# Deep Learning-Based Device-Free Localization in Wireless Sensor Networks

Osamah A. Abdullah1, Hayder Al-Hraishawi2, and Symeon Chatzinotas2
1Dept. of Electrical and Computer Engineering, Alma’moon University College,
Baghdad, Iraq 2Interdisciplinary Centre for Security, Reliability and Trust
(SnT), University of Luxembourg, L-1855, Luxembourg
Email<EMAIL_ADDRESS><EMAIL_ADDRESS>and
<EMAIL_ADDRESS>
###### Abstract

Location-based services (LBS) are witnessing a rise in popularity owing to
their key features of delivering powerful and personalized digital
experiences. The recent developments in wireless sensing techniques make the
realization of device-free localization (DFL) feasible in wireless sensor
networks. The DFL is an emerging technology that utilizes radio signal
information for detecting and positioning a passive target while the target is
not equipped with a wireless device. However, determining the characteristics
of the massive raw signals and extracting meaningful discriminative features
relevant to the localization are highly intricate tasks. Thus, deep learning
(DL) techniques can be utilized to address the DFL problem due to their
unprecedented performance gains in many practical problems. In this direction,
we propose a DFL framework consists of multiple convolutional neural network
(CNN) layers along with autoencoders based on the restricted Boltzmann
machines (RBM) to construct a convolutional deep belief network (CDBN) for
features recognition and extracting. Each layer has stochastic pooling to
sample down the feature map and reduced the dimensions of the required data
for precise localization. The proposed framework is validated using real
experimental dataset. The results show that our algorithm can achieve a high
accuracy of 98% with reduced data dimensions and low signal-to-noise ratios
(SNRs).

##  I Introduction

Contextualization and personalized services are of the most feature
applications envisioned in the forthcoming sixth-generation (6G) wireless
systems, and communication perception has been steadily growing to become one
of the essential business application scenarios [1]. Therefore, it is
particularly important to enhance the location-based services (LBS) to provide
context-aware and personalized solutions for mobile users in diverse
applications as well as for some critical scenarios such as patient tracking,
intruder detection, and elderly surveillance [2]. Additionally, the precise
localization of devices is fundamental in the context of Internet of Things
(IoT) applications and future Industry 4.0 technologies. Further, the
localization of smartphones has been used for contact tracing during the fight
against the Covid-19 pandemic [3]. However, traditional localization
techniques such as radio frequency identification (RFID) and global
positioning system (GPS) are not always applicable because they need a
tracking device to be attached to the target. To solve this issue, the concept
of a passive wireless monitoring system, also known as device free
localization (DFL), is introduced based on the wireless sensor networks [4,
5].

In DFL systems, wireless sensor nodes, also known as anchor points (APs), are
used to sense and accumulate target positions via collaborative communications
with other neighboring APs. Specifically, targets existence, absence, or
appearing at different locations will definitely change the transmitting-
receiving correspondences among the APs. Accordingly, the position of the
target can by analyzed/determined through the variations in the radio
frequency (RF) signals. For instance, human movements have different effects
on the received signal strength (RSS), which can be utilized to locate the
target [6]. In this setting, when a target enters the DFL system’s tracking
area, certain RSS metrics are obtained and analyzed to estimate the target
location. Namely, the tracking area is discretized into grids and the
variations in RSS measurements due to the target movements can be regarded as
a class of possibilities inside each grid cell, and hence, the DFL can be
viewed as a classification problem. This observation has motivated the
researchers to utilize deep learning (DL) techniques to improve DFL
performance [7].

RSS signals in the wireless sensor networks are easily affected by the
surrounding environment and the target movements, which add random noise to
the collected RSS measurements and make them fluctuating as multimodal
signals. Additionally, indoor localization is more challenging than outdoor
localization due to the multi-path interference, scattering and reflecting
from different sources such as walking people, furniture, walls, and other
objects [8]. Therefore, attaining a satisfactory localization accuracy
requires deploying an adequate number of APs and collect large amounts of RSS
measurements, which impose heavy computational burdens to the DFL process,
especially in the emergency scenarios when the positioning speed is necessary.
In this context, various prior studies have considered machine learn (ML)
approaches and the most popular DL algorithms such as K-nearest-neighbor (KNN)
and support vector machines (SVM) to tackle the DFL problem [9].

Although conventional DL algorithms are effective in solving the
classification problems, their performance within DFL systems diminishes with
the high-dimensional data and occasionally fail to provide an accurate
localization in a timely fashion [10]. Inspired by this observation, this
paper aims at developing a DFL framework that is able to efficiently process
high dimensional data and capable of obtaining high levels of location
accuracy in noisy environments. In this direction, a combination of
convolutional deep belief network (CDBN) with feature autoencoding algorithm
is applied for layer-wise learning. Specifically, CDBN is a hierarchical
generative model that is used with probabilistic max-pooling to extract high-
level features by replacing the restricted Boltzmann machine (RBM) in the deep
belief networks that are used for the individual layers by convolutional RBMs,
which has been proved as a useful algorithm for dimensionality reduction,
collaborative filtering, feature learning and classification[11]. In this
framework, pooling layers are added between the convolutional layers and the
training of the network is divided into two successive stages in order to
reduce the dimension of upper layers. Specifically, first the pre-training
stage where CDBN is used as a generative model to extract the features
automatically from the RSS dataset, then the training stage is conducted by
fine-tuning the parameters through the autoencoder, where the contrastive
divergence is employed. Finally, the learned features are merged into the
autoencoder of the neural network to locate the target by using the training
parameters. In brief, our main contributions in this work can be summarized as
follows:

  * •

Applying the CDBN as a dimensionality reduction approach to solve the DFL
classification problem by extracting high-level features from the wireless
signals.

  * •

Developing a DL-based DFL framework that is efficiently able to . The obtained
results show that the proposed algorithm outperforms the conventional
autoencoders.

The remainder of the paper is organized as follows. The system model with the
DFL problem formulation and the proposed approach are discussed in Section II.
The simulation results and conclusion remarks are given in Section III and IV,
respectively.

Figure 1: A schematic diagram of a device-free localization system. Figure 2:
Illustration of the proposed framework for device free localization (DFL)
using convolutional deep belief networks (CDBN).

##  II DFL Problem Formulation

We consider a DFL system consists of $N$ APs that are covering the area of
interest $D$, and these APs are communicating with each other through wireless
links, as shown in Fig. 1. In this system, the $R^{target}_{i,j}$ represents
the RSS measurements that is transmitted from the $j$-th AP to the $i$-th AP
when there is a target within $D$, while $R^{vacant}_{i,j}$ represents the RSS
measurements when there is no target. Accordingly, the difference in RSS
measurements is denoted by $\Delta\mathrm{R}_{i,j}$ and can be formulated as:

$\Delta\mathrm{R}_{i,j}=\mathrm{R}_{i,j}^{\text{target
}}-\mathrm{R}_{i,j}^{\text{vacant }},$ (1)

where

$\Delta\mathrm{R}=\left[\begin{array}[]{cccc}\Delta\mathrm{R}_{1,1}&\Delta\mathrm{R}_{1,2}&\cdots&\Delta\mathrm{R}_{1,D}\\\
\Delta\mathrm{R}_{2,1}&\Delta\mathrm{R}_{2,2}&\cdots&\Delta\mathrm{R}_{2,D}\\\
\vdots&\vdots&\ddots&\vdots\\\
\Delta\mathrm{R}_{D,1}&\Delta\mathrm{R}_{D,2}&\cdots&\Delta\mathrm{R}_{D,D}\end{array}\right].$
(2)

In this setting, the transmitted signal can be absorbed and scattered in all
directions, and hence, when the target is moving the RSS measurements will be
changed accordingly, which produces a different RSS matrix, i.e. each matrix
represents a different pattern of RSS measurements. These resulted different
patterns can be described as classification problem and could be solved using
DL algorithms [12]. To this end, $D$ is subdivided into $L$ grid cells and
each cell is represented as a class and each class will be treated as a
potential class; namely, for each gird cell $l\in\\{1,\cdots L\\}$, we perform
$p\in\\{1,\cdots,P\\}$ trails and vectorizing the dimensional into one
dimensional shape as one input data with location information and trait as
$V=[v_{11}\cdots v_{lp}\cdots v_{LP}]$.

The overall framework of proposed approach to solve the DFL problem is
depicted in Fig. 2. First step is to collect the DFL data, and then, divide it
into grid cells in order to be fed the deep learning architecture. In this
framework, the CDBN used as feature recognizing and extractor in the pre-
training stage that will be merged with an autoencoder for fine-tuning.
Afterwards, the extracted features are employed for classification through via
softmax regression block to determine the potential grid. The RBM is
probabilistic joint distribution with bipartite graph with visible input
variable $v=[v_{1},v_{2},\cdots,v_{N}]^{T}$ of dimension $D$ and set of hidden
random variables $h$ with dimension $K$, $h=[h_{1},h_{2},\cdots,h_{N}]^{T}$,
it has symmetrical connections between the visible and hidden layers defined
by a weight matrix $W\in R^{(D\times K)}$. The RBM can be represented as
Markov random field, where the visible units represent the input data, and the
hidden units are the latent factors. Hence, the weights represent the
statistical relationship encoding between the visible nodes and hidden nodes.
In term of Bernoulli distribution, the formal probabilistic of RBM is defined
by its energy function as follows:

$\vspace{-1mm}p(v,h)=\frac{1}{Z}\exp(-\mathrm{E}(v,h)),$ (3)

where $Z$ represents the normalization constant. The energy function is
defined as follows

$\vspace{-1mm}\mathrm{E}(v,h)=-\sum_{i=1}^{D}\sum_{j=1}^{K}v_{i}W_{ij}h_{j}-\sum_{j=1}^{K}b_{j}h_{j}-\sum_{i=1}^{D}c_{i}v_{i},$
(4)

where $c_{i}$ account for the visible unit biases, $b_{i}$ represent the
hidden unit biases, and $W_{ij}$ are the connection weights between the hidden
and visible layers. Since the input layer have a real value, the energy
function can be defined by adding quadratic term as expressed below:

$\vspace{-1mm}\mathrm{E}(v,h)=\\!\frac{1}{2}\sum_{i=1}^{D}v_{i}^{2}-\\!\\!\sum_{i=1}^{D}\sum_{j=1}^{K}v_{i}W_{ij}h_{j}-\\!\\!\sum_{j=1}^{K}b_{j}h_{j}-\\!\\!\sum_{i=1}^{D}c_{i}v_{i}.$
(5)

The energy function in (5) represents the conditional probability distribution
and joint probability distribution, which leads to define the hidden unit as
conditionally independent with visible layer. The binary hidden layers are
conditionally independent on visible layers and can be found by using
Bernoulli random variables as follows:

$\vspace{-3mm}p\left(h_{j}=1\mid
v\right)=\sigma\left(\sum_{i}W_{ij}v_{i}+b_{j}\right),$ (6)

where $\sigma$ stands for sigmoid function. Likewise, if the visible layer is
conditionally independent on hidden layer and binary valued the Bernoulli
random variable becomes:

$p\left(v_{i}=1\mid h\right)=\sigma\left(\sum_{j}W_{ij}h_{i}+c_{i}\right).$
(7)

Figure 3: Construction of a CRBM with probabilistic max-pooling. The CDBN is a
hierarchical generative model composed of stacked CRBMs.

###  II-A Convolutional Restricted Boltzmann Machine (CRBM)

The CRBM consists of RBMs integrated with a convolutional neural network (CNN)
that have convolutional and pooling layers. In CRBM, the weights of all
locations are shared by the convolutional layer. Meanwhile, the translation-
invariant representations are extracted by pooling layer via aggregating the
features resulted from the convolutional layer. For probabilistic maximum
pooling, the energy function takes the form in (7), which allows the
bidirectional inference [13], which can be defined as:

$\displaystyle
E(v,h)=-\sum_{k=1}^{K}\sum_{i,j=1}^{N_{H}}\sum_{r,s=1}^{N_{w}}h_{ij}^{k}W_{rs}^{k}v_{i+r-1,j+s-1}$
$\displaystyle-\sum_{k=1}^{K}b_{k}\sum_{i,j=1}^{N_{H}}h_{ij}^{k}-c\sum_{i,j=1}^{N_{v}}v.$
(8)

In (II-A), $v$ denotes the input dataset, $c$ and $b_{k}$ account for the
shared weights of the location $(i,j)$ over all the hidden layers within the
same group. Each CRBM consists of a visible layer ($V$) that consist of
$N_{v}\times N_{v}$ array, a hidden layer ($H$) that consist of $N_{H}\times
N_{H}$ array, and a pooling layer as presented in Fig. 3. The CRBM has $K$
convolutional kernels of size $N_{w}\times N_{w}$ array such that
$N_{W}\stackrel{{\scriptstyle\Delta}}{{=}}N_{V}-N_{H}+1$ resulting in hidden
unit. In this context, the Gibbs sampler can be applied to approximate the
conditional distribution by a discrete set of points, similar to the standard
RBM, as detailed below.

$\displaystyle
E(v,h)=-\sum_{k=1}^{K}h^{k}\\!\\!\cdot\left(\tilde{W}^{k}*v\right)\\!-\\!\\!\sum_{k=1}^{K}b_{k}\sum_{i,j}h_{i,j}^{k}\\!-c\\!\sum_{i,j}\\!v_{ij},\\!\\!\\!$
(9a) $\displaystyle P\left(h_{ij}^{k}=1\mid
v\right)=\sigma\left(\left(\tilde{W}^{k}{}_{*}v\right)_{ij}+b_{k}\right),$
(9b) $\displaystyle P\left(h_{ij}=1\mid
h\right)=\sigma\left(\left(\sum_{k}W^{k}*h^{k}\right)_{\\!\\!ij}+c\right).$
(9c)

###  II-B Convolutional deep belief network (CDBN)

The CDBN is a multi-layer model extracts high-level features from the low-
level ones using a hierarchical structure: lower layers extract low-level
features and feed into the higher layers. In other words, the CDBNs are
hierarchical generative models composed of multiple stacked CRBMs. This
architecture is based on a novel concept called probabilistic max-pooling. In
general, convolutional networks frequently require two kinds of alternating
layers: “convolutional” and “pooling” layers, that will shrink the performance
of the detection layer by a constant factor, where each unit in pooling layer
estimates the maximum value of the detection layer in small region and that
will reduce the computational complexity. In our implementation, the detection
and pooling layers consist of $K$ groups, the pooling layer partitioned the
detection layer into two or three blocks, where each block ($\alpha$) is
connected to the same pooling layer $P_{\alpha}^{k}$. In other words, the
sampling of the visible layer $V$ produces the hidden layer $H$, which takes
place in a parallel manner as a mulitmodal distribution by sampling the
$h^{k}_{ij}$ for each block $\alpha$. Next, each block will be sampled
independently as a multimodal function, where $h^{k}_{ij}$ is contained as
block $\alpha$, i.e., $(i,j)\in B$, and that leads to increase the energy by
turning on unit $h^{k}_{ij}$, and the conditional probabilities are

$\displaystyle P\left(h_{i,j}^{k}\\!=\\!1\mid
v,h^{\prime}\right)\\!=\\!\frac{\exp\left(I\left(h_{i,j}^{k}\right)+I\left(p_{\alpha}^{k}\right)\right)}{1+\sum\limits_{\left(i^{\prime},j^{\prime}\right)\in
B_{\alpha}}\\!\\!\\!\\!\\!\\!\exp\left(I\left(h_{i,j}^{k}\right)+I\left(p_{\alpha}^{k}\right)\right)},$
(10a) $\displaystyle P\left(p_{\alpha}^{k}\\!=\\!0\mid
v,h^{\prime}\right)\\!=\\!\frac{1}{1+\sum\limits_{\left(i^{\prime},j\right)\in
B_{\alpha}^{\prime}}\exp\left(I\left(h_{i,j}^{k}\right)+I\left(p_{\alpha}^{k}\right)\right)}.$
(10b)

As an alternative way to represent the block Gibbs sampling, which will be
used to estimate the posterior distribution. In our model, the overcomplete of
the data representation is much larger than the input. Since the first hidden
layer contains roughly $K$ groups of units, models with unnecessary or overly
detailed features risk learning trivial solutions. A frequently implemented
solution is to require a sparse to activate only a tiny fraction of the
available units. To encourage each hidden unit group to have a mean activation
near a small constant, we regularize the objective function (log-likelihood).
Thus, we have determined the following update, followed by contrastive
divergence update, appears to be an effective strategy in the field:

$\Delta b_{k}^{\text{sparsity }}\propto
p-\frac{1}{N_{H}^{2}}\sum\nolimits_{i,j}P\left(h_{i,j}^{k}=1\mid
v\right),\vspace{-1mm}$ (11)

where $p$ represents the target sparsity, and each input data is treated as a
mini-batch. The learning rate for sparsity update is chosen to make the hidden
group’s average activation close to the target sparsity. Since this gradient
required a high computational cost, a contrastive-divergence learning is used
to address this issue, [14] proved that the approximate the log-likelihood
gradient is sufficient as a replacement to calculate the second term of log-
likelihood gradient that needs only a few iterations that modeled by using
Gibbs sampling distribution, based on the mentioned theory, the key parameter
is derived as follows:

$\displaystyle\Delta
W^{k}\propto\frac{1}{N_{H}^{2}}\left(\tilde{Q}^{(0),k}*V^{(0)}-\tilde{Q}^{(n),k}*V^{(n)}\right),$
(12a) $\displaystyle\Delta
b_{k}\propto\frac{1}{N_{H}^{2}}\sum_{ij}\left(Q_{ij}^{(0),k}-Q_{ij}^{(n),k}\right)+\Delta
b_{k}^{\text{sparsity }},$ (12b) $\displaystyle\Delta
c\propto\frac{1}{N_{v}^{2}}\sum_{ij}\left(V_{ij}^{(0)}-V_{ij}^{(n)}\right).$
(12c)

where $Q^{(0)}$ represents the posterior computation for (10a) and (10b), $k$
represents the number of hidden layers, by updating rules of (12a), (12b), and
(12c), CDBN block can be trained efficiently, the unsupervised pre-training
process presented in Algorithm 1.

Input : $V$, epoch number, RBM number $N$

Output : $\nabla_{o}w_{ij},\nabla_{o}c_{j}$

1 Initialize $\nabla w_{ij},\nabla b_{i},\nabla c_{j}$ randomly,
$\mathbf{v}_{dm}^{1}\leftarrow\mathbf{v}$

2 Calculate the posterior $Q^{(0)}$ using (10a) and (10b)

3 Sample $H^{(0)}$ from $Q^{(0)}$

4 while  _for each epoch_ do

5 while  _$n\leq N$_ do

6 Sample $V^{n}$ from $P(v|H^{(n-1)})$ in (9b)

7 Calculate the posterior $Q^{(n)}=P(H|v^{n})$ using (10a) and (10b)

8 Sample $H^{(0)}$ from $Q^{(0)}$

9

10 end while

11 Update biases and weight with sparsity regularization and contrastive
divergence using (12a), (12b), and (12c), respectively.

12 Repeat until convergence

13 Unsupervised of autoencoder

14 Initialize: $\Delta W^{k}$, $\Delta b_{k}$, and $\Delta c$ from (12a),
(12b), and (12c), respectively.

15 for  _$n=1:N$_ do

16 Compute the decoder output using (14)

17 end for

18 Compute MSE using (15)

19 Fine-turning via backpropagation until convergence

20 end while

Algorithm 1 The proposed algorithm

After a series training of CDBN, the data will be unrolled as an autoencoder
which constrict of two phases: encoder and decoder. The encoder output of CDBN
can be written as

$a(v)=f\left(c_{j}+\sum_{i}w_{ij}\frac{v_{i}}{\sigma_{i}^{2}}\right).$ (13)

The decoder output after unrolling can be reconstructed as

$d(\boldsymbol{v})=f\left(c_{j}+\sum_{i}\sigma_{i}^{2}w_{ij}^{T}a(\boldsymbol{v})\right).$
(14)

Next, fine-tuning for optimal reconstruction of mean square error (MSE) is:

$\operatorname{MSE}(\boldsymbol{V})=\frac{1}{s}\sum_{i=1}^{s}(d(v)-v)^{2}$
(15)

where $s$ represents the input dataset $v$. The purpose of autoencoder is to
build the input data that does not have any information of class labels.
Afterwards, a softmax regression is applied to estimate the optimal parameters
for the output layer to predict the output class by using labeled data.
Subsequently, cross entropy error function is used to estimate the prediction
error between predicted data $y^{\prime}$ and the real data $y$, with a cost
function that is defined below:

$J(\theta)=\frac{1}{s}\sum_{i=1}^{s}y_{s}\times\log\left(y_{s}^{\prime}(\theta)\right),\vspace{-1mm}$
(16)

where $\theta$ represents the parameters of the encoder network.

##  III Performance Evaluation

In this study, a real experimental dataset from the sensing and processing
across networks (SPAN) Laboratory at the University of Utah is used [15]. The
area of interest $D$ in the experiment setup is divided into 36 grid cells and
covered by a wireless sensor network consists of 28 wireless sensor nodes
(APs). This wireless sensor network operates within 2.4 GHz frequency band
based on the IEEE 802.15.4 protocol. Each AP is placed in three feet apart in
a square area with heights of three feet above the ground to construct 36 grid
cells. In this setup, 30 different RSS measurements were collected and send to
the computer withing a short period of time, where the data will be
partitioned into training and test samples. The data dimension for the
training consists of $784\times 900$, while the testing data includes
$784\times 1$. Localization accuracy is used as a metric to evaluate the
performance of the proposed algorithm. Furthermore, in real-world scenarios,
noise from the surrounding environment is inevitable, which definitely
disturbs the DFL performance. Therefore, a random Gaussian noise is added to
each collected RSS to examine our algorithm robustness against noise and
signal distortions.

The proposed algorithm has many parameters need to be optimized and set, i.e.
number of hidden layers, number of epochs and different number of each group
in every hidden layer. Thus, the number of hidden layers versus classification
accuracy is evaluated using the proposed algorithm, and the results are shown
in Table I. Clearly, using thee layers gives the highest accuracy, that is
98.02%, which will be considered in the rest of the running experiments.
Additionally, for these three hidden layers, different number of groups are
tested to compute the accuracy of CDBN, the highest accuracy is obtained when
the number of groups for the first, second and third layers are 28, 36 and 36,
respectively.

TABLE I: Classification accuracy versus number of hidden layers Number of hidden layers | Classification accuracy (%)
---|---
1 | 75.13
2 | 89.21
3 | 98.02
Figure 4: Localization performance of the CDBN-AE method with data from 10 to
150 dimensions versus the number of epochs.

To assess the performance of the proposed algorithm in terms of dimensional
reduction and feature extraction, the RSS dimensions are reduced from 784
dimensions to 150, 50, 25, and 15 dimensions and used to evaluate the
classification accuracy as shown in Fig. 4. Obviously, the highest
classification accuracy (98.02%) is achieved when 150 dimensions with around
35 epochs. Beyond the 35 epochs, the classification accuracy is stable as the
epoch number increased. Meanwhile, the 25 dimensions reaches classification
accuracy of 97.8% after a 100 number of epochs. In addition, the 15 data
dimensions has the lower classification accuracy with respect to all other
numbers despite the increment in the epoch numbers. Interestingly, Fig. 4
reveals that the classification accuracy during the training stage can reach
97.8% for 25 dimensions with a slight increase in the number of epochs. These
findings validate the outstanding performance of the proposed CDBN-based
autoencoder (CDBN-AE) method in performing feature extraction along with data
dimension reduction.

Intuitively, using large data dimensions during the testing stage increases
the computational complexity and slows down the classification process.
Thereby, it is critical to find an optimal data dimension that provides an
acceptable accuracy. To this end, after completing the DFL training procedure,
reduced data ranging from 3 to 150 dimensions is used for the testing stage,
and the results are shown in Fig. 5, which presents the classification
accuracy versus testing data dimensions. It can be readily seen that the
accuracy reaches a maximum of 98.02% and remains constant when data dimension
is greater than 25 for the proposed CDBN-AE method. Further, we compare our
CDBN-AE algorithm to the CDBN coder and the autoencoder without CDBN in Fig.
5, which indicates that the developed CDBN-AE has better localization accuracy
with the reduced data dimensions. Thus, the 25 dimensions can be considered as
the optimal data dimension for achieving accurate localization.

Figure 5: Localization accuracy performance of the CDBN-AE, CDBN, and
autoencoder algorithms versus different dimensional testing data. Figure 6:
Comparison of average localization accuracy between the CDBN-AE and
autoencoder in the testing stage using noisy dataset with various SNR.

Next, the testing performance of the proposed framework is investigated in
Fig. 6 using noisy data with varying signal-to-noise ratios (SNRs) and
different data dimensions. It is also compared to the autoencoder without
CDBN. Clearly, the localization accuracy of our CDBN-AE method reaches 98%
with 25 data dimensions and when SNR is higher than 10 dB. In addition, the
accuracy decreases to 96.2% and 96% levels when the SNR values are 0 dB and 5
dB, respectively. Furthermore, at lower SNR values, the location accuracy can
be improved to reach 96% by using the CDBN-AE method and increasing the data
dimensions to 150. This demonstrates that the proposed GBRBM-AE algorithm is
robust and well-suited for DFL even at low SNR values.

##  IV Conclusion

This paper constructed a novel DL-based DFL approach using the variations in
RSS measurements in wireless sensor networks. Specifically, the DFL problem is
treated as a classification problem having multiple dynamic classes and
modeled based on the CDBN with stacked autoencoders. In the proposed
framework, pooling layers are added between the convolutional layers of the
CDBN, which allow for a reduction in data dimension requirements for
localizing a target. The proposed framework offers high levels of location
accuracy and robustness against the added random noise from the surrounding
environment and the target movements. In particular, the experiment results
have showed that with noiseless data the localization accuracy can reach up to
98% with only 25 data dimensions. More importantly, considering dataset with
noise has proved that the proposed CDBN-AE with 25 data dimensions is able to
obtain 98% accuracy when SNR=10 dB and is resilient to low SNR values around 5
dB with low data dimensions. This proves the applicability of the CDBN-AE
approach to real-world DFL scenarios.

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