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An accurate prediction method for moving target localization and tracking in wireless sensor networks
Accepted Manuscript
An accurate Prediction Method for Moving Target Localization and Tracking in Wireless Sensor Networks Hanen Ahmadi, Federico Viani, Ridha Bouallegue PII: DOI: Reference:
S1570-8705(17)30207-X 10.1016/j.adhoc.2017.11.008 ADHOC 1608
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Ad Hoc Networks
Received date: Revised date: Accepted date:
9 September 2017 5 November 2017 14 November 2017
Please cite this article as: Hanen Ahmadi, Federico Viani, Ridha Bouallegue, An accurate Prediction Method for Moving Target Localization and Tracking in Wireless Sensor Networks, Ad Hoc Networks (2017), doi: 10.1016/j.adhoc.2017.11.008
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An accurate Prediction Method for Moving Target Localization and Tracking in Wireless Sensor Networks
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Hanen Ahmadia,b,∗, Federico Vianic , Ridha Boualleguea a Innov’COM,
Supcom, University of Carthage/University of Tunis El Manar, Tunis, Tunisia b ELEDIA Research Center (ELEDIA@Innov’COM - University of Carthage, Tunis, Tunisia) c ELEDIA Research Center (ELEDIA@UniTN - University of Trento, Trento, Italy)
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Abstract
With the large use of wireless sensor devices, the interest in positioning and tracking by means of wireless sensor networks is expected to grow further. Particularly, accurate localization of a moving target is a fundamental requirement in several Machine to Machine monitoring applications. Tracking using Re-
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ceived Signal Strength Indicator (RSSI) has been frequently adopted thanks to the availability and the low cost of this parameter. In this paper, we propose an innovative target tracking algorithm which combines learning regression tree
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approach and filtering methods using RSSI metric. Regression Tree algorithm is investigated in order to estimate the position using the RSSI. This method is combined to filtering approaches yielding to more refined results. The suggested
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approach is evaluated through simulations and experiments. We also compare our method to existing algorithms available in the literature. The numerical
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and experimental results show the relevance and the efficiency of our method. Keywords: target tracking, localization, wireless sensor networks, learning
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algorithm, pervasive computing, filtering
∗ Corresponding author Email address: [email protected]
Preprint submitted to Journal of LATEX Templates
November 14, 2017
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1. Introduction Wireless Sensor Networks (WSN) have attracted more and more attention in the last few years. This interest is expected to grow further with the high evolu-
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tion of application for wireless systems. Among the significant area of research, the localization which presents an important challenge in various applications
using WSN such as disasters monitoring, environment control, smart building [1] [2] , agriculture [3] , logistics and transport [4].
Node position determination is critical since it is important to take into con-
sideration many criteria. In fact, the developed localization solution should be
able to provide a tradeoff between accuracy, robustness and complexity. Global
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Positioning System (GPS) is one of the well-known solutions to the localization problem, but its application to indoor environments is still an open issue. Alternative positioning and tracking solution using WSNs have been proposed. Range based localization methods are widely investigated in the literature. Among the range based parameters, we find the angle of arrival (AOA) [5],
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the time difference of arrival (TDOA) [6], the ultra-wideband (UWB) frequency spectrum. The main constraint of these techniques is the high cost since they
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require extra hardware to measure such parameters. Accordingly, the development of novel methods of localization has became a great concern for the 20
wireless sensor networks. Among the available solutions for indoor localization,
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the ones based on the received signal strength indicator (RSSI) [7] [8] have been widely investigated since the RSSI is available in most of the commercial
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wireless devices without the need of any additional sensors or hardware customization. However, signal propagation inside buildings is affected by many
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environmental constraints such as reflections, interference, pathloss fading and
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shadowing. Thus, the main challenge in localization is to reduce the RSSI fluctuations. Thus, researchers have been motivated to develop improved solutions to enhance efficiency and accuracy of positioning. Machine learning is the field of the artificial intelligence that deals with the design and the development of
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algorithms and techniques which allow the system to learn the rules and the
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models from data. It has attracted more and more attention for the solution of localization problems [9] [10] , employing learning methods like support vector machines (SVMs) [11], neural networks (NNs) , k-nearest neighbor as well as
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fuzzy logic, which proved their suitability in the understanding of the complex relations between the RSSI behavior and the target position.
In this paper, the problematic of moving target is addressed. Thus, we
propose an original method that combines RT based localization method with the Bayesian filtering approach. In fact, the process starts with the positions
estimation using previous proposed methods based on RT [12] by exploiting our
optimized channel model. This prediction is considered as the observation model
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of the filtering process. Consequently, the filter is used afterwards to estimate the instantaneous positions. Both Kalman filter and Particle filter are studied and compared using experiments and simulation. The proposed algorithm has been experimentally evaluated using real measurement of a moving target in an 45
office room. The performance results have been analyzed through a comparison
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2. Related Work
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with existing methods in the literature.
Range free algorithms include neighborhood and Hop counting techniques [13] [14] [15] . These techniques only use connectivity information to determine node’s location and are cost effective techniques because there is no need of
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extra hardware but results are not much accurate. In [14], the authors propose
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a range free technique RAL (Reliable Anchor-based Localization) that focuses on searching minimal hop length to approximate the distance between node and anchor. We point out that anchors are nodes with known positions and used as reference points to estimate the locations of the sensors with unknown position.
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It has been shown that the proposed scheme improves the localization accuracy by selecting only the reliable anchors. El Assaf et al. [13] propose a novel anchor selection strategy for anistropic WSN using hop count information. In this paper, regular nodes calculates their positions using multilateration method
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and exploiting the distances’ estimates between nodes and reliable anchors. The adopted solution outperforms the DV-hop algorithm and the RAL method in terms of accuracy. A more robust anchor selection based algorithm has been
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proposed in [15] where, each normal node selects reliable anchor pairs based on the average hop progresses considering the geometric approximation of the node 65
location with respect to the anchor pairs. This algorithm performs better than other methods available in the literature. Range free based anchor selection methods present low cost since they are based on the network connectivity which is an available information in most of hardware. However, they depends
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entirely on connectivity of the sensor networks and thereby on the environment.
In fact, the localization area has to be a multi hop scenario. Another limitation is that hop count based algorithm is not robust when the number of anchors is small. Therefore, range-based localization algorithm is more robust to topology variation.
Many works focus on using Machine Learning concept for localization in WSNs. In particular, based on SVR, Kim et al. [16] developed a localization
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algorithm using RSSI. The experiment shows that this estimator is performing
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in terms of accuracy and robustness. Also, Neural Network is widely used for localization in WSNs. For instance, a feed-forward three-layered structure for neural network is proposed for position localization in indoor environment [17]. The study result shows that the proposed artificial neural network has
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the lowest error and the highest efficiency. The authors in [18] proposed a
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Bayesian algorithm which enables accurate localization in large scale systems. Additionally, a K nearest neighbor (KNN) profiling-based localization method using RSSI has been proposed. It has been demonstrated that this method offers high estimation accuracy with low cost algorithm.
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Merhi et al. [19] developed an acoustic target localization method for WSNs
using the TDOA parameter in a spatial correlation decision tree. Also, this work proposed the design of “Event Based MAC” (EB-MAC) protocol, that enables event-based localization and targeting in acoustic WSNs.
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The constant growth of the proposed indoor localization approaches points 4
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out that the accurate and robust localization of moving devices using common wireless technologies is still an open issue. Many RSSI-based tracking techniques have been proposed. For instance, [20] proposes a target tracking technique us-
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ing a particle filter with the exact RSSI channel model. However, such an approach is not reliable with the highly varying RSSIs, due to the signal fading, the additive noise, etc. Moreover, tracking algorithms using filtering [21] have
been extensively used. One of the highly diffused filters is the Kalman filter (KF), which introduces a recursive procedure to estimate the current target
state over the time taking into consideration the previous state. In [20], authors have proposed an efficient tracking algorithm by means of KF. It has been
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shown that KF method outperforms the simultaneous localization and tracking (SLAT) and the distributed variational filtering for simultaneous localization and tracking (DVaSLAT) methods by providing reduced energy consumption, minimized missing rate, and low localization error. In [22] the authors have 105
presented an accurate and robust KF-based infrared sensor algorithm with low
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localization error. Moreover, new improved versions of KF have been employed in target tracking such as the extended Kalman filter (EKF) [23] and the Kalman
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smoother (KS) [24]. These techniques have improved the accuracy of localization.
3. Proposed tracking algorithms
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3.1. Problem statement
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Let us consider a moving target in a two-dimensional indoor environment
with size X[m] and Y [m] and a set of L anchor nodes are deployed at fixed
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locations as previously shown in Fig. 1. During the movement, the mobile node
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gathers the RSSI information from the stationary anchor nodes. Let us denote the unknown state vector at time t, containing the position coordinates of the moving target and its velocity ν. X (t) =
x (t) ν (t)
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(1)
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The state evolution over time is described through the motion model defined as: (2)
X (t) = F X (t − 1) + W
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where F is the state transition matrix which relates the state vector with its previous state and W = N (0, Q) is the vector containing the noise term presented by a normal distribution with zero mean and covariance Q. The measurements related to the state can also be defined according to the observation equation: Z (t) = HX (t) + V
(3)
Where H is the observation matrix relating the measurement Z (t) with the state be zero mean and with covariance R.
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x (t) and describes the observation noise with normal distribution assumed to
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Figure 1: Target tracking problem
Targets motion information is very important to perform tracking. To this
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end, it is necessary to define the model that describes the target movement. We describe in the following two main deterministic mobility prediction models taken into account the acceleration information.
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The first order deterministic model considers that the velocities are constant
during the followed path yields to a null acceleration γ = 0. x (t) = x (t − 1) + ν (t) ∆ (t)
(4)
We take into account the case where the acceleration value is constant between two consecutive time steps, to this end the second order deterministic model 6
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based on Euler’s laws of motion is defined as follow: 2
x (t) = x (t − 1) + ν (t − 1) ∆ (t) + γ (t)
(5)
3.2. Observation model: Localization by means of Regression Tree
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∆ (t) 2
Classification and regression trees are machine-learning methods for con-
structing prediction models from data. The models are obtained by recursively partitioning the data space and fitting a simple prediction model within each partition. As a result, the partitioning can be represented graphically as a de140
cision tree. Classification trees are designed for dependent variables that take
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a finite number of unordered values, with prediction error measured in terms of misclassification cost. Regression trees are for dependent variables that take continuous or ordered discrete values, with prediction error typically measured by the squared difference between the observed and predicted values. The different steps of regression tree based localization [12] method is de-
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scribed in details in the following subsections. 3.2.1. Acquisition procedure
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The mobile node receives signal from the all anchor nodes. It collects all the RSSI values from the anchor nodes. In previous work [25], it has been proved 150
that the localization efficiency and accuracy is highly dependent on the anchor
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selection. To this end, during the training and testing process we consider the selection of only the optimal anchor nodes using KNN algorithm. Then, the
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prediction model obtained in the training phase is applied. The RT algorithm is divided into two main phases as shown in Fig.2: offline training phase and
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online localization phase. We assume that M training samples are distributed
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uniformly over the input space during the training phase. The training data are a set of M examples that is used during the learning
process to solve the objective function related the input and output. During the training phase, we consider M training samples distributed in uniform grid
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in a two dimensional area X × Y m2 . The number of training samples can be
changed by varying the distance between two training samples denoted δ. The 7
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training input data are generated by the Path-loss channel model and given as the received power Pm,l at a sample m = 1..L and transmitted by the anchor node index l = 1..L and position rl = {xl , yl }. More in details, because the an-
chors locations are known, the distances between anchor nodes and samples are
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known. Therefore, the received signal strength at a sample can be calculated by means of the calibrated pathloss model described in the following. Accordingly,
the training input is formed by the received signal strength denoted by the ma-
trix P and the corresponding positions of the training samples. Each sample 170
corresponds to the training coordinate denoted as rm = {xm , ym }. following expression: · · · p1,L .. .. . . · · · pm,L .. .. . . · · · pM,L
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The global training input has the p1,1 . . . P = pm,1 . ..
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pM,1
(6)
The suggested localization solution employs RSSI measurements. Hence, it is necessary to optimize the indoor propagation model in order to provide a
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good matching between real RSSI values and the training ones. The pathloss log-normal model has been largely used in literature for its simple formulation
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and ease of integration in localization methods. Consequently, the generated
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received power can be defined as; Prx = Ptx + Kc − 10ηlog(
d ) + Xσ d0
(7)
where Ptx is the transmitted power in [dBm], Kc is a propagation given by
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Kc = 20log(
4π ) λ
(8)
η is the pathloss coefficient, d0 is the reference distance while d is the transmitter-
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receiver distance. Xσ is a Gaussian random variable with zero-mean and vari-
ance σ taking into account the noise contribution. The proper characterization of the indoor wireless propagation is fundamental for the description of the localization problem. The pathloss log-normal 8
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model has been frequently used for its simple formulation and ease of integration 185
in localization methods. For the sake of simplification in the propagation modelling, let us suppose identification of the optimal path-loss exponent η.
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the noiseless case Xσ = 0. The model optimization has been recast in the A common solution for the determination of such a parameter is the mini190
mization of the minimum mean square error (MMSE) min = |Pr x (η) − RSSIrx |2 η
(9)
where RSSIrx is the RSSI measured by one of the selected anchors.
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In order to further improve the accuracy of the propagation model, two different path-loss exponents have been considered. More in detail, it has to be noticed that the path-loss exponent changes its behaviour according to the 195
distance between the transmitting and the receiving nodes. As an example, at shortest distances (e.g.,d < 20λ) the behaviour is more representative of a
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non line-of-sight (NLOS) propagation [26]. More specifically, the attenuation level of signal strength at shortest distances is highly different from the farthest distances. Thus, two categories of η should be discussed and analysed separately. Two path-loss exponents are used to characterize the propagation. Therefore,
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the proposed channel model has been revised as follows.
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P
Prx =
tx
P
tx
+ Kc − 10η1 log( dd0 ) if d < 20λ + Kc − 10η2 log( dd0 ) otherwise
(10)
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where η1 and η2 are the two optimized pathloss exponents. The training output r presented below denotes the coordinates of the training
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nodes. The training phase of our algorithm presents the first phase where the
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matrix S is the training input and the known positions are the training output. The purpose of the training phase is to construct the prediction model. x1 y1 .. . r = .. . xM yM 9
(11)
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The training input set and the known training output set consist on building the tree model using RT approach. This model is used to represent the learned
3.2.2. Regression tree based localization algorithm
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relation between the RSSI and position.
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Figure 2: Block-scheme of the RT-based localization algorithm
The proposed localization algorithm is organized in two main phases, the
training phase and the localization phase. During the training phase the RSSI
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values represent the training input and the known target positions are the training output. The purpose of the training phase is to construct the prediction
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model that will be exploited for the successive estimation of target position during the localization phase, once the regression tree has been calculated. The algorithm receives as input the training data denoted P . For each
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training input sample, it has been associated the known position of the training samples denoted as rm . The adopted regression tree is a tree-based model, which aims at minimizing
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ε=
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the mean square error ε given by the following equation: M 1 X 2 (rm − rb) M m=1
(12)
Where rb is the estimated position. The RT method applies successive splits
of the input training set to predict the node position with a reduced value
of error. The regression trees are obtained using a fast divide algorithm that recursively partitions the given training data into smaller subsets. The proposed
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algorithm starts the creation of the regression tree from a single node position corresponding to all the training points given by; rb =
M 1 X rm M m=1
(13)
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Successively, the training input set P is divided into two subsets. This partition is defined by selecting at each time the j-th column of matrix P and the cut-point a(from the training sample) that minimize the split error εsplit .
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All the possible binary splits are applied where two sub-nodes are resulted from each partitioning and then the optimal split which minimizes the error is chosen.
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The error of a split computed as the weighted errors of the resulting sub-nodes.
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εsplit =
M (lef t) M
X
j m:Pm
(rb1 − rm ) +
M (right) M
X
j m:Pm ≥a
(rb2 − rm )
(14)
where M (lef t) is the number of cases in the left subset, M (right) is the number
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of cases in the right subset, rb1 and rb2 are the estimated output corresponding
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to the two sub-nodes. The partitioning continues until the mean squared error for the observed node is lower than a specific threshold.
Once the tree is built, the output for a new instance is estimated by following
the branches of the obtained tree which is presented by the “if. . . then. . . else”
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rule (Fig.3).
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Figure 3: Tree structure
3.3. Kalman Filter
A Kalman Filter (KF) is an optimal recursive data processing algorithm, representing an efficient solution to the problem of estimating the state of a
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discrete-time controlled process. One of the underlying assumptions of the Kalman filter is that it is designed to estimate the states of a linear system
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based on measurements that are a linear function of the states.. Two main phases compose the KF algorithm: the prediction phase and the correction phase. The prediction process aims at predicting the future location based on
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the current position. In more details, KF model assumes that the state at time t is evolved from a prior state (at time t − 1). Thus, the estimated state vector
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x(t/t − 1) at time t is given using the state equation (2).
More in details, taken into account the first order mobility (4) model de-
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scribed previously, the state equation is defined as follows: 1 0 ∆ (t) 0 0 1 0 ∆ (t) x (t − 1) + W x (t) = 0 0 1 0 0 0 0 1
(15)
For the second scenario presented in equation (5) , the target state is written 12
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as follows:
1 0 ∆ (t) 0 1 0 X (t) = 0 0 1 0 0 0
0
∆(t)2 ∆ (t) X (t − 1) + γ (t) 2 +W γ (t) ∆ (t) 0 1
The associated covariance given by:
P (t \ t − 1) = F P (t − 1) F T + Q
(16)
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(17)
The initial covariance denoted P (0) is null since X(0) is assumed to be known.
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Applying iteratively the updating equations defined above, the state vector and its covariance can be constructed. During the correction phase, the predicted 260
terms X(t) and P (t) are improved using the observed model Z(t) described in section 3.2. To this end, the Kalman gain is calculated as:
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G (t) = P (t \ t − 1) H T HP (t \ t − 1) H T + R
−1
(18)
Therefore, the state vector and the corresponding covariance matrix at time t
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are updated as follows:
P (t \ t − 1) = (I − G (t) H) P (t \ t − 1)
(20)
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(19)
3.4. Particle filter
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X (t \ t) = X (t \ t − 1) + (Z (t) − X (t \ t − 1) H) G (t)
The particle filter (PF) was introduced in 1993 as a numerical approximation
to the non-linear Bayesian filtering problem. Since that date, several applica-
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tions that used PF approach have been proposed in literature. Particle filtering provides a probabilistic framework for recursive dynamic state estimation. It is
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a recursive inference procedure composed by three main steps as illustrated by Fig. 4: i) the first step deals with sampling where hypotheses about the states are generated from a candidate probability distribution. Then, the posterior distribution over the states is approximated by weighted samples. ii) the second 13
Figure 4: Particle filter scheme
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step has to do with the dynamical model. And iii) the last step is the observa275
tion phase where the hypotheses that agree at best with an observation model
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are selected.
To define the problem of non-linear filtering, the state space representation of dynamic system is given by the following discrete-time stochastic model : (21)
Zt = ht (Xt , wt−1 )
(22)
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Xt = ft (xt−1 , νt−1 )
where xt , Zt are the state and observation vectors respectively, ft and ht are
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the non linear function of the state and the observed measurement respectively, νt−1 and wt−1 are the process and noise sequences respectively. The aim of non linear filtering function is to recursively estimate the state from noisy ob-
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served measurement, where the initial target state is estimated by means of the learning method. As previously detailed, the posterior distribution is ob-
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tained recursively by applying the prediction and the update phases. During the prediction process, the prediction density at time t is obtained using the
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Chapman-Kolmogorov equation [27] : Z P (Xt \ Zt−1 ) = P (Xt \ Xt−1 ) P (Xt−1 \ Zt−1 ) dXt−1
(23)
The update stage is carried out while the measurement Zt becomes available at
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time step t. This involves an update of the prediction pdf via Bayes rule: P (Xt \ Zt ) =
P (Zt \ Xt ) P (Xt \ Zt−1 ) P (Zt \ Zt−1 ) 14
(24)
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In order to solve the equation (24), the sampling process approximates the N
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p p posterior pdf with a discrete set of particles noted {Xti }i=1 where {wti }i=1 are
the corresponding weights. The approximation of the posterior density is given
P (Xt \ Zt ) ≈ 295
Np X i=1
wti δ xt − xit
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by : (25)
where δ is a Dirac function and the weights are updated by the following equation:
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1 i
wt−1 wti =
dxit − Zt
(26)
Where dxit is the distance between anchor node and the particle. Resampling is a crucial step in the PF. It deals with replacing unlikely samples by more likely ones. Without resampling, the PF would break down to a 300
set of independent simulations yielding trajectories xit with relative probabilities
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wti .
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4. Performance Evaluation 4.1. Numerical results
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We have organized 10 anchor nodes uniformly distributed in a 100m X 100m area where 2 mobile nodes follow random trajectories. The number of particles is 100 when we apply particle filtering. Simulations are done under
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“MatlabR2014a” on an i7 Pc using a “Windows8”. A comparison among the proposed algorithm combining RT with PF, RT
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with KF and a learning ensemble based localization method proposed in previous
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work [28] is illustrated in Fig. 5. By analysing the cumulative localization error distribution of the studied methods, it is clear that the PF is more accurate than the KF and the ensemble method. Table 1 reports the average localization error in the case of σ = 4. As it can be seen, combining RT with PF provides low localization error = 0.35m comparing with the KF and the ensemble method. 15
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1
PF KF Ensemble method
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0.8
CDF
0.6
0.4
0 0
0.5
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0.2
1
1.5
2
2.5
3
3.5
4
Localization error [m]
Figure 5: Cumulative localization error distribution for PF vs KF vs Ensemble method
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Table 1: Localization error for the proposed algorithms vs Ensemble method
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Proposed methods
ε[m]
PF+RT
0,35
KF+RT
0,54
Ensemble method
0,73
Figure 6 illustrates the average localization error in function of σ. The PF
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based method outperforms the KF particularly for high value of σ. Such results can be explained by the observation error distribution. In the case of Kalman
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filter, the distributions are assumed to be guassian. To this end, KF performs similarly to PF for low values of σ. While it gives higher localization error than
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the PF when σ increases.
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3.5 KF PF
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2.5 2 1.5 1 0.5 0 0
2
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Localization error, ε[m]
3
4
6
8
10
σ[dB]
Figure 6: Localization error vs σ for the PF and the KF
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Table. 2 shows the running time of the simulated algorithms using Matlab for KF and PF approachs. It is clear that the PF is more complex than he KF.
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This is due to the sampling phase which requires more computation complexity. Accordingly, we conclude that a PF may be more adequate for multi-tracking 325
tasks in complex situations, and a KF should be the selected solution in simpler
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ones, such as STT in low populated areas. Table 2: Running time for KF and PF
Method
Running time [ms]
PF
142.42
KF
93.13
4.2. Experimental results In this section, we evaluate the performance of suggested algorithms through experiments. Towards this end, the suggested solutions has been experimentally 17
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tested in a real office indoor environment with size X = 9[m] and Y = 7.1[m]. Tmote Sky WSN platform based on IEEE802.15.4 standard and working at the operating frequency f=2.4 [GHz] are used for the real measurements. The
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following the trajectory presented in figure 7.
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representative test case is concerned with a human being moving inside the room
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Figure 7: Indoor environment
The goal of the experimental assessment is to study two different scenarios,
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where the first scenario (Fig.8-A) deals with a moving target in the investi-
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gated area with a constant velocity and the second scenario (Fig.8-B) presents a moving target with a varying velocity. Consequently, in the first scenario,
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the acceleration γ is assumed equal to zero. While in the second scenario the target follows various velocities leading to an acceleration different from zero. The evaluation deals with estimating nine test positions (9 time instant) for the
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two scenarios. Accordingly, the localization process is initiated by exploiting the new measurements of RSSI at each time step corresponding to these predefined
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positions.
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We will basically analyse the average localization error. The estimation is
evaluated for K=9 acquisitions at different time instant. More details about the localization error values for each time instant for respectively the first and the second scenario are reported in Tables 3 and 4. As it can be observed, there is a good matching between the actual path and the estimated one. The 18
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(A)
(B)
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Figure 8: Simulation environment for (A) scenario 1 and (B) scenario 2
proposed algorithm provides an accurate position estimation. As clearly shown, for different time instant lower error is obtained using KF and PF based method. In fact, the average localization error is about 0.72m when using KF, while its value is 0.55m for PF for scenario 1. In the mean while, the localization error
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and its variance increases slightly in the case of the second scenario with an average localization error 0.94m for the KF method and 0.56m when using PF.
t=1
t=2
t=3
t=4
t=5
t=6
t=7
t=8
t=9
0,46
0,61
1,04
0,91
1,10
1,30
0,95
0,11
0,75
PF
0,34
0,81
0,35
0,30
0,92
1,08
0,44
0,10
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time instant t KF
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Table 3: Localization error using KF and PF for different time instant of scenario 1
Table 4: Localization error using KF and PF for different time instant of scenario 2
t=1
t=2
t=3
t=4
t=5
t=6
t=7
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t=9
KF
0,56
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1.31
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PF
0,31
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0,53
0,41
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1,21
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time instant t
Figure 9 and 10 plot the root mean square error versus the number of den19
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sity of training set for respectively the scenario 1 and scenario 2. The proposed approach is compared to other localization algorithms existing in the literature. For this, the SVR (Support Vector Regression), Naive Bayes and trilateration are implemented using the same experimental scenario to have a fair compari-
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son. As it can be observed, the proposed algorithms outperforms the existing
works by providing lower localization error when varying the number of training samples. 3.5
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KF SVR Naive Bayes Trilateration ¨PF
2.5 2 1.5 1
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Localization error, ǫ [m]
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0.2
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Figure 9: Localization error versus training samples number
Table 5 illustrates the comparison among previous proposed algorithm and the filter based methods for the two scenario. As expected, combining the
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learning method with the Kalman filtering improve significantly the accuracy
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since it takes into account the motion model of the target.
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3.5
KF SVR Naive Bayes Trilateration ¨PF
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3 2.5 2 1.5 1 0.5 0 0.5
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Localization error, ǫ [m]
4
0,3
0.2
0.1
δ
Figure 10: Localization error versus training samples number
Scenario 2
Ensemble method
0.71
1.24
RT+KF
0.66
0.82
RT+PF
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Scenario 1
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Table 5: Localization error in dynamic case
The proposed approach has been experimentally evaluated in an indoor en-
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vironment submitted to high level of RSSI fluctuations. Experimental results
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demonstrate that the suggested algorithm provides optimal target state esti-
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mates and robust to noisy data. Accordingly, the accuracy has been significantly improved compared to existing approach. It is obvious that PF method outperforms the KF method in terms of accuracy. however, it is necessary to take into consideration the real time aspect of our application that cannot accept a high
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delay.
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5. Conclusion This article has considered target tracking in indoor environment for WSN. To this end, the previous proposed method have been associated to Bayesian
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filtering techniques to solve the tracking problematic. It has been demonstrated that the suggested algorithms present a good tradeoff between accuracy and robustness.
The algorithm assessment shows that the proposed tracking methods is accu-
rate, robust to environmental change compared to the existing methods in the literature. Compared with Kalman filter, the Particle filter is robust to noisy environment and provides lower localization error. However, we find that Parti-
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cle filter is computationally more expensive particularly when dealing with more complicated environment. Hence, this challenge of reducing the complexity of Particle filter algorithm will be considered in future works.
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Hanen Ahmadi received the Telecommunications Engineer Diploma from the National Engineering School of Tunis (ENIT), El Manar University, in 2011.
She has got the Research Master’s Degree in Communication Systems in 2012,
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and the PhD. degree in Telecommunications in 2017 from the same university.
She is researcher at Innov’COM Laboratory at SupCom in Tunisia in cooperation with Eledia Research Center at university of Trento in Italy. She is currently a teaching assistant at Supcom. Her research areas of interest include the Localization in Wireless Sensor Networks, Wireless Networks, M2M and signal processing.
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Federico Viani received the M.S. degree in telecommunication engineering from the University of Trento, Trento, Italy, in 2007, and the Ph.D. degree in
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Information and Communication Technology in 2010 from the same University.
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He is a Research Associate (Post Doc) at the University of Trento and a member of the ELEDIA Research Center. He is an author/co-author of more than 100 peer reviewed papers in international journals and conferences, where he has also co-organized and co-chaired convened sessions. His research activities
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are oriented to the design and development of wireless systems, devices, and 525
methodologies in the framework of electromagnetic fields for the solution of complex electromagnetic problems, such as the wireless localization and track-
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ing of active/passive targets. He is also involved in the design of distributed monitoring systems by means of wireless technologies for smart farming, smart
cities, energy efficient smart buildings, and in the development of decision support strategies for emergency-related applications.
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Ridha Bouallegue is professor at the National Engineering School of Tunis,
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Tunisia (ENIT) with experience in teaching since 1990. Since 1995, he is professor at the High School of Communications of Tunis (Sup’Com). He is currently the General Director of the Technological Studies at the Ministry of Higher
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Education and Research. He is the founder in 2012 and the General Chair of the International Conference on Information Processing and Wireless Systems (IP-WiS). He is the founder in 2012 and the President of the “Tunisian Association for Scientific Innovation and Technology” (TASIT). He founded in 2005
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and he is the Director of the Research Laboratory Innov’COM “Innovation of
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communicating and Cooperative Mobile Laboratory”. He founded in 2005 and he is the Director of the National School of Engineers of Sousse and he is the Director of the School of Technology and Computer Science from 2010. He obtained his doctorate in 1998 and his HDR in 2003 on the multi-user detection
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in cellular radio systems of the next generation. His research and fundamental development are on the physical layer of communication systems, particularly on digital communications systems and information theory, the next generation of wireless networks, and technology MIMO Wireless Communications.
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An accurate Prediction Method for Moving Target Localization and Tracking in Wireless Sensor Networks Hanen Ahmadi, Federico Viani, Ridha Bouallegue PII: DOI: Reference:
S1570-8705(17)30207-X 10.1016/j.adhoc.2017.11.008 ADHOC 1608
To appear in:
Ad Hoc Networks
Received date: Revised date: Accepted date:
9 September 2017 5 November 2017 14 November 2017
Please cite this article as: Hanen Ahmadi, Federico Viani, Ridha Bouallegue, An accurate Prediction Method for Moving Target Localization and Tracking in Wireless Sensor Networks, Ad Hoc Networks (2017), doi: 10.1016/j.adhoc.2017.11.008
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An accurate Prediction Method for Moving Target Localization and Tracking in Wireless Sensor Networks
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Hanen Ahmadia,b,∗, Federico Vianic , Ridha Boualleguea a Innov’COM,
Supcom, University of Carthage/University of Tunis El Manar, Tunis, Tunisia b ELEDIA Research Center (ELEDIA@Innov’COM - University of Carthage, Tunis, Tunisia) c ELEDIA Research Center (ELEDIA@UniTN - University of Trento, Trento, Italy)
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Abstract
With the large use of wireless sensor devices, the interest in positioning and tracking by means of wireless sensor networks is expected to grow further. Particularly, accurate localization of a moving target is a fundamental requirement in several Machine to Machine monitoring applications. Tracking using Re-
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ceived Signal Strength Indicator (RSSI) has been frequently adopted thanks to the availability and the low cost of this parameter. In this paper, we propose an innovative target tracking algorithm which combines learning regression tree
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approach and filtering methods using RSSI metric. Regression Tree algorithm is investigated in order to estimate the position using the RSSI. This method is combined to filtering approaches yielding to more refined results. The suggested
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approach is evaluated through simulations and experiments. We also compare our method to existing algorithms available in the literature. The numerical
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and experimental results show the relevance and the efficiency of our method. Keywords: target tracking, localization, wireless sensor networks, learning
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algorithm, pervasive computing, filtering
∗ Corresponding author Email address: [email protected]
Preprint submitted to Journal of LATEX Templates
November 14, 2017
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1. Introduction Wireless Sensor Networks (WSN) have attracted more and more attention in the last few years. This interest is expected to grow further with the high evolu-
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tion of application for wireless systems. Among the significant area of research, the localization which presents an important challenge in various applications
using WSN such as disasters monitoring, environment control, smart building [1] [2] , agriculture [3] , logistics and transport [4].
Node position determination is critical since it is important to take into con-
sideration many criteria. In fact, the developed localization solution should be
able to provide a tradeoff between accuracy, robustness and complexity. Global
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Positioning System (GPS) is one of the well-known solutions to the localization problem, but its application to indoor environments is still an open issue. Alternative positioning and tracking solution using WSNs have been proposed. Range based localization methods are widely investigated in the literature. Among the range based parameters, we find the angle of arrival (AOA) [5],
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the time difference of arrival (TDOA) [6], the ultra-wideband (UWB) frequency spectrum. The main constraint of these techniques is the high cost since they
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require extra hardware to measure such parameters. Accordingly, the development of novel methods of localization has became a great concern for the 20
wireless sensor networks. Among the available solutions for indoor localization,
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the ones based on the received signal strength indicator (RSSI) [7] [8] have been widely investigated since the RSSI is available in most of the commercial
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wireless devices without the need of any additional sensors or hardware customization. However, signal propagation inside buildings is affected by many
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environmental constraints such as reflections, interference, pathloss fading and
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shadowing. Thus, the main challenge in localization is to reduce the RSSI fluctuations. Thus, researchers have been motivated to develop improved solutions to enhance efficiency and accuracy of positioning. Machine learning is the field of the artificial intelligence that deals with the design and the development of
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algorithms and techniques which allow the system to learn the rules and the
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models from data. It has attracted more and more attention for the solution of localization problems [9] [10] , employing learning methods like support vector machines (SVMs) [11], neural networks (NNs) , k-nearest neighbor as well as
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fuzzy logic, which proved their suitability in the understanding of the complex relations between the RSSI behavior and the target position.
In this paper, the problematic of moving target is addressed. Thus, we
propose an original method that combines RT based localization method with the Bayesian filtering approach. In fact, the process starts with the positions
estimation using previous proposed methods based on RT [12] by exploiting our
optimized channel model. This prediction is considered as the observation model
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of the filtering process. Consequently, the filter is used afterwards to estimate the instantaneous positions. Both Kalman filter and Particle filter are studied and compared using experiments and simulation. The proposed algorithm has been experimentally evaluated using real measurement of a moving target in an 45
office room. The performance results have been analyzed through a comparison
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2. Related Work
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with existing methods in the literature.
Range free algorithms include neighborhood and Hop counting techniques [13] [14] [15] . These techniques only use connectivity information to determine node’s location and are cost effective techniques because there is no need of
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extra hardware but results are not much accurate. In [14], the authors propose
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a range free technique RAL (Reliable Anchor-based Localization) that focuses on searching minimal hop length to approximate the distance between node and anchor. We point out that anchors are nodes with known positions and used as reference points to estimate the locations of the sensors with unknown position.
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It has been shown that the proposed scheme improves the localization accuracy by selecting only the reliable anchors. El Assaf et al. [13] propose a novel anchor selection strategy for anistropic WSN using hop count information. In this paper, regular nodes calculates their positions using multilateration method
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and exploiting the distances’ estimates between nodes and reliable anchors. The adopted solution outperforms the DV-hop algorithm and the RAL method in terms of accuracy. A more robust anchor selection based algorithm has been
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proposed in [15] where, each normal node selects reliable anchor pairs based on the average hop progresses considering the geometric approximation of the node 65
location with respect to the anchor pairs. This algorithm performs better than other methods available in the literature. Range free based anchor selection methods present low cost since they are based on the network connectivity which is an available information in most of hardware. However, they depends
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entirely on connectivity of the sensor networks and thereby on the environment.
In fact, the localization area has to be a multi hop scenario. Another limitation is that hop count based algorithm is not robust when the number of anchors is small. Therefore, range-based localization algorithm is more robust to topology variation.
Many works focus on using Machine Learning concept for localization in WSNs. In particular, based on SVR, Kim et al. [16] developed a localization
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algorithm using RSSI. The experiment shows that this estimator is performing
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in terms of accuracy and robustness. Also, Neural Network is widely used for localization in WSNs. For instance, a feed-forward three-layered structure for neural network is proposed for position localization in indoor environment [17]. The study result shows that the proposed artificial neural network has
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the lowest error and the highest efficiency. The authors in [18] proposed a
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Bayesian algorithm which enables accurate localization in large scale systems. Additionally, a K nearest neighbor (KNN) profiling-based localization method using RSSI has been proposed. It has been demonstrated that this method offers high estimation accuracy with low cost algorithm.
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Merhi et al. [19] developed an acoustic target localization method for WSNs
using the TDOA parameter in a spatial correlation decision tree. Also, this work proposed the design of “Event Based MAC” (EB-MAC) protocol, that enables event-based localization and targeting in acoustic WSNs.
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The constant growth of the proposed indoor localization approaches points 4
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out that the accurate and robust localization of moving devices using common wireless technologies is still an open issue. Many RSSI-based tracking techniques have been proposed. For instance, [20] proposes a target tracking technique us-
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ing a particle filter with the exact RSSI channel model. However, such an approach is not reliable with the highly varying RSSIs, due to the signal fading, the additive noise, etc. Moreover, tracking algorithms using filtering [21] have
been extensively used. One of the highly diffused filters is the Kalman filter (KF), which introduces a recursive procedure to estimate the current target
state over the time taking into consideration the previous state. In [20], authors have proposed an efficient tracking algorithm by means of KF. It has been
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shown that KF method outperforms the simultaneous localization and tracking (SLAT) and the distributed variational filtering for simultaneous localization and tracking (DVaSLAT) methods by providing reduced energy consumption, minimized missing rate, and low localization error. In [22] the authors have 105
presented an accurate and robust KF-based infrared sensor algorithm with low
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localization error. Moreover, new improved versions of KF have been employed in target tracking such as the extended Kalman filter (EKF) [23] and the Kalman
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smoother (KS) [24]. These techniques have improved the accuracy of localization.
3. Proposed tracking algorithms
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3.1. Problem statement
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Let us consider a moving target in a two-dimensional indoor environment
with size X[m] and Y [m] and a set of L anchor nodes are deployed at fixed
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locations as previously shown in Fig. 1. During the movement, the mobile node
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gathers the RSSI information from the stationary anchor nodes. Let us denote the unknown state vector at time t, containing the position coordinates of the moving target and its velocity ν. X (t) =
x (t) ν (t)
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(1)
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The state evolution over time is described through the motion model defined as: (2)
X (t) = F X (t − 1) + W
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where F is the state transition matrix which relates the state vector with its previous state and W = N (0, Q) is the vector containing the noise term presented by a normal distribution with zero mean and covariance Q. The measurements related to the state can also be defined according to the observation equation: Z (t) = HX (t) + V
(3)
Where H is the observation matrix relating the measurement Z (t) with the state be zero mean and with covariance R.
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x (t) and describes the observation noise with normal distribution assumed to
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Figure 1: Target tracking problem
Targets motion information is very important to perform tracking. To this
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end, it is necessary to define the model that describes the target movement. We describe in the following two main deterministic mobility prediction models taken into account the acceleration information.
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The first order deterministic model considers that the velocities are constant
during the followed path yields to a null acceleration γ = 0. x (t) = x (t − 1) + ν (t) ∆ (t)
(4)
We take into account the case where the acceleration value is constant between two consecutive time steps, to this end the second order deterministic model 6
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based on Euler’s laws of motion is defined as follow: 2
x (t) = x (t − 1) + ν (t − 1) ∆ (t) + γ (t)
(5)
3.2. Observation model: Localization by means of Regression Tree
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∆ (t) 2
Classification and regression trees are machine-learning methods for con-
structing prediction models from data. The models are obtained by recursively partitioning the data space and fitting a simple prediction model within each partition. As a result, the partitioning can be represented graphically as a de140
cision tree. Classification trees are designed for dependent variables that take
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a finite number of unordered values, with prediction error measured in terms of misclassification cost. Regression trees are for dependent variables that take continuous or ordered discrete values, with prediction error typically measured by the squared difference between the observed and predicted values. The different steps of regression tree based localization [12] method is de-
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scribed in details in the following subsections. 3.2.1. Acquisition procedure
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The mobile node receives signal from the all anchor nodes. It collects all the RSSI values from the anchor nodes. In previous work [25], it has been proved 150
that the localization efficiency and accuracy is highly dependent on the anchor
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selection. To this end, during the training and testing process we consider the selection of only the optimal anchor nodes using KNN algorithm. Then, the
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prediction model obtained in the training phase is applied. The RT algorithm is divided into two main phases as shown in Fig.2: offline training phase and
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online localization phase. We assume that M training samples are distributed
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uniformly over the input space during the training phase. The training data are a set of M examples that is used during the learning
process to solve the objective function related the input and output. During the training phase, we consider M training samples distributed in uniform grid
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in a two dimensional area X × Y m2 . The number of training samples can be
changed by varying the distance between two training samples denoted δ. The 7
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training input data are generated by the Path-loss channel model and given as the received power Pm,l at a sample m = 1..L and transmitted by the anchor node index l = 1..L and position rl = {xl , yl }. More in details, because the an-
chors locations are known, the distances between anchor nodes and samples are
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known. Therefore, the received signal strength at a sample can be calculated by means of the calibrated pathloss model described in the following. Accordingly,
the training input is formed by the received signal strength denoted by the ma-
trix P and the corresponding positions of the training samples. Each sample 170
corresponds to the training coordinate denoted as rm = {xm , ym }. following expression: · · · p1,L .. .. . . · · · pm,L .. .. . . · · · pM,L
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The global training input has the p1,1 . . . P = pm,1 . ..
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pM,1
(6)
The suggested localization solution employs RSSI measurements. Hence, it is necessary to optimize the indoor propagation model in order to provide a
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good matching between real RSSI values and the training ones. The pathloss log-normal model has been largely used in literature for its simple formulation
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and ease of integration in localization methods. Consequently, the generated
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received power can be defined as; Prx = Ptx + Kc − 10ηlog(
d ) + Xσ d0
(7)
where Ptx is the transmitted power in [dBm], Kc is a propagation given by
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Kc = 20log(
4π ) λ
(8)
η is the pathloss coefficient, d0 is the reference distance while d is the transmitter-
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receiver distance. Xσ is a Gaussian random variable with zero-mean and vari-
ance σ taking into account the noise contribution. The proper characterization of the indoor wireless propagation is fundamental for the description of the localization problem. The pathloss log-normal 8
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model has been frequently used for its simple formulation and ease of integration 185
in localization methods. For the sake of simplification in the propagation modelling, let us suppose identification of the optimal path-loss exponent η.
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the noiseless case Xσ = 0. The model optimization has been recast in the A common solution for the determination of such a parameter is the mini190
mization of the minimum mean square error (MMSE) min = |Pr x (η) − RSSIrx |2 η
(9)
where RSSIrx is the RSSI measured by one of the selected anchors.
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In order to further improve the accuracy of the propagation model, two different path-loss exponents have been considered. More in detail, it has to be noticed that the path-loss exponent changes its behaviour according to the 195
distance between the transmitting and the receiving nodes. As an example, at shortest distances (e.g.,d < 20λ) the behaviour is more representative of a
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non line-of-sight (NLOS) propagation [26]. More specifically, the attenuation level of signal strength at shortest distances is highly different from the farthest distances. Thus, two categories of η should be discussed and analysed separately. Two path-loss exponents are used to characterize the propagation. Therefore,
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the proposed channel model has been revised as follows.
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P
Prx =
tx
P
tx
+ Kc − 10η1 log( dd0 ) if d < 20λ + Kc − 10η2 log( dd0 ) otherwise
(10)
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where η1 and η2 are the two optimized pathloss exponents. The training output r presented below denotes the coordinates of the training
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nodes. The training phase of our algorithm presents the first phase where the
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matrix S is the training input and the known positions are the training output. The purpose of the training phase is to construct the prediction model. x1 y1 .. . r = .. . xM yM 9
(11)
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The training input set and the known training output set consist on building the tree model using RT approach. This model is used to represent the learned
3.2.2. Regression tree based localization algorithm
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relation between the RSSI and position.
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Figure 2: Block-scheme of the RT-based localization algorithm
The proposed localization algorithm is organized in two main phases, the
training phase and the localization phase. During the training phase the RSSI
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values represent the training input and the known target positions are the training output. The purpose of the training phase is to construct the prediction
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model that will be exploited for the successive estimation of target position during the localization phase, once the regression tree has been calculated. The algorithm receives as input the training data denoted P . For each
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training input sample, it has been associated the known position of the training samples denoted as rm . The adopted regression tree is a tree-based model, which aims at minimizing
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ε=
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the mean square error ε given by the following equation: M 1 X 2 (rm − rb) M m=1
(12)
Where rb is the estimated position. The RT method applies successive splits
of the input training set to predict the node position with a reduced value
of error. The regression trees are obtained using a fast divide algorithm that recursively partitions the given training data into smaller subsets. The proposed
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algorithm starts the creation of the regression tree from a single node position corresponding to all the training points given by; rb =
M 1 X rm M m=1
(13)
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Successively, the training input set P is divided into two subsets. This partition is defined by selecting at each time the j-th column of matrix P and the cut-point a(from the training sample) that minimize the split error εsplit .
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All the possible binary splits are applied where two sub-nodes are resulted from each partitioning and then the optimal split which minimizes the error is chosen.
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The error of a split computed as the weighted errors of the resulting sub-nodes.
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εsplit =
M (lef t) M
X
j m:Pm
(rb1 − rm ) +
M (right) M
X
j m:Pm ≥a
(rb2 − rm )
(14)
where M (lef t) is the number of cases in the left subset, M (right) is the number
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of cases in the right subset, rb1 and rb2 are the estimated output corresponding
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to the two sub-nodes. The partitioning continues until the mean squared error for the observed node is lower than a specific threshold.
Once the tree is built, the output for a new instance is estimated by following
the branches of the obtained tree which is presented by the “if. . . then. . . else”
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rule (Fig.3).
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Figure 3: Tree structure
3.3. Kalman Filter
A Kalman Filter (KF) is an optimal recursive data processing algorithm, representing an efficient solution to the problem of estimating the state of a
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discrete-time controlled process. One of the underlying assumptions of the Kalman filter is that it is designed to estimate the states of a linear system
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based on measurements that are a linear function of the states.. Two main phases compose the KF algorithm: the prediction phase and the correction phase. The prediction process aims at predicting the future location based on
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the current position. In more details, KF model assumes that the state at time t is evolved from a prior state (at time t − 1). Thus, the estimated state vector
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x(t/t − 1) at time t is given using the state equation (2).
More in details, taken into account the first order mobility (4) model de-
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scribed previously, the state equation is defined as follows: 1 0 ∆ (t) 0 0 1 0 ∆ (t) x (t − 1) + W x (t) = 0 0 1 0 0 0 0 1
(15)
For the second scenario presented in equation (5) , the target state is written 12
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as follows:
1 0 ∆ (t) 0 1 0 X (t) = 0 0 1 0 0 0
0
∆(t)2 ∆ (t) X (t − 1) + γ (t) 2 +W γ (t) ∆ (t) 0 1
The associated covariance given by:
P (t \ t − 1) = F P (t − 1) F T + Q
(16)
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(17)
The initial covariance denoted P (0) is null since X(0) is assumed to be known.
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Applying iteratively the updating equations defined above, the state vector and its covariance can be constructed. During the correction phase, the predicted 260
terms X(t) and P (t) are improved using the observed model Z(t) described in section 3.2. To this end, the Kalman gain is calculated as:
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G (t) = P (t \ t − 1) H T HP (t \ t − 1) H T + R
−1
(18)
Therefore, the state vector and the corresponding covariance matrix at time t
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are updated as follows:
P (t \ t − 1) = (I − G (t) H) P (t \ t − 1)
(20)
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(19)
3.4. Particle filter
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X (t \ t) = X (t \ t − 1) + (Z (t) − X (t \ t − 1) H) G (t)
The particle filter (PF) was introduced in 1993 as a numerical approximation
to the non-linear Bayesian filtering problem. Since that date, several applica-
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tions that used PF approach have been proposed in literature. Particle filtering provides a probabilistic framework for recursive dynamic state estimation. It is
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a recursive inference procedure composed by three main steps as illustrated by Fig. 4: i) the first step deals with sampling where hypotheses about the states are generated from a candidate probability distribution. Then, the posterior distribution over the states is approximated by weighted samples. ii) the second 13
Figure 4: Particle filter scheme
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step has to do with the dynamical model. And iii) the last step is the observa275
tion phase where the hypotheses that agree at best with an observation model
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are selected.
To define the problem of non-linear filtering, the state space representation of dynamic system is given by the following discrete-time stochastic model : (21)
Zt = ht (Xt , wt−1 )
(22)
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Xt = ft (xt−1 , νt−1 )
where xt , Zt are the state and observation vectors respectively, ft and ht are
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the non linear function of the state and the observed measurement respectively, νt−1 and wt−1 are the process and noise sequences respectively. The aim of non linear filtering function is to recursively estimate the state from noisy ob-
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served measurement, where the initial target state is estimated by means of the learning method. As previously detailed, the posterior distribution is ob-
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tained recursively by applying the prediction and the update phases. During the prediction process, the prediction density at time t is obtained using the
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Chapman-Kolmogorov equation [27] : Z P (Xt \ Zt−1 ) = P (Xt \ Xt−1 ) P (Xt−1 \ Zt−1 ) dXt−1
(23)
The update stage is carried out while the measurement Zt becomes available at
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time step t. This involves an update of the prediction pdf via Bayes rule: P (Xt \ Zt ) =
P (Zt \ Xt ) P (Xt \ Zt−1 ) P (Zt \ Zt−1 ) 14
(24)
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In order to solve the equation (24), the sampling process approximates the N
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p p posterior pdf with a discrete set of particles noted {Xti }i=1 where {wti }i=1 are
the corresponding weights. The approximation of the posterior density is given
P (Xt \ Zt ) ≈ 295
Np X i=1
wti δ xt − xit
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by : (25)
where δ is a Dirac function and the weights are updated by the following equation:
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wt−1 wti =
dxit − Zt
(26)
Where dxit is the distance between anchor node and the particle. Resampling is a crucial step in the PF. It deals with replacing unlikely samples by more likely ones. Without resampling, the PF would break down to a 300
set of independent simulations yielding trajectories xit with relative probabilities
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wti .
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4. Performance Evaluation 4.1. Numerical results
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We have organized 10 anchor nodes uniformly distributed in a 100m X 100m area where 2 mobile nodes follow random trajectories. The number of particles is 100 when we apply particle filtering. Simulations are done under
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“MatlabR2014a” on an i7 Pc using a “Windows8”. A comparison among the proposed algorithm combining RT with PF, RT
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with KF and a learning ensemble based localization method proposed in previous
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work [28] is illustrated in Fig. 5. By analysing the cumulative localization error distribution of the studied methods, it is clear that the PF is more accurate than the KF and the ensemble method. Table 1 reports the average localization error in the case of σ = 4. As it can be seen, combining RT with PF provides low localization error = 0.35m comparing with the KF and the ensemble method. 15
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1
PF KF Ensemble method
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0.8
CDF
0.6
0.4
0 0
0.5
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0.2
1
1.5
2
2.5
3
3.5
4
Localization error [m]
Figure 5: Cumulative localization error distribution for PF vs KF vs Ensemble method
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Table 1: Localization error for the proposed algorithms vs Ensemble method
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Proposed methods
ε[m]
PF+RT
0,35
KF+RT
0,54
Ensemble method
0,73
Figure 6 illustrates the average localization error in function of σ. The PF
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based method outperforms the KF particularly for high value of σ. Such results can be explained by the observation error distribution. In the case of Kalman
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filter, the distributions are assumed to be guassian. To this end, KF performs similarly to PF for low values of σ. While it gives higher localization error than
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the PF when σ increases.
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3.5 KF PF
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2.5 2 1.5 1 0.5 0 0
2
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Localization error, ε[m]
3
4
6
8
10
σ[dB]
Figure 6: Localization error vs σ for the PF and the KF
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Table. 2 shows the running time of the simulated algorithms using Matlab for KF and PF approachs. It is clear that the PF is more complex than he KF.
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This is due to the sampling phase which requires more computation complexity. Accordingly, we conclude that a PF may be more adequate for multi-tracking 325
tasks in complex situations, and a KF should be the selected solution in simpler
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ones, such as STT in low populated areas. Table 2: Running time for KF and PF
Method
Running time [ms]
PF
142.42
KF
93.13
4.2. Experimental results In this section, we evaluate the performance of suggested algorithms through experiments. Towards this end, the suggested solutions has been experimentally 17
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tested in a real office indoor environment with size X = 9[m] and Y = 7.1[m]. Tmote Sky WSN platform based on IEEE802.15.4 standard and working at the operating frequency f=2.4 [GHz] are used for the real measurements. The
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following the trajectory presented in figure 7.
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representative test case is concerned with a human being moving inside the room
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Figure 7: Indoor environment
The goal of the experimental assessment is to study two different scenarios,
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where the first scenario (Fig.8-A) deals with a moving target in the investi-
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gated area with a constant velocity and the second scenario (Fig.8-B) presents a moving target with a varying velocity. Consequently, in the first scenario,
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the acceleration γ is assumed equal to zero. While in the second scenario the target follows various velocities leading to an acceleration different from zero. The evaluation deals with estimating nine test positions (9 time instant) for the
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two scenarios. Accordingly, the localization process is initiated by exploiting the new measurements of RSSI at each time step corresponding to these predefined
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positions.
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We will basically analyse the average localization error. The estimation is
evaluated for K=9 acquisitions at different time instant. More details about the localization error values for each time instant for respectively the first and the second scenario are reported in Tables 3 and 4. As it can be observed, there is a good matching between the actual path and the estimated one. The 18
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(A)
(B)
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Figure 8: Simulation environment for (A) scenario 1 and (B) scenario 2
proposed algorithm provides an accurate position estimation. As clearly shown, for different time instant lower error is obtained using KF and PF based method. In fact, the average localization error is about 0.72m when using KF, while its value is 0.55m for PF for scenario 1. In the mean while, the localization error
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and its variance increases slightly in the case of the second scenario with an average localization error 0.94m for the KF method and 0.56m when using PF.
t=1
t=2
t=3
t=4
t=5
t=6
t=7
t=8
t=9
0,46
0,61
1,04
0,91
1,10
1,30
0,95
0,11
0,75
PF
0,34
0,81
0,35
0,30
0,92
1,08
0,44
0,10
0,75
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time instant t KF
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Table 3: Localization error using KF and PF for different time instant of scenario 1
Table 4: Localization error using KF and PF for different time instant of scenario 2
t=1
t=2
t=3
t=4
t=5
t=6
t=7
t=8
t=9
KF
0,56
0,51
1.31
1.45
0.76
1.61
0.36
0,97
0,84
PF
0,31
0,61
0,53
0,41
0,62
1,21
0.91
0,26
0,25
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time instant t
Figure 9 and 10 plot the root mean square error versus the number of den19
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sity of training set for respectively the scenario 1 and scenario 2. The proposed approach is compared to other localization algorithms existing in the literature. For this, the SVR (Support Vector Regression), Naive Bayes and trilateration are implemented using the same experimental scenario to have a fair compari-
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son. As it can be observed, the proposed algorithms outperforms the existing
works by providing lower localization error when varying the number of training samples. 3.5
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KF SVR Naive Bayes Trilateration ¨PF
2.5 2 1.5 1
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Localization error, ǫ [m]
3
0 0.5
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0.5
0.4
0.3
0.2
0.1
δ
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Figure 9: Localization error versus training samples number
Table 5 illustrates the comparison among previous proposed algorithm and the filter based methods for the two scenario. As expected, combining the
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learning method with the Kalman filtering improve significantly the accuracy
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since it takes into account the motion model of the target.
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3.5
KF SVR Naive Bayes Trilateration ¨PF
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3 2.5 2 1.5 1 0.5 0 0.5
0.4
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Localization error, ǫ [m]
4
0,3
0.2
0.1
δ
Figure 10: Localization error versus training samples number
Scenario 2
Ensemble method
0.71
1.24
RT+KF
0.66
0.82
RT+PF
0.51
0.56
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Scenario 1
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Table 5: Localization error in dynamic case
The proposed approach has been experimentally evaluated in an indoor en-
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vironment submitted to high level of RSSI fluctuations. Experimental results
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demonstrate that the suggested algorithm provides optimal target state esti-
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mates and robust to noisy data. Accordingly, the accuracy has been significantly improved compared to existing approach. It is obvious that PF method outperforms the KF method in terms of accuracy. however, it is necessary to take into consideration the real time aspect of our application that cannot accept a high
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delay.
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5. Conclusion This article has considered target tracking in indoor environment for WSN. To this end, the previous proposed method have been associated to Bayesian
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filtering techniques to solve the tracking problematic. It has been demonstrated that the suggested algorithms present a good tradeoff between accuracy and robustness.
The algorithm assessment shows that the proposed tracking methods is accu-
rate, robust to environmental change compared to the existing methods in the literature. Compared with Kalman filter, the Particle filter is robust to noisy environment and provides lower localization error. However, we find that Parti-
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cle filter is computationally more expensive particularly when dealing with more complicated environment. Hence, this challenge of reducing the complexity of Particle filter algorithm will be considered in future works.
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Hanen Ahmadi received the Telecommunications Engineer Diploma from the National Engineering School of Tunis (ENIT), El Manar University, in 2011.
She has got the Research Master’s Degree in Communication Systems in 2012,
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and the PhD. degree in Telecommunications in 2017 from the same university.
She is researcher at Innov’COM Laboratory at SupCom in Tunisia in cooperation with Eledia Research Center at university of Trento in Italy. She is currently a teaching assistant at Supcom. Her research areas of interest include the Localization in Wireless Sensor Networks, Wireless Networks, M2M and signal processing.
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Federico Viani received the M.S. degree in telecommunication engineering from the University of Trento, Trento, Italy, in 2007, and the Ph.D. degree in
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Information and Communication Technology in 2010 from the same University.
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He is a Research Associate (Post Doc) at the University of Trento and a member of the ELEDIA Research Center. He is an author/co-author of more than 100 peer reviewed papers in international journals and conferences, where he has also co-organized and co-chaired convened sessions. His research activities
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are oriented to the design and development of wireless systems, devices, and 525
methodologies in the framework of electromagnetic fields for the solution of complex electromagnetic problems, such as the wireless localization and track-
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ing of active/passive targets. He is also involved in the design of distributed monitoring systems by means of wireless technologies for smart farming, smart
cities, energy efficient smart buildings, and in the development of decision support strategies for emergency-related applications.
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Ridha Bouallegue is professor at the National Engineering School of Tunis,
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Tunisia (ENIT) with experience in teaching since 1990. Since 1995, he is professor at the High School of Communications of Tunis (Sup’Com). He is currently the General Director of the Technological Studies at the Ministry of Higher
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Education and Research. He is the founder in 2012 and the General Chair of the International Conference on Information Processing and Wireless Systems (IP-WiS). He is the founder in 2012 and the President of the “Tunisian Association for Scientific Innovation and Technology” (TASIT). He founded in 2005
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and he is the Director of the Research Laboratory Innov’COM “Innovation of
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communicating and Cooperative Mobile Laboratory”. He founded in 2005 and he is the Director of the National School of Engineers of Sousse and he is the Director of the School of Technology and Computer Science from 2010. He obtained his doctorate in 1998 and his HDR in 2003 on the multi-user detection
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in cellular radio systems of the next generation. His research and fundamental development are on the physical layer of communication systems, particularly on digital communications systems and information theory, the next generation of wireless networks, and technology MIMO Wireless Communications.
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