position estimation of each
device/user, and the last phase is devoted to collaboratively estimate the
position of the target device/user and combine it with the non-collaborative
position estimate.

We evaluated our collaborative system in an indoor scenario (Office) and
compared it with a lateration baseline. Our indoor scenario presents the
aforementioned typical adverse conditions: an inadequate deployment of BLE
anchors, rich NLOS conditions and heterogeneity among mobile devices used,
causing a considerably reduction of positioning accuracy in RSS-based
approaches. Experimental results show the feasibility and benefits of our
proposed collaborative approach to outperform the positioning accuracy of the
traditional lateration baseline under these adverse conditions. Particularly,
our approach decreases, with respect to the lateration baseline, the mean,
median, RMSE and $75^{th}$ percentile positioning error metrics with
$15.11\%$, $12.63\%$, $9.37\%$ and $5.64\%$ respectively.

Furthermore, the results highlighted the usefulness of an MLP neural network
model to model the signal propagation at short distance considering the
inherent characteristic of each receiving device and in NLOS conditions, which
is essential for estimating the distance between (heterogeneous) collaborative
devices in real-world conditions.

As future work, we plan to use robust baseline approaches, which are able to
provide a better positioning accuracy. We will consider more complex
algorithms to combine independent collaborative estimates and reduce the
overall positioning error. Additionally, we will enhance the neural network
tuning, testing it in diverse and complex scenarios.

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  *[LBS]: location-based service
  *[BLE]: Bluetooth Low Energy
  *[RSS]: Received Signal Strength
  *[NLOS]: Non-line-of-sight
  *[RF]: Radio Frequency
  *[MLP]: Multilayer Perceptron
  *[ANN]: Artificial Neural Network
  *[LOS]: Line-of-sight
  *[IPS]: Indoor Positioning System
  *[LBSs]: location-based service
  *[LDPL]: Logarithm Distance Path Loss
  *[ANNs]: Artificial Neural Network
  *[LSTM]: Long Short-Term Memory
  *[IPSs]: Indoor Positioning System
  *[GT]: Ground-Truth
  *[RSSs]: Received Signal Strength
  *[GDOP]: Geometric Dilution of Precision
  *[RMSE]: Root Mean Square Error
  *[ECDF]: Empirical Cumulative Distribution Function