Target localization and tracking based on improved Bayesian enhanced least-squares algorithm in wireless sensor networks

Target Localization and Tracking Based on Improved Bayesian Enhanced Least-Squares Algorithm in Wireless Sensor Networks

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Target Localization and Tracking Based on Improved Bayesian Enhanced Least-Squares Algorithm in Wireless Sensor Networks Tao Wang, Xiang Wang, Wei Shi, Zongmin Zhao, Zhenxue He, Tongsheng Xia PII: DOI: Reference:

S1389-1286(18)30640-6 https://doi.org/10.1016/j.comnet.2019.106968 COMPNW 106968

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Computer Networks

Received date: Revised date: Accepted date:

1 August 2018 24 October 2019 24 October 2019

Please cite this article as: Tao Wang, Xiang Wang, Wei Shi, Zongmin Zhao, Zhenxue He, Tongsheng Xia, Target Localization and Tracking Based on Improved Bayesian Enhanced Least-Squares Algorithm in Wireless Sensor Networks, Computer Networks (2019), doi: https://doi.org/10.1016/j.comnet.2019.106968

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Target Localization and Tracking Based on Improved Bayesian Enhanced Least-Squares Algorithm in Wireless Sensor Networks

Tao Wanga,∗ , Xiang Wangb,∗ , Wei Shib , Zongmin Zhaob , Zhenxue Hec and Tongsheng Xiab a The

School of Information and Communication Engineering, Beijing Information Science and Technology University, Beijing 100101, China School of Electronic and Information Engineering, Beihang University, Beijing 100191, China c The School of Information science and technology, Hebei Agricultural University, Baoding 071001, China b The

ARTICLE INFO

ABSTRACT

Keywords: Wireless sensor networks Localization and tracking Improved Bayesian enhanced Least-Squares Prediction position

Classical tracking algorithms, such as the Bayesian algorithm, extended Kalman filter (EKF), and classical least-square (CLS) algorithm, have been extensively implemented at target localization and tracking in wireless sensor networks (WSNs). In this paper, an enhanced least-square algorithm based on improved Bayesian was developed for moving target localization and tracking in WSNs. We apply an improved Bayesian algorithm to obtain a set of sub-range probability based on target predictive location, and forming a range joint probability matrix. The range joint probability matrix is only automatically updated when the WSN testbed is in a dormant state. Then, the weight of every measurement is calculated and normalized based on the range probability matrix. Finally, the correction value of the target prediction position is calculated according to the weighted least-square algorithm. The experimental results show that compared with EKF, the weighted K-nearest neighbor algorithm (WKNN), the position Kalman filter (PKF), the fingerprint Kalman filter (FKF), variational Bayesian adaptive Kalman filtering (VBAKF), dual-factor enhanced VBAKF (EVBAKF), and variational Bayes expectation maximization (VBEM) algorithms, the proposed algorithm improves the positioning accuracy by 35%, 32%, 18%, and 13%, 9%, 6%, and 0.4% respectively. In addition, the proposed algorithm reduces the computational burden by more than 80 percent compared with the Bayesian algorithm.

1. Introduction

Wireless sensor networks (WSNs) have been applied to many domains, such as border monitoring [1], navigation for the blind person, Moving target tracking, traffic control [2], and military surveillance. Moving target tracking is a representative application of WSNs, Localization and tracking of the air or ground target needs to be supported by mobile target tracking technology in military surveillance. Although the advantages of WSNs (such as low cost, easy deployment, and long-term work) bring new perspective for positioning applications [3, 4, 5, 6, 7, 8], the characteristics of sensor nodes with limited energy, poor reliability, large scale, random distribution, and communication distance also present great challenges to localization in WSNs. Therefore, it is challenging to track maneuvering targets in WSNs. The accuracy and computation time are significantly affected by the tracking algorithm [9, 10] in the target localization and tracking [11, 12]. The classical tracking algorithms, such as Bayesian algorithm [13, 14, 15, 16, 17], track association algorithm of fuzzy comprehensive function [18, 19, 20], Kalman filter [21, 10], and CLS algorithm [22, 23, 24] etc. There are also some other localization and tracking methods, such as energy-based multiple target localization and pursuit in mobile sensor networks [25], hidden Markov estimation of bistatic range from cluttered ultrawideband impulse responses [26], efficient cluster-based tracking mechanisms for camera-based wireless sensor networks [27], real-time compressive tracking [28], GDOP analysis ∗ Corresponding

author

[email protected] (T. Wang); [email protected] (X. Wang)

ORCID (s):

Tao Wang et al.: Preprint submitted to Elsevier

for positioning system design [29], and online identification and tracking of subspaces from highly incomplete information [30], adaptive trajectory tracking of nonholonomic mobile robots Using vision-based position and velocity estimation [31]. Some methods are also used to evaluate the performance of the algorithms [32]. In practice, due to the receiver noise in each sensor node and errors associated with multipath and signal shadowing effects, there will be errors in the measurement [33] of both range and code phases. Therefore, pseudorange measurement errors will result in errors in position estimation. Because of disturbance and sensor noise in reality, the result of target tracking in WSNs is influenced at different levels. However, most research work assumes that the collected sensory data in the WSN can accurately reflect the target information. Only several studies have considered the error of sensory data. The error of sensory data represents one of the key factors that affect the accuracy of target tracking in WSNs [34, 35, 36]. In addition, the time consumption of some tracking algorithms can be reduced by aggregating the complex calculation of the algorithms into a probability matrix and judging the measurements in each cycle based on the probability matrix. In this way, it is not necessary to perform complex operations in each cycle but only needs to update the matrix once when the system is dormant. Therefore, we can improve the real-time performance of some tracking algorithms with complex computation according to this idea. This paper mainly examines ways to reduce the error of sensor measurement data and improve the real-time performance of the tracking algorithm, that is, to meet the WSN positioning requirements with limited energy and computational performance. Page 1 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN Y(m) Node 2

Node 1 ρ2 ρ1

MP1

Node 3

MP2

ρ3

FP k+1

X(m)

ρ4 ρ6 ρ5

Node 6

Threshold

Node 4

Node 5

TP k

TP k-1

Figure 1: Geometry of the target in relationship to the nodes

After the sensor nodes are activated, a large number of measurement data related to the target are collected from the sensor nodes at the initial time in the WSN, and then analyze the data through the proposed algorithm. The target localization and tracking system are considered to be defined by the geometry of a mobile target and nodes, as showed in Fig.1. The black points (TP) represent the true position of the moving target; 𝑘 and 𝑘 − 1 represent the time of the moving target [37]. The center point of the coordinate system in Fig.1 represents the calculated position of the moving target according to the previous state of motion at time 𝑘 + 1, and this point is called the target prediction position (FP 𝑘 + 1). When the moving target is near the FP position, it can be measured by 𝑛 sensor nodes. At time 𝑘 + 1, the sensor position (𝑥𝑠 , 𝑦𝑠 ), the direction angle 𝜃 and the measured distance 𝜌 are received. The measured distance 𝜌𝑖 of 𝑖-th sensor is as follows: √ 𝜌𝑖 = (𝑥 − 𝑥𝑠𝑖 )2 + (𝑦 − 𝑦𝑠𝑖 )2 , 𝑖 = 1, 2, ⋯ , 𝑛 (1) According to these data, the measured position (MP) of the target by each sensor node can be obtained. The distance Δ𝜌𝑖 between MP𝑖 and FP is calculated, and the larger Δ𝜌𝑖 is filtered by the set threshold [37]. After that, we apply an improved Bayesian algorithm to obtain a set of sub-range probability based on target predictive location, and forming a range probability matrix. The region probability matrix is only automatically updated when the WSN testbed is asleep. Then, the weight of every measurement is calculated and normalized based on the region probability matrix. Finally, the correction value of the target prediction position is calculated according to the weighted least-square algorithm [38]. The proposed algorithm first integrates the distribution and the true attributes of each measurement data, and forming a range joint probability matrix. Then, the true probability of each measurement data can be obtained by the measured data contrastive operation with the range joint probability matrix. That is, the system can save a lot of time in the process of removing outliers. The proposed algorithm can not only be applied to different motion characteristics Tao Wang et al.: Preprint submitted to Elsevier

of the target, but can also greatly filter out erroneous data or noise data in WSNs. Therefore, the localization accuracy is improved in compared with many EKF-based frameworks algorithm, and the computing efficiency is improved in compared with many Bayesian-based frameworks algorithm. The proposed algorithm is deployed in the sink node, which first updates the range joint probability matrix when the system is dormant. When the target appears, the measurement data from other sensor nodes are gathered in each cycle, and the remaining steps of the proposed algorithm are executed for real-time location and tracking in the sink node. In summary, the main contributions to the paper are as follows: 1)We introduce the geometric model of target localization and tracking based on ranging, and calculate the corresponding target measurement position according to the geometric model and measurement data. 2)The theoretical basis of Bayesian classifiers is further explored. An improved Bayesian algorithm is proposed for measurement data of range-based localization. The improved Bayesian algorithm fuses the distribution and the true attributes of the measurement data, and forming a range joint probability matrix. The matrix is only automatically updated when the WSN testbed is in a dormant state. 3)High localization accuracy and good real-time tracking performance. In the running of the system, the true probability of each measurement data can be obtained by the measured data contrastive operation with the range joint probability matrix. That is, the system can save a lot of time in the process of removing outliers. 4)A kind of range-based localization sensor node is designed, which is mainly composed of the power module, a wireless communication module, processor module, angle measurement module, and infrared ranging module. In addition, according to the experimental requirements of this work, we have completed the verification of the proposed algorithm in the designed experiment platform based on the range-finding sensor nodes. The rest of this paper is organized as follows. Section 2 discusses some related work. In Section 3, the target location prediction and the method for position determination are discussed in a Cartesian coordinate. In Section 4, the theoretical background underlying the proposed algorithm is described. Section 5 describes the WSN Testbed. Section 6 shows how the reasonable parameter can be calculated from the training data, and the simulation results of the experiment in the WSN Testbed. Section 7 concludes this paper.

2. Related Work

In this section, an overview of EKF-based frameworks [38, 39, 40] and Bayesian-based frameworks [14, 15, 16, 17, 41] methods is given, though different approaches have been proposed.

2.1. KF-based framework

In [42, 43], these algorithms are still based on the KF frameworks, which is more suitable for the cases that the Page 2 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

maneuvering target state equation is linear. For the nonlinear maneuvering target tracking and non-Gaussian noise, these algorithms cannot guarantee accurate tracking performance. Multi-sensor data fusion (MSDF) techniques are defined as a process of integrating information and data from multiple sources to produce the most specific unified data. The process is supposed to obtain more accurate, efficient, and meaningful information that may not be possible to detect with a single sensor alone [44]. Since the measurement model of a maneuvering target is nonlinear, an EKF cannot achieve accurate estimation. Thus, to achieve more accurate estimation, combining EKF with soft computing technology is a valuable research topic. However, little work has been done to explore architectures that take into account the combination of both these approaches. In recent years, these algorithms have been further developed, but it is still difficult for the tracking of nonlinear maneuvering target to achieve the optimal performance. [45] explores a novel MSDF architecture that combines a cerebellar model articulation controller (CMAC) with an EKF tracker for MSDF and target tracking. CMACs can be applied to approximate a nonlinear function or to identify complex dynamical systems due to their good generalization capability and fast learning properties [46]. The advantages of using a CMAC over a neural network in certain applications have been presented in some literature [47, 48]. Thus, in [45], a CMAC is introduced to improve the linearization approximation error and the uncertainty of the EKF, and an intelligent EKF-CMAC algorithm is provided for locating and tracking a moving target. After researchers combine KF with an indoor positioning algorithm, a new point of view about Kalman Filter classification is presented, namely Position Kalman Filter (PKF) and Fingerprint Kalman Filter (FKF). Compared with FKF, the PKF uses the position estimated by the fingerprint matching algorithm as the system measurement instead of the measurement data, which does not directly filter the noise of the measurement data, but only indirectly reduces the fluctuation in the position estimates caused by the noise. As a result, PKF works well when we have reasonably accurate static position solutions. Compared with PKF and traditional KF, FKF does not need an analytic formula of the measurement equation, it directly uses the measured data as system measurement, in such a way that it has a better filtering effect on the noise than PKF [10, 49].

2.2. Bayesian-based framework

For linear and Gaussian systems, the KF-based framework is optimal in the minimum mean squared error sense. However, for nonlinear or non-Gaussian systems, the estimation of states or parameters is a challenging problem [17]. It is well acknowledged that naive Bayesian classifiers (NBC) can be implemented efficiently on classification problems with nominal attributes. For tasks with continuous attributes, we usually have two handling strategies. One is the discretization and the other is the density estimation. The former has been widely studied in NBC [50, 51]. The latest obTao Wang et al.: Preprint submitted to Elsevier

servation shows that the combination of various discretization methods can result in an improved classification accuracy [52, 53]. The probability hypothesis density (PHD) filter [54] views the targets as random finite sets and propagates the first order moment of the posteriors of multiple targets in a tractable way. Besides, the use of particle filtering in multiple target tracking (MTT) is a popular approach to deal with nonlinear and non-Gaussian MTT models, see [55] for an example. In [15], a new Bayesian tracking and parameter learning algorithm for non-linear and non-Gaussian target tracking models are proposed, but this algorithm is not a competitor to online tracking methods when online requirement is essential. Therefore, most particle filters are not suitable for online tracking algorithm in WSN with high real-time requirement. Currently, the pattern matching algorithm, whose outstanding representatives are the nearest neighbor algorithm (NN), the K-nearest neighbor algorithm (KNN), and the weighted K-nearest neighbor algorithm (WKNN), are often used as the performance benchmark of the newly proposed fingerprint positioning algorithm. The NN uses only one nearest calibration point as the location estimate of the target node [10], while the KNN directly uses the average coordinates of the multiple nearest calibration points as the estimated node position. Obviously, the location estimate of the KNN is more accurate than that of the NN. In contrast to the KNN, the WKNN assigns different weights to the different nearest calibration points. As a result, the target position estimated by the WKNN is typically more accurate than that estimated by the KNN Besides, variational Bayesian is an inference method that uses simple distribution to approximate the true posterior distribution of hidden variables. It is usually assumed that the hidden variables are independent of each other. Variational learning has two main purposes: a) Approximation of edge likelihood function to achieve model selection; b) The posterior probability distribution containing all parameters is approximated to realize the prediction of hidden variables. It is assumed that the prior distribution of all parameters in the full Bayesian model of hidden variables is known. The purpose of the variation is to find a variational distribution of the posterior probability distribution function (PDF) to minimize the KL divergence between the posterior PDF and the real posterior PDF. The dual-factor EVBAKF algorithm takes the advantages of dual-factor VBAKF and dynamic nominal covariance estimation (DNCE) to achieve the adaptive estimate of time-varying the measurement noise covariance matrix (MNCM) and process noise covariance matrix (PNCM). Compared with the traditional VBAKF, the dual-factor EVBAKF does not need the prior knowledge of process noise and has the stronger adaptability of time-varying noise [56]. The VBEM algorithm consists of a VBE-step and a VBM-step. In each iteration, the sparse measurement data is updated in the VBE-step while the grid parameter is updated in the subsequent VBM-step [57]. In this paper, we focus on the actual probability problems of measuring data and assume that probabilistic generative classifiers are used to solve these problems. Probabilistic Page 3 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

classifiers provide outputs that can be interpreted as conditional probabilities as they model the conditional distribution of classes given an input sample. Generative classifiers aim at modeling the processes from which the sample data are assumed to originate [58]. Probabilistic generative classifiers are usually based on NBC theorem. The proposed algorithm first fuses the distribution and the true attributes of each measurement data, and the effective measurement data region is divided into 𝑛 × 𝑛 sub-regions. Based on NBC theorem, the true probability of each measurement data in each sub-region is calculated, and a range joint probability matrix is obtained. Then, the true probability of each measurement data can be calculated by the measurement data contrastive operation with the range joint probability matrix. According to the true probability of each measurement data, we can effectively remove the outliers. Finally, the remaining effective measurement data are analyzed. Where the joint probability matrix of the proposed method can be obtained from the measurement data of the previous location and tracking, and it does not need to be calculated in real-time tracking. Therefore, the calculation cost of the proposed algorithm is greatly reduced. Meanwhile, because a large number of outliers can be removed through the range joint probability matrix, the positioning accuracy of the proposed algorithm is improved effectively compared with the algorithms of KFbased framework.

3. Prediction Position Analysis and System Model

The measurements of the target are collected through sensor nodes in a WSN, and are then analyzed by the proposed algorithm. In this section, the target position prediction and the method for position determination are discussed in a Cartesian coordinate. The section is divided into two parts: prediction position analysis and position determination method.

3.1. Prediction Position

The state variable method is an effective method to describe the dynamic system [39]. With this approach, the relationship between the input data and the output data of the system can be discussed in time domain by the state transition model and the output observation model. The input data can be described by a dynamic model that determines the time function and the random process representing the variables that cannot be predicted. The output is a function of the state, which is usually disturbed by the random observation error [40]. This process is described in detail as follows. There are many uncertain events in the process of tracking the moving target when it is accelerating, slowing down, or changing the direction of motion at the next time in WSNs. If the target maneuver model is not matched with the actual moving model, the false or the target loss may be caused. However, when the time interval between two adjacent measurements is small enough, the target motion model is similar to the uniform motion (acceleration is 0), constant deTao Wang et al.: Preprint submitted to Elsevier

celeration (acceleration is negative) or constant acceleration (acceleration is positive). The two adjacent measurements can be associated with a state equation, and the expression is as follows: (2)

X𝑘 = T̃ ⋅ X𝑘−1 + T̂ ⋅ 𝝎

where,

[ ]𝑇 X𝑘 = 𝑥𝑘 , 𝑥′𝑘 , 𝑥′′𝑘 , 𝑦𝑘 , 𝑦′𝑘 , 𝑦′′𝑘 ⎡ ⎢ ⎢ T̃ = ⎢ ⎢ ⎢ ⎢ ⎣ [

T̂ =

𝑡2 2

0

𝑡

1 𝑡 0 1 0 0 0 0 0 0 0 0

1 2 𝑡 2

1

0

0 0

2

𝑡

0 0

𝑡2

𝑡 1 0 0 0

1

0 0 0 0 0 0 1 𝑡 0 1 0 0 ]𝑇

0 0 0 1 2 𝑡 2 𝑡 1

, 𝝎=

[

(2a) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(2b)

𝜔𝑥 𝜔𝑦

] (2c)

where X𝑘 ∈ ℜ6×1 is the state vector of the target. 𝑥𝑘 , 𝑥′𝑘 , and 𝑥′′𝑘 are the position, velocity, and acceleration of the moving target in the 𝑥 axis, respectively. Similarly, 𝑦𝑘 , 𝑦′𝑘 , and 𝑦′′𝑘 are the position, velocity, and acceleration of the moving target in the 𝑦 axis, respectively. 𝑡 is the sampling period. 𝜔𝑦 and 𝜔𝑦 are independent of each other with zero meaning Gauss white noise and the variance being 𝜎𝜔𝑥 and 𝜎𝜔𝑦 . Equation (2) can be changed to the following equation: (3)

X𝑘 = F𝑘, 𝑘−1 X𝑘−1 + W𝑘−1

where F𝑘,𝑘−1 ∈ ℜ6×6 is the state transition matrix. 𝑊𝑘 ∈ ℜ6×2 is zero mean white Gauss noise matrix, and the covariance is U𝑘 : { ] [ U𝑘 , 𝑖 = 𝑘 𝑇 𝔼 W𝑖 ⋅ W𝑘 = (4) 0, 𝑖 ≠ 𝑘 the minimum mean square error of the state vector at time 𝑘 − 1 is estimated as: ] [ ̂ 𝑘−1|𝑘−1 = 𝔼 X𝑘−1 |Z𝑘−1 X (5) { } where 𝑍𝑘−1 = 𝜀𝑘−1 (𝑖), 𝑖 = 1, 2, 3, ⋯ , 𝑛 is the measurement vector at time 𝑘 − 1; 𝑛 is the total number of the measured values. The state error covariance matrix of (5) is expressed as follows: S𝑘−1|𝑘−1 [

̂ 𝑘−1|𝑘−1 ) ⋅ (X𝑇 − X ̂𝑇 = 𝔼 (X𝑘−1 − X 𝑘−1|𝑘−1 )|Z𝑘−1 𝑘−1 [ ] 𝑇 ̃ 𝑘−1|𝑘−1 ⋅ X ̃ =𝔼 X 𝑘−1|𝑘−1 |𝑍𝑘−1

]

(6)

̃ 𝑘−1|𝑘−1 is the filter error, and the mean square error where X prediction matrix of the state can be obtained from the state equation at the next moment as shown in the following: [ ] ̂ 𝑘|𝑘−1 = 𝔼 X𝑘 |Z𝑘−1 X [ ] = 𝔼 (F𝑘, 𝑘−1 X𝑘−1 + W𝑘−1 )|Z𝑘−1 (7) ̂ 𝑘−1|𝑘−1 = F𝑘, 𝑘−1 X Page 4 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN North

Y(m)

where (Δ𝜌𝑖 , Δ𝜃𝑖 ) represents the error of the predictive value of the sensor 𝑆𝑖 . According to the geometric relationship of Fig.2, the equation is obtained as follows: { Δ𝑥𝑘𝑖 = (𝑥𝑘 − 𝑥𝑠𝑖 ) − 𝜌𝑖 sin 𝜃𝑖 (12) Δ𝑦𝑘𝑖 = (𝑦𝑘 − 𝑦𝑠𝑖 ) − 𝜌𝑖 cos 𝜃𝑖

Predictive Position

( xk , y k ) Measured Position ( xki , yki )

ri qi '

Dri

using (12), the corresponding Δ𝑥𝑘𝑖 and Δ𝑦𝑘𝑖 of the 𝑛𝑠 measurement data of the sensors were calculated at time 𝑘. The matrix of the corresponding Δ𝑥𝑘𝑖 and Δ𝑦𝑘𝑖 of the measurement data is defined as follows:

ri '

Dqi

qi

𝛀𝑘 = (𝝊𝑘𝑥 , 𝝊𝑘𝑦 )𝑇

Sensor Si Position

( xsi , ysi )

X(m)

Figure 2: Geometry of the predictive position in relationship to measured position and the nodes 𝑖.

the error of the predicted value at the next moment is: ̃ 𝑘|𝑘−1 = X𝑘 − X ̂ 𝑘|𝑘−1 = F𝑘, 𝑘−1 X ̃ 𝑘−1|𝑘−1 + W𝑘−1 (8) X The covariance of the predicted error at the next moment is: ] [ ̃ 𝑘|𝑘−1 ⋅ X ̃𝑇 S𝑘|𝑘−1 = 𝔼 X 𝑘|𝑘−1 | Z𝑘−1

(9)

where S𝑘|𝑘−1 is a symmetric matrix, which could be used to measure the uncertainty of the predictive value. The smaller the value is, and the more accurate the prediction is.

3.2. Position Determination

In the process of target localization and tracking, the whole detection system needs a mathematical model. The model includes the predicted position of the target, the position of the sensor and the measured value of the sensor. Then the deviation between the predicted position and the measured value is calculated according to the geometry of the predictive position in relationship to measured position and the nodes. First, geometric relations are established according to the predicted position of the target at time 𝑘, the position of the sensor 𝑖 and the measurement position of the target, as showed in Fig.2. In Fig.2, the predicted position of the target is (𝑥𝑘 , 𝑦𝑘 ) at time 𝑘, and the coordinate of the sensor 𝑆𝑖 is (𝑥𝑠𝑖 , 𝑦𝑠𝑖 ). The measurement position of the sensor 𝑆𝑖 is (𝑥𝑘𝑖 , 𝑦𝑘𝑖 ) from the target, and the following equations are obtained: { Δ𝑥𝑘𝑖 = 𝑥𝑘 − 𝑥𝑘𝑖 = 𝜌𝑖 ′ sin(𝜃𝑖 ′ ) − 𝜌𝑖 sin(𝜃𝑖 ) (10) Δ𝑦𝑘𝑖 = 𝑦𝑘 − 𝑦𝑘𝑖 = 𝜌𝑖 ′ cos(𝜃𝑖 ′ ) − 𝜌𝑖 cos(𝜃𝑖 ) where (𝜌𝑖 , 𝜃𝑖 ) represents the measured value of the sensor 𝑆𝑖 in the polar coordinate; (𝜌𝑖 ′ , 𝜃𝑖 ′ ) represents the distance and angle between the sensor and the predicted position of the target in the polar coordinate. The equations for measurement and measurement error are as follows: { 𝜌𝑖 = 𝜌𝑖 ′ − Δ𝜌𝑖 (11) 𝜃𝑖 = 𝜃𝑖 ′ − Δ𝜃𝑖 Tao Wang et al.: Preprint submitted to Elsevier

= (𝜺𝑘1 , 𝜺𝑘2 , ⋯ 𝜺𝑘𝑛𝑠 ) [ Δ𝑥𝑘1 Δ𝑥𝑘2 ⋯ = Δ𝑦𝑘1 Δ𝑦𝑘2 ⋯

Δ𝑥𝑘𝑛𝑠 Δ𝑦𝑘𝑛𝑠

]

(13)

using (13), the distance Δ𝝆𝑘𝑖 between the corresponding predicted position of each 𝜺𝑘𝑖 and the measurement position of the target from the sensor 𝑖 was calculated. The equation for Δ𝝆𝑘𝑖 is as follows: ‖ Δ𝝆𝑘𝑖 = ‖ ‖𝜺𝑘𝑖 ‖2

(14)

according to the above calculation, each node needs not only to transmit the target location of the measurement information, but also to send to the serial number of the corresponding node in the WSN. These serial numbers could determine the location information of the nodes. The location of the target is accurately calculated according to the position of the node and the measurement information. In this process, we need to know the location information of each node in order to locate the target effectively. The position information of nodes in the WSN can be obtained according to the relevant location algorithm.

4. Analysis of Improved Bayesian Enhanced Least-Squares Algorithm

The measurements in WSNs are integrated to acquire more accurate position of the target. In this context, the Bayesian evolutionary algorithm analysis [15] and CLF [23, 24] can be used. However, they all have some shortcomings. Therefore, we improve the Bayesian algorithm, the CLS is enhanced according to the improved Bayesian algorithm, and obtain a new filtering algorithm.be selected.

4.1. Improved Bayesian Evolutionary Algorithm Analysis

It is assumed that the conditional distribution of the measurement conforms to the Gauss distribution at every moment. According to the calculation process of Δ𝝆𝑘𝑖 , we can know that the row vector 𝝊𝑥 and 𝝊𝑦 also accord with Gauss distribution. The covariance of each row vector is 𝝈 = (𝜎𝑥 , 𝜎𝑦 )𝑇 , and the mean and covariance is as follows: [ ] [ ] [ ] 𝝊𝑥 𝜇𝑥 1 𝑟 𝔼 = = 𝜇, S̃ = , 𝝊𝑦 𝜇𝑦 𝑟 1 (15) [ ] 𝜎𝑥2 𝑟𝜎𝑥2 𝜎𝑦2 ̂S = 𝑟𝜎𝑥2 𝜎𝑦2 𝜎𝑦2 Page 5 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

where 𝑆̃ is the covariance matrix of the row vectors 𝝊𝑥 and 𝝊𝑦 . The probability density of (Δ𝑥, Δ𝑦) ∼ 𝑁[𝜇𝑥 , 𝜎𝑥 ; 𝜇𝑦 , 𝜎𝑦 ; 𝑟] is as follows: 𝑓𝜐𝑥 𝜐𝑦 (Δ𝑥, Δ𝑦) =

1 1 | ̂ |− 2 𝑺 | | 2𝜋 | |

exp[− 12 (𝜺𝑖 − 𝝁)𝑇

−1 ⋅ Ŝ (𝜺𝑖 − 𝝁)]

(16)

using (16), the probability of the sub-range of the target measured was calculated. This will provide an important basis for the probability calculation of the measurement in each range. There are true relevant data as well as various noises and disturbances data from sensor nodes in a WSN. If all kinds of noise and disturbance data in the measured data are not processed effectively, the accuracy of target localization and tracking will be seriously affected. Because true measurements are mixed with false measurements, it is needed to identify the false and true measurement when the target state is updated. This paper uses a Bayesian evolutionary algorithm in order to effectively distinguish the true measurements from the false measurement (interference), and improve the efficiency of the least-square algorithm. Bayesian evolutionary algorithm is a kind of statistical evolutionary algorithm based on the existing statistical results. According to the updated measurements in each time tracking, Bayesian evolutionary algorithm is trained, and the greater the number of the measurements is, the better the training effect is. The whole training process is as follows: 1).The system receives measurements at every moment, and the predictive position of the target is set as the center. After that, the whole measurement range is divided into two sections. Setting a threshold value 𝜁 ; when the range from the center is greater than 𝜁 , the range is defined as outside the threshold range, otherwise, the threshold range. 2).The probability for false measurement is close to 1, when the measurement is outside the threshold range (Δ𝑥𝑖 ∉ [−𝜁 , 𝜁] or Δ𝑦𝑖 ∉ [−𝜁 , 𝜁]). The measurement will be classified as a false measurement. 3).When the measurement is in the threshold range (Δ𝑥𝑖 ∉ [−𝜁 , 𝜁] or Δ𝑦𝑖 ∉ [−𝜁 , 𝜁]), the threshold range is divided into 𝑛 × 𝑛 sub-ranges (𝑛 is even), that is, the threshold range is divided into 𝑛 rows and 𝑛 columns sub-ranges. The value range of the 𝑖-th row and 𝑗-th column sub-range is Δ𝑥 ∈ [(𝜁 − (2𝜁 (𝑗 − 1)∕𝑛)), (𝜁 −2𝜁 𝑗∕𝑛)] and Δ𝑦 ∈ [(𝜁 −(2𝜁 (𝑖 − 1)∕𝑛)), (𝜁 − 2𝜁𝑖∕𝑛)], respectively. Assuming that there is no noise, the probability of the measurement in this sub-range is: 𝑝̂𝑖𝑗 =

𝜁 − 2𝜁(𝑗−1) 𝑛

∫𝜁− 2𝜁𝑗 𝑛

𝜁 − 2𝜁(𝑖−1) 𝑛

∫𝜁 − 2𝜁𝑖

𝑓𝜐𝑥 𝜐𝑦 (Δ𝑥, Δ𝑦)dΔ𝑥dΔ𝑦 (17)

𝑛

using (17), the range probability matrix P̂ ∈ ℜ𝑛×𝑛 of the measurements was calculated in the condition of no noise. Then, The measurements are trained in the 𝑖-th row and the 𝑗-th column sub-range. For example, all measurements in the threshold range before the current tracking are analyzed and calculated. Firstly, we obtain the training data by moving the target based on precise trajectory in the monitoring Tao Wang et al.: Preprint submitted to Elsevier

area (the training data are obtained at 𝑚1 times, and the 𝑚1 precise positions are obtained according to the precise trajectory). Then the predicted position of each time is calculated and the sub-region is divided based on the predicted position. The 𝑚1 precise positions are assigned to the corresponding sub-region. The number of precise positions in the 𝑖-th row and 𝑗-th column sub-region is calculated as 𝑚[𝑖𝑗] , 1 and the true probability of measurement in this sub-region is 𝑝(𝜆𝑖𝑗 |𝐴) = 𝑚[𝑖𝑗] ∕𝑚1 (A represents the true measurement). 1 When the system is running, the sink node records which sub-region is the optimal estimate at each time, and the number of precise positions in this sub-region plus 1. When the joint probability matrix is updated, the true probability of measurement is updated based on the number of precise positions in each sub-region. There are 𝑚2 precise positions in the threshold range, and there are 𝑚[𝑖𝑗] precise positions in 1 the 𝑖-th row and the/𝑗-th column sub-range. The probability ∑ ∑ 𝑝(𝐴) is 𝑛𝑖 𝑛𝑗 𝑚[𝑖𝑗] 𝑚1 = 𝑚2 ∕𝑚1 in the threshold range. In 1 order to avoid the true probability of measurement is zero in some sub-range, we must first set an initial value for 𝑝(𝜆𝑖𝑗 |𝐴) and 𝑝(𝜆𝑖𝑗 |𝐵) (B represents the false measurement) of the 𝑖-th and the 𝑗-th column sub-range (the initial value can be obtained by training or previous experiments). The probability of the true measurement is 𝑝(𝐴) in the threshold range, the probability of the false measurement is 𝑝(𝐵) in the threshold range, and 𝑝(𝐴) + 𝑝(𝐵) = 1. Then, assuming that the measurement is in the 𝑖-th row and the 𝑗-th sub-range. The probability for the false measurement is as follows: 𝑝(𝐵|𝜆𝑖𝑗 ) =

𝑝(𝜆𝑖𝑗 |𝐵)𝑝(𝐵)

𝑝(𝜆𝑖𝑗 |𝐵)𝑝(𝐵) + 𝑝(𝜆𝑖𝑗 |𝐴)𝑝(𝐴) 𝑖, 𝑗 = 1, 2, ⋯ 𝑛

;

(18)

using (18), the probability matrix P(𝐵|𝜆) of the false measurements in the threshold range was calculated. In (17) and (18), the probability 𝑝̂𝑖𝑗 and the probability 𝑝(𝐵|𝜆𝑖𝑗 ) in the 𝑖-th row and the 𝑗-th sub-range can be calculated, separately. The two probabilities are combined, and the judgment condition of the probability of the sub-range is obtained. After all measurements of every moment were judged according to the judgment condition, a set 𝕍𝑘 (𝛾) of effective measurement vectors is obtained. In the process of calculating the judgment condition, the range probability matrix P̃ must be calculated firstly. The calculation equation is as follows: 𝑇 P̃ = P(𝐵|𝜆)P̂ = ∑ ∑ 𝑝(𝐵|𝜆1𝑖 )𝑝̂1𝑖 𝑝(𝐵|𝜆1𝑖 )𝑝̂2𝑖 ⎡ 𝑖 𝑖 ∑ ⎢ ∑ 𝑝(𝐵|𝜆2𝑖 )𝑝̂1𝑖 𝑝(𝐵|𝜆2𝑖 )𝑝̂2𝑖 ⎢ 𝑖 ⎢ 𝑖 ⋮ ⋮ ⎢ ∑ ∑ ⎢ 𝑝(𝐵|𝜆𝑛𝑖 )𝑝̂1𝑖 𝑝(𝐵|𝜆𝑛𝑖 )𝑝̂2𝑖 ⎣ 𝑖 𝑖

⋯ ⋯ ⋱ ⋯

∑

𝑝(𝐵|𝜆1𝑖 )𝑝̂𝑛𝑖 ⎤ ⎥ 𝑝(𝐵|𝜆2𝑖 )𝑝̂𝑛𝑖 ⎥ 𝑖 ⎥ ⋮ ⎥ ∑ 𝑝(𝐵|𝜆𝑛𝑖 )𝑝̂𝑛𝑖 ⎥ ⎦ 𝑖 (19)

𝑖 ∑

̃ the false According to the range joint probability matrix P, joint probability 𝑝̃′𝑖𝑗 of 𝑖-th row and 𝑗-th sub-range is obPage 6 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

tained. The specific equation is as follows: ∑ 𝑝(𝐵|𝜆𝑖𝑙2 )𝑝̂𝑗𝑙2 𝑙2

𝑝̃′𝑖𝑗 = ∑ ∑ 𝑙1 𝑙2

𝑝(𝐵|𝜆𝑖𝑙2 )𝑝̂𝑙1 𝑙2

because the high-order item has little effect on the results, equation (24) was further simplified as: (20)

According to the false joint probability 𝑝̃′𝑖𝑗 , the set 𝕍𝑘 (𝛾) of effective measurement vectors is as follows: { ̂ 𝜆𝑖𝑗 ) = 𝑝̂′ ≤ 𝛾; 𝕍𝑘 (𝛾) = 𝜺̂ 𝑘 (𝑙) ∶ 𝑝(𝐵|P, 𝑖𝑗 (21) } 𝑙 = 1, 2, ⋯ 𝑚𝑘 ; 𝑖, 𝑗 = 1, 2, ⋯ 𝑛

where 𝑚𝑘 represents the total number of the filtered true measurements based on condition 𝛾 at time 𝑘; 𝜺̂ 𝑘 (𝑙) represents the 𝑙-th measurement vector based on condition 𝛾 in the true measurement vector set; 𝛾 represents the threshold value of the joint probability when the measurement is a false measurement. However, Bayesian evolutionary algorithm has its limitations. If the range joint probability matrix P̃ is the updated at every moment in the target tracking, it will greatly influence computation efficiency of the algorithm. Besides, there is no need for the real-time update range joint probã So we only need to store the trace data, and bility matrix P. after the every tracking it is updated when WSN testbed is in a dormant state. The true probability of each measurement data can be obtained by the measured data contrastive operation with the range joint probability matrix. For the sink node with limited resources, it can improve the realtime performance of the sink node. If the complex particle filter algorithm is used, the computation of the sink node will be greatly increased, and then the tracking performance of WSN will be affected. So this algorithm is suitable for WSN, and has high accuracy without affecting the real-time performance. As we all know, all the measurements that have been generated contain a lot of prior knowledge (or experience). Bayesian school also has the theory that prior distribution and Bayesian formula, the posterior distribution is established according to current measurements. Therefore, according to the empirical Bayesian estimation method, the probability of the reasonable measurement is predicted in the threshold range.

4.2. CLS analysis

Using (10) and (11), the following equation was calculated: { Δ𝑥𝑘𝑖 = (𝜌𝑖 + Δ𝜌𝑖 ) sin(𝜃𝑖 + Δ𝜃𝑖 ) − 𝜌𝑖 sin 𝜃𝑖 (22) Δ𝑦𝑘𝑖 = (𝜌𝑖 + Δ𝜌𝑖 ) cos(𝜃𝑖 + Δ𝜃𝑖 ) − 𝜌𝑖 cos 𝜃𝑖 first, Δ𝑥𝑘𝑖 is calculated according to the above equation: Δ𝑥𝑘𝑖 = 𝜌𝑖 sin 𝜃𝑖 cos Δ𝜃𝑖 + 𝜌𝑖 cos 𝜃𝑖 sin Δ𝜃𝑖 +Δ𝜌𝑖 sin 𝜃𝑖 cos Δ𝜃𝑖 + Δ𝜌𝑖 cos 𝜃𝑖 sin Δ𝜃𝑖 − 𝜌𝑖 sin 𝜃𝑖

(23)

in the actual target position detection, the error is less than the measurement, Δ𝜌𝑖 ≪ 𝜌𝑖 and Δ𝜃𝑖 ≪ 𝜃𝑖 . The value of Δ𝜃𝑖 tends to be zero, and cos Δ𝜃𝑖 ≈ 1, sin Δ𝜃𝑖 ≈ Δ𝜃𝑖 . Therefore, equation (23) can be simplified as: Δ𝑥𝑘𝑖 ≈ 𝜌𝑖 Δ𝜃𝑖 cos 𝜃𝑖 + Δ𝜌𝑖 sin 𝜃𝑖 + Δ𝜌𝑖 Δ𝜃𝑖 cos 𝜃𝑖 (24)

Tao Wang et al.: Preprint submitted to Elsevier

Δ𝑥𝑘𝑖 ≈ 𝜌𝑖 Δ𝜃𝑖 cos 𝜃𝑖 + Δ𝜌𝑖 sin 𝜃𝑖

(25)

Δ𝑦𝑘𝑖 ≈ −𝜌𝑖 Δ𝜃𝑖 sin 𝜃𝑖 + Δ𝜌𝑖 cos 𝜃𝑖

(26)

similarly, Δ𝑦𝑘𝑖 was calculated as:

using (25) and (26), the following equation was calculated: { Δ𝑥𝑘𝑖 sin 𝜃𝑖 + Δ𝑦𝑘𝑖 cos 𝜃𝑖 = Δ𝜌𝑖 (27) sin 𝜃 cos 𝜃 Δ𝑥𝑘𝑖 𝜌 𝑖 − Δ𝑦𝑘𝑖 𝜌 𝑖 = Δ𝜃𝑖 𝑖

𝑖

for the classical range case, it is assumed that error is equal to zero. Note that (27) depends on the angular position 𝜃𝑖 and the distance 𝜌𝑖 of the node relative to the measurement. Equation (27) gives the measurements as a function of the positional and bias errors associated with the initial starting point for the iteration. However, the analysis requires estimates of the positional error in terms of range errors. This is achieved by performing a CLS on the linear equations represented by using (27), so that the differences between the measured ranges and that given by (27) is minimized. It is convenient to perform the analysis using matrix algebra, so that (27) can be expressed as: (28)

H𝜹 = 𝝃

where,

⎡ sin 𝜃1 ⎢ cos 𝜃1 𝜌1 ⎢ ⎢ ⋮ H= ⎢ sin 𝜃 ⎢ cos 𝜃 𝑚𝑘 𝑚𝑘 ⎢ ⎣ 𝜌𝑚𝑘

cos 𝜃1 ⎤ sin 𝜃 − 𝜌 1 ⎥ [ ] ⎥ 1 ⎥ , 𝜹 = Δ𝑥𝑘 , ⋮ Δ𝑦𝑘 cos 𝜃𝑚𝑘 ⎥ sin 𝜃𝑚𝑘 ⎥ ⎥ − 𝜌 ⎦ 𝑚𝑘 ⎡ ⎢ ⎢ 𝝃=⎢ ⎢ ⎢ ⎣

and

Δ𝜌1 Δ𝜃1 ⋮ Δ𝜌𝑚𝑘 Δ𝜃𝑚𝑘

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(28a)

⎧ Δ𝜃 ≈ sin Δ𝜃 = √𝑥𝑠𝑖 cos 𝜃𝑖 −𝑦𝑠𝑖 sin 𝜃𝑖 𝑖 ⎪ (𝑥𝑘 −𝑥𝑠𝑖 )2 +(𝑦𝑘 −𝑦𝑠𝑖 )2 √ ⎨ ⎪ Δ𝜌𝑖 = (𝑥𝑘 − 𝑥𝑠𝑖 )2 + (𝑦𝑘 − 𝑦𝑠𝑖 )2 − 𝜌𝑖 ⎩

(28b)

in typical practical situations, (28) [45] are overly defined, so that a CLS solution was calculated from: 𝚽𝜹 = d

(29)

where,

𝚽 = 𝑯𝑇 𝑯 = 𝑚 ⎡ ∑𝑘 (sin2 𝜃 + cos2 𝜃𝑖 ) 𝑖 ⎢ 𝜌2𝑖 𝑖 𝑚𝑘 ⎢ ∑ ⎢ (1 − 12 ) sin 𝜃𝑖 cos 𝜃𝑖 ⎣ 𝑖 𝜌𝑖

𝑚𝑘 ∑ 𝑖

(1 −

𝑚𝑘 ∑ 𝑖

1 ) sin 𝜃𝑖 cos 𝜃𝑖 𝜌2𝑖

(cos2 𝜃𝑖 +

sin2 𝜃𝑖 ) 𝜌2𝑖

⎤ ⎥ ⎥ ⎥ ⎦ (29a)

Page 7 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

and 𝑚𝑘

⎡ ∑ (Δ𝜌 sin 𝜃 + Δ𝜃𝑖 cos 𝜃𝑖 ) 𝑖 𝑖 𝜌𝑖 ⎢ d = H𝑇 𝝃 = ⎢ 𝑚𝑖𝑘 ∑ Δ𝜃 sin 𝜃 ⎢ (Δ𝜌𝑖 cos 𝜃𝑖 − 𝑖 𝜌 𝑖 ) ⎣ 𝑖 𝑖

⎤ ⎥ ⎥ ⎥ ⎦

and the 𝑗-th sub-range. The specific equation is as follows: ∑ 𝑝(𝐴|𝜆𝑖𝑙2 )𝑝̂𝑗𝑙2 (29b)

𝑙1 𝑙2

the solution to linear matrix (29) can be expressed in the form: 𝜹 = (H𝑇 H)−1 (H𝑇 𝝃) = 𝚽−1 d

(30)

the vector 𝝃 provides an estimate for the correction required to the initial estimate of the two variables Δ𝑥 and Δ𝑦. Thus, better estimates are: ] [ ] ] [ [ 𝑥𝑘|𝑘−1 𝑥𝑘|𝑘 Δ𝑥𝑘 + (31) = 𝑦𝑘|𝑘−1 Δ𝑦𝑘 𝑦𝑘|𝑘 Equation (30) [45] is applied iteratively until the increments are sufficiently small. Note that these corrections are not the errors in the target predictive location, which are dependent on the measurement errors, but are increments in the iterative process. As the solution converges, these increments will approach zero in most situations, although the algorithm may not converge with large measurement errors.

4.3. Improved Bayesian Enhanced Least-Squares Algorithm Analysis

In the previous section, the CLS algorithm is described to account for bias errors. This section analyzes the improved Bayesian enhanced least-squares algorithm. It is important to realize the results of CLS in (30), in which the measurement matrix H and the dependent variable 𝝃 are processed by the Bayesian algorithm. However, there may also be an unpleasant situation that is the overadaptation of the data. The model parameters may contain undesirable effects in the solution for 𝜹 by using (30), and the calculated result will be affected. These undesirable effects may be related to measurement noise or any other irrelevant factor, and can be seen as noise in the broad sense. After the previous Bayesian algorithm, the larger noise has been removed, but the rest of the data may still have some noises. After that, we need to use empirical data to further improve the accuracy of the target tracking. According to the empirical data, we can set a different weight for each data, and the ̂ 𝑘 ∈ ℜ𝑛×1 . weight vector is w Using (18), the probability of measuring the data for the true measurement was calculated in the 𝑖-th row and the 𝑗-th sub-range. The specific equation is as follows: 𝑝(𝐴|𝜆𝑖𝑗 ) = 1 − 𝑝(𝐵|𝜆𝑖𝑗 ) 𝑝(𝜆𝑖𝑗 |𝐴)𝑝(𝐴) = ; 𝑝(𝜆𝑖𝑗 |𝐵)𝑝(𝐵) + 𝑝(𝜆𝑖𝑗 |𝐴)𝑝(𝐴)

(32)

𝑖, 𝑗 = 1, 2, ⋯ 𝑛

according to the similarly calculation method with (19) and (20), the true joint probability was calculated in the 𝑖-th row Tao Wang et al.: Preprint submitted to Elsevier

𝑙2

𝑝̃′′ 𝑖𝑗 = ∑ ∑

𝑝(𝐴|𝜆𝑖𝑙2 )𝑝̂𝑙1 𝑙2

(33)

in the CLS, the filtered measurements are calculated directly, and the true degree of each data is not taken into account. Therefore, the finally calculated results may have some deviation, and it is thus necessary to correct the CLS algorithm. According to the true joint probability 𝑝̃′′ 𝑖𝑗 of 𝜺̂ 𝑘 (𝑙) in (21) and (33), the set of true joint probabilities can be obtained from { ′′ ℙ𝑘 = 𝑝𝑡𝑟𝑢𝑒 (𝑖) = 𝑝̃′′ 𝑙1 𝑙2 ∶ 𝑝̃𝑙1 𝑙2 ← 𝜺̂ 𝑘 (𝑙); (34) } 𝑖, 𝑙 = 1, 2, ⋯ 𝑚𝑘 ; 𝑙1 , 𝑙2 = 1, 2, ⋯ 𝑛 using (34), the expected value of the true joint probability 𝑝𝑡𝑟𝑢𝑒 (𝑖) of 𝜺̂ 𝑘 (𝑙) was calculated from: [ ] 𝔼 𝑝𝑡𝑟𝑢𝑒 = 𝜇𝑝 (35) after the expected value of the true measurement probability of the data vector 𝜺̂ 𝑘 (𝑙) was calculated by using (35), the weight parameters of each data vector 𝜺̂ 𝑘 (𝑙) are calculated by the bias parameter 𝜅. The specific equation is as follows: 𝑤𝑘 (𝑖) = 𝑒𝜅(𝑝𝑡𝑟𝑢𝑒 (𝑖)−𝜇𝑝 ))

(36)

the weight parameters are normalized: 𝑤 (𝑖) 𝑤̂ 𝑘 (𝑖) = ∑ 𝑘 𝑤𝑘 (𝑗)

(37)

𝑗

using (37), the weight vector 𝑤̂ 𝑘 was calculated. Therefore, the diagonal weight matrix 𝚲 is given by: { 𝚲 = 𝑑𝑖𝑎𝑔 𝑤̂ 𝑘 (1), 𝑤̂ 𝑘 (1), 𝑤̂ 𝑘 (2), 𝑤̂ 𝑘 (2), }⋯ , (38) 𝑤̂ 𝑘 (𝑚𝑘 ), 𝑤̂ 𝑘 (𝑚𝑘 ) in (29), (30), and (37), the data matrix H is corrected by the diagonal weight matrix 𝚲. The corrected equation is as follows: ̂ = 𝚲H H

(39)

the corresponding vector 𝝃 is corrected by the diagonal weight matrix 𝚲, and the corrected vector is as follows: [ 𝝃̂ = Δ𝜌1 ⋅ 𝑤̂ 𝑘 (1), Δ𝜃1 ⋅ 𝑤̂ 𝑘 (1), ⋯ , ]𝑇 (40) Δ𝜌𝑚𝑘 ⋅ 𝑤̂ 𝑘 (𝑚𝑘 ), Δ𝜃𝑚𝑘 ⋅ 𝑤̂ 𝑘 (𝑚𝑘 ) the solution vector of the improved Bayesian enhanced leastsquares algorithm can be obtained from: [ ]−1 [ ] 𝜹̂ = (𝚲H)𝑇 𝚲H (𝚲H)𝑇 𝝃̂ ̂ 𝑇 H) ̂ −1 (H ̂ 𝑇 𝝃) ̂ −1 d̂ ̂ =𝚽 = (H

(41) Page 8 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN 𝑚 ⎡ ∑𝑘 𝑤̂ 2 (𝑖)(sin2 𝜃 + cos2 𝜃𝑖 ) 𝑖 𝑘 𝜌2𝑖 ̂ 𝑇H ̂ = ⎢⎢ 𝑚 𝑖 ̂ =H 𝚽 𝑘 ∑ ⎢ (1 − 𝜌12 )𝑤̂ 2𝑘 (𝑖) sin 𝜃𝑖 cos 𝜃𝑖 ⎣ 𝑖 𝑖

̂ see equation (41a), and where 𝚽 𝑚 ⎡ ∑𝑘 𝑤̂ 2 (𝑖)(Δ𝜌 sin 𝜃 + Δ𝜃𝑖 cos 𝜃𝑖 ) 𝑖 𝑖 𝑘 𝜌𝑖 ̂ 𝑇 𝝃̂ = ⎢⎢ 𝑚𝑖 d̂ = H ∑𝑘 2 Δ𝜃 sin 𝜃 ⎢ 𝑤̂ (𝑖)(Δ𝜌𝑖 cos 𝜃𝑖 − 𝑖 𝜌 𝑖 ) ⎣ 𝑖 𝑘 𝑖

⎤ ⎥ ⎥ ⎥ ⎦

(41b)

using (41), the classical least-squares algorithm is corrected. First of all, in the Bayesian algorithm, the probability that the measurement is a false measurement is considered based on the empirical parameter. Second, the weighting parameter of each measurement is calculated based on the calculated probabilities of each measurement. Finally, the Bayesianfiltered measurements are fused according to the least-squares algorithm and the weighting parameters. The details are presented in Algorithm 1. However, the selection of the bias parameter 𝜅 has a direct impact on the whole performance of the proposed algorithm. The method for selecting the reasonable 𝜅 is described in detail in the next section. Algorithm 1 The improved Bayesian enhanced least-squares Scheme Require: Data 𝑝𝑘 (𝐴|𝜆𝑖𝑗 ), P̂ 𝑘 ∈ ℜ𝑛×𝑛 , and â 𝑘 (𝑙). Ensure: Optimal target location (𝑥𝑘|𝑘 , 𝑦𝑘|𝑘 ). 1: initialization: Set 𝜁 and 𝛾; 2: Target prediction position: (𝑥𝑘|𝑘−1 , 𝑦𝑘|𝑘−1 ); 3: for 𝑖 = 0, 1, ..., 𝑛 do 4: for 𝑗 = 0, 1, ..., 𝑛 do 5: Calculate 𝑝̃′′ 𝑖𝑗 ; 6: end for (𝑗) 7: end for (𝑖) 8: Calculate ℙ𝑘 ; [ ] 9: Calculate 𝔼 𝑝𝑡𝑟𝑢𝑒 ; 10: for 𝑖 = 0, 1, ..., 𝑚𝑘 do 𝜅(𝑝 (𝑖)−𝜇𝑝 )) 11: 𝑤𝑘 (𝑖) = 𝑒 𝑡𝑟𝑢𝑒 ; 12: end for (𝑖) ̂ 𝑘 (𝑖); 13: Normalized 𝑤𝑘 (𝑖) ⇒ 𝑤 ̂ 𝑘 (𝑖) ⇒ 𝚲; 14: Establish diagonal matrix 𝑤 ̂ 15: Calculate 𝝃; ̂ 16: Calculate 𝜹; 17: Optimal target location: [ ] 𝑥𝑘|𝑘 , 𝑦𝑘|𝑘 = [𝑥𝑘|𝑘−1 , 𝑦𝑘|𝑘−1 ] + 𝜹̂𝑇 .

5. Measurement Modeling

This section describes the WSN Testbed and experimental details. There is a sink node in the WSN Testbed, which has the same measurement function as other nodes, but its Tao Wang et al.: Preprint submitted to Elsevier

𝑚𝑘 ∑ 𝑖

cos 𝜃𝑖 ⎤ ⎥ 𝑚𝑘 ⎥ ∑ sin2 𝜃𝑖 2 2 𝑤̂ 𝑘 (𝑖)(cos 𝜃𝑖 + 𝜌2 ) ⎥ ⎦ 𝑖 𝑖 (1 −

1 )𝑤̂ 2𝑘 (𝑖) sin 𝜃𝑖 𝜌2𝑖

(41a)

processor performance, storage capacity, and battery capacity have been greatly enhanced. In order to facilitate the deployment of sensor nodes, we use wireless module for data transmission. According to the sampling frequency of infrared ranging module, a node needs to send about 50 groups of data (about 3Kb) at each cycle. Each group of data contains the direction angle and the distance between the node and the target, and the number of the sensor is labeled on the data. The sink node stores the precise position and the corresponding number of each node. The measured position can be calculated by the precise position of the sensor corresponding to the number, the direction angle and the distance between the node and the target in the sink node. Then, the sink node transmits the calculated results to the computer.

5.1. WSN Testbed

The proposed algorithm was validated in experiments carried out in the WSN Testbed. The computer outside the WSN Testbed can receive the optimal evaluation track from the sink node, and we evaluate the performance of the algorithm by comparing and analyzing the optimal evaluation track with the real track. The real track is a fixed ground route that can be accurately measured. We deploy a WSN of nodes based on ZigBee cc2530F256 module from TI as our testbed. The objective of the experiments was to track people acting as targets. A total of 20 sensor nodes were deployed on the floor or table, as shown in Fig.3(b) and 3(c). We randomly selected 1000 measuring times for analysis based on the measuring angle and distance of the sensor node, the size of our experimental environment, and the attributes of the experimental target. There is no blind area in the surveillance area during these 1000 measurement times. Therefore, we believe that the probability of blind area occurrence is very low when 20 nodes from different directions are measured simultaneously, and the probability of blind area occurrence on tracking is within acceptable range. In addition, the CPU of the sink node uses the ARM Cortex series, which is enough to deal with the proposed algorithm, but the battery capacity must ensure that the sink node survives longer than other ordinary nodes. The CPU of other common sensor nodes uses lower version ARM9. The sensor node in this paper includes an infrared LiDAR ranging sensor(the model is HPS-166 from HYPERSEN), which can be used to measure the distance between the node and the target by sending and receiving infrared rays. Each node also consisted of an angle module, which includes a motor and a rheostat. When the sensor node rotates through the motor, the rheostat also adjusts the voltage of the intermediate joint. Then, the sensor angle is obtained by A/D conversion module, as shown in Fig.3(a). The measured angle of the infrared rangPage 9 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

(a)

(b)

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Figure 3: The photographs of sensor node and two experimental scenes: (a) Sensor node. (b) Experimental scene 1. (c) Experimental scene 2.

ing module is controlled by the angle module. Then, measured distance 𝜌𝑖 and angle 𝜃𝑖 of each node is transmitted to the base station. In the WSN Testbed, the datasets used include the precise location and number of sensor nodes, the measured dataset from the corresponding node, the predicted location of each time in the previous tracking, the all precise positions of optimal estimation in the previous tracking, the number of precise positions and the true probability in each sub-region. Mathematical library, operation coincidence logic library, time and date library, matrix and linear algebraic library, basic matrix and matrix operation library are used in our sensors [59]. These libraries are well-known libraries. Meanwhile, the TI Z-Stack protocol and the time synchronization are applied. The prototype was developed in c language. A set of experiments on the Integrated Testbed was conducted to evaluate the performance of the proposed algorithm. The set aimed at the performance and feasibility of the proposed algorithm in terms of mean error and computation time with target tracking application in WSN. In timing experiments it was shown that each sampling cycle of sensor required less than 250 × 10−3 s. The execution of each measurement in the infrared ranging module and angle module required roughly 200 × 10−3 s, the AD transforming and data gathering required roughly 30 × 10−3 s, the sensor activation mechanism required roughly 10 × 10−3 s.

5.2. Experiment Details

We use measurements from several data sets in this paper. In all data sets, we first collect data from the sensors during a room calibration period. Next, a person walks around in the living room at a constant speed of about 2m∕s, as shown in Fig.3, using a metered path so that the position of the person at any particular time is known. Details of two experimental scenes are given as the follows.

5.2.1. Scene 1 The uncluttered indoor experimental environment is located in room F904 of New Main Building at Beihang University. As showed in Fig.3(b), 20 wireless nodes are deployed to cover a 5m × 8m rectangle sensing area being free. The interval between two adjacent nodes is roughly 1m. The Tao Wang et al.: Preprint submitted to Elsevier

node height is 1.15m.

5.2.2. Scene 2 This obstructed indoor environment is located in the same room. As showed in Fig.3(c), there exists a table and obstacles inside the sensing area. 20 wireless nodes are located around a 5m × 8m rectangle sensing area. The interval and height of the nodes is the same as above.

6. Parameter Determination and Experiment Results

This section describes the analytical method for determining the reasonable parameter, and how the reasonable parameter can be obtained from the training data in WSN Testbed. Then, the proposed algorithm is compared with the classical Bayesian algorithm and EKF. The tracking results show that the proposed algorithm is more robust to large localization errors. The selection of threshold 𝜁 is the simulation results from MATLAB 2014a, and the following experiments are all based on real nodes.

6.1. Selection of Threshold 𝜁

Before selecting the reasonable threshold, we analyze the factors that affect the performance of the CLS with the threshold based on measured data of the WSN Testbed in this paper.

6.1.1. Number of measured data In general, if there is no noise in the measured data, the data are random Gaussian error of zero mean at every moment. However, less measured data is, the worse the stability of the algorithm analysis results is. Conversely, if there is enough measured data, the stability of the algorithm is better. As shown in Fig.4, the relationship between the number of training data of the two figures is 𝑎 < 𝑏, and it is obvious the calculation results of b are the most stable. 6.1.2. Accuracy of predicted position (stability of distance between predictive position and center of measured data) When the moving direction of the target changes suddenly, the distance between the predicted position and center Page 10 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

(a)

Figure 6: Distance between predictive value and center of the measured data in relationship to the standard error. (b)

Figure 4: Correct distance of the target in relationship to distance between predictive position and center of measured data. (a) Number of the measurements is 200. (b) Number of the measurements is 2000.

between the center of measurements and the predicted position is 0 − 30cm). Then, the standard error of CLS can be used to verify. The equation is as follows: 𝑆𝐸𝑃 =

]1 [𝑚 𝑘 ‖ ‖2 2 ∑ ‖𝜺̂ 𝑘 (𝑖) − 𝜹‖2 𝑖=1

Figure 5: Threshold in relationship to the correct distance parameter.

of measured data will be changed dramatically. If the threshold is too low, there will be a large number of measured data out the threshold range, and it is easy to lose the target when the distance between the predicted position and the actual position of the target is made larger; On the contrary, most measured data and noise are in the threshold range, and the threshold setting is quite meaningless. Therefore, the reasonable threshold will be greatly affected by the reliability of the correction of the predictive position. As shown in Data1 in Fig.5. In order to the reasonable threshold is obtained, the relationship curves between the threshold and the corrected distance are established by experiment based on training data. It is shown in Fig.5 that three relationship curves have a different number of training data. If the threshold setting is too low, it’s meaningless in the "Low Threshold Range". However, the corrected distance is stable in the "Stable Range" when the threshold setting is large enough. This is because most of the true measurements have been in the threshold range, and the mean corrected distance tends to be stable. According to Fig.5, the reasonable threshold is 90 − 100cm (the standard error of training data is 30cm, and the distance Tao Wang et al.: Preprint submitted to Elsevier

𝑚𝑘

(42)

the verification results are shown in Fig.6, in which threshold 100 − 120cm are the more reasonable (the threshold of six curves is 40cm, 60cm, 80cm, 100cm, 120cm, and 140cm, respectively). In Fig.6, the two curves are very similar when the thresholds are 120cm and 140cm, respectively. This is due to the threshold is large enough, and all training data are in the threshold range. In addition, the standard error is smaller when the thresholds are 40cm, 60cm, and 80cm, respectively. This is due to the threshold is low and some training data are out the threshold range. Some target location information may be lost in this situation. So the reasonable threshold 𝜁 is 90 − 100cm. In the paper, the choice of threshold 𝜁 is very important to the performance of the algorithm. According to the previous analysis, the threshold 𝜁 is affected by the number of measurements and the accuracy of the predicted position. Normally, the sensor network cannot return a large number of measurements, and it contains only the few necessary information about target localization at time 𝑘. Therefore, the threshold value 𝜁 must be obtained by off-line "training" of the WSN Testbed.

6.2. Determining Bias Parameter 𝜅

Similarly, the reasonable bias parameter 𝜅 can be also obtained by off-line "training" of the WSN Testbed. Firstly, we measure the moving target to obtain a set of trajectory data, and is defined as the training trajectory. Using (36), the relationship between the weight parameter and the true joint probability is established by the bias parameter 𝜅. Its main purpose and meaning are to better reflect the actual situation of every measured data according to the true joint probability, and this helps improve the reliability of the target localization and tracking in WSN. In (42), the calculation result 𝜹 of CLS algorithm is checked by the standard error SEP. Similarly, the calculation result 𝜹̂ of the Page 11 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

(a)

Figure 7: Position of the trajectories in relationship to different bias parameters in Scene 1.

(b)

improved Bayesian enhanced least-squares algorithm can be checked by the standard error. The equation is as follows: 𝜅0 = 𝑆𝐸𝑃min (𝜅) = ]1 ⎫ ⎧[ 𝑚 𝑘 2 2⎪ ⎪ ∑ ‖ ‖ ̂ ‖ ;𝜅 ≥ 0 𝑤̂ 𝑘 (𝑖) ⋅ ‖𝜀̂ 𝑘𝑖 − 𝛿(𝜅) ⎨ ‖ ‖2 ⎬ ⎪ ⎪ 𝑖=1 ⎭ ⎩

(43)

Using (43), the relationship between the bias parameter 𝜅 and the standard error can be computed. The selection of the reasonable bias parameter 𝜅 will be explained according to the training trajectory of the moving target. Based on the proposed algorithm in this paper and the measured data of training track, the position of the trajectories in relationship to different bias parameters 𝜅 is obtained, as shown in Fig.7 (the scale of abscissa and the ordinate is linear in meter, the measured data are returned every 0.3s from the WSN, and the moving speed of the target is about 2m∕s). The measured data of training track from the WSN contains some interfering signals and true track measurements. The trajectory 2 is computed according to the proposed algorithm and the bias parameter 𝜅 is set to be 4. The trajectory 3, 4, 5, and 6 are similar to trajectory 2, but the bias parameter 𝜅 is 7, 10, 13, and 16, respectively. As shown in Fig.7, the deviations between calculated trajectories and true trajectory can be clearly observed about the effects of different bias parameters 𝜅. Fig.8 shows the mean error at each scenario of the moving target for the four different choices for 𝜅 at the proposed algorithm. For comparing results, the mean error for 𝜅 = 10 is smaller than others for 𝜅 is equal to 4, 7, and 13, respectively. Similarly, Fig.9 shows the time consumption at each scenario of the moving target for the four different choices for 𝜅 at the proposed algorithm. For comparing results, the time consumption has not changed much when 𝜅 is equal to 4, 7, 10, and 13, respectively. Then comparing results from 𝜅 = 1 to 𝜅 = 16, the mean error is the smallest when 𝜅 is roughly equal to 10 (see the Fig.10). On the other hand, the time consumption has not changed much from 𝜅 = 1 to 𝜅 = 16. According to the data in Fig.10, Table 1 is obtained. Tao Wang et al.: Preprint submitted to Elsevier

(c)

Figure 8: Comparison of the mean error of different bias parameters. Table 1 Performance Comparison of Different Bias Parameters Bias Parameter𝜅 16 15 14 13 12 11 10 9

Mean Error(cm) 16.15561 15.07899 15.16054 16.01044 16.11236 14.55473 14.53893 14.69384

Bias Parameter𝜅 8 7 6 5 4 3 2 1

Mean Error(cm) 15.31098 15.73581 16.75991 17.74508 18.99213 20.08225 21.75656 23.94014

Table 1 shows the standard deviation of the calculation results of the proposed algorithm in this paper on the basis of several special bias parameters. Therefore, we set the bias parameter 𝜅 to be 10 in the experimental scene.

6.3. Resource Consumption Evaluation of WSN

The designed sensor nodes in this paper are powered by lithium batteries. The capacity of the lithium battery is 4800 mAh, the common node uses one, and the sink node uses two. Firstly, according to the power ratings analysis of each module for the designed sensor, the power consumption is mainly on the motor of the angle module, while the power consumption of other modules is relatively small. Therefore, according to every module manual information, the normal node can work for more than 4 hours (non-dormant state. The emphasis of the experiment in this paper is to verify the Page 12 of 18

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Figure 9: Comparison of the time consumption of different bias parameters.

Figure 10: Relationship curve between average standard error and the bias parameter 𝜅

improved algorithm based on the WSN Testbed. The verification time only needs tens of minutes for the system to run normally. The duration of the battery is just over four hours, which is sufficient for our algorithm validation.) and the sink node can work for more than 8 hours (ensure that the running time of the sink node is longer than that of the normal node). Next, we carried out experiments for network survival time and CPU energy consumption of sink node in the designed network. The survival time experiment of the node is shown in Fig.11(a), 20 sensor nodes are running normally, the first node stops running at 4 hours and 57 minutes, all normal nodes stop running at 5 hours and 41 minutes, and the sink node stops running at 9 hours and 25 minutes. Meanwhile, the CPU energy consumption test of sink node based on the different algorithms (Classical Bayesian algorithm, proposed algorithm, EKF, WKNN, PKF, and FKF) is shown in Fig.11(b), the energy consumption of Classical Tao Wang et al.: Preprint submitted to Elsevier

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Figure 12: CPU energy consumption experiment of the common nodes based on the application program.

Bayesian algorithm is obviously higher than the other two algorithms. The proposed algorithm in this paper only runs in the sink node, which receives measurement data from the common nodes and performs data calculation. The common nodes only collect data and send the collected measurement data to the sink node at each cycle. In the common nodes, we write an application program that can control the normal operation of each module of the node. The function of the application program includes power management, switching between sleep and wake-up mode, receiving data, sending data, storing data, extracting measurement data, running management of 10-bit ADC module, time synchronization calculation and so on. The program has two modes: running mode and dormant mode. All modules and the application program run normally in the running mode. In the dormant mode, only the communication module processor module runs normally, and the application disconnects the power of other modules and is in the awakening mode. The application program disconnects the power of other modules and is in the waiting wake-up mode. When the sensor nodes are in running mode and dormant mode respectively, the CPU energy consumption based on this application program is shown in Fig. 12.

6.4. Tracking Performance Evaluation

Fig.13 shows the single-target tracking results of the different algorithms in Scene 2. The ground truth is in the black solid line, and the estimated trajectory is in the red solid line. Page 13 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN

(a)

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Figure 13: The single-target tracking results in scene 2: (a) Classical Bayesian algorithm. (b) Improved Bayesian enhanced least-squares algorithm. (c) EKF.

Tao Wang et al.: Preprint submitted to Elsevier

Table 2 Performance Comparison of Different Bias Parameters Type of Algorithm

Average RMSE

Enhanced LS Improve Percentage(%)

15.2105

-

14.8561 23.5423

-2.4 35.4

Proposed Algorithm (𝜅 = 10) Bayesian EKF




  

The calculated trajectories are compared as shown in Fig.13 (a, b, and c, the standard error 𝜎 of the track measurements is 30cm). The adaptive EKF-CMAC multi-sensor data fusion algorithm is proposed for a 3-D maneuvering target in [45]. The EKF algorithm in this Section is based on the EKF-CMAC algorithm, which is used in 2-D maneuvering target tracking. Meanwhile, considering the real-time problem of online target location and tracking, the Bayesian filtering algorithm in [17] is used. For nonlinear dynamical systems, the classical Bayesian algorithm in [17] was used as a basis for Bayesian-based framework filters. The tracking results show that the accuracy of estimated trajectories based on the classical Bayesian algorithm and the proposed algorithm in the paper is better than those based on the EKF algorithm. Fig.14 shows the position error (PE) between the estimated location and the real ground location of the target at each cycle according to the proposed algorithm, the classical Bayesian algorithm, and EKF. The cumulative distribution functions (CDFs) of the tracking errors in Scene 2 are shown in Fig.15. We see that the EKF tracking results have many more large errors than the classical Bayesian algorithm and proposed algorithm. For improved Bayesian enhanced least-squares algorithm, 96 percent of the tracking errors are less than 23.55cm, while 96 percent of the tracking errors from EKF is less than 34.68cm, a 32.1 percent improvement. However, for the classical Bayesian algorithm, 96 percent of the errors are less than 23.1cm, nearly equal compared to the proposed algorithm. We use the CDFs to show the tracking results from the classical Bayesian algorithm and the proposed algorithm is more robust to these large errors. We also compare the RMSEs of the tracking results from three algorithms, which are listed in Table 2. The tracking RMSE from the proposed algorithm is 15.2cm, a 35.4 percent improvement compared to the RMSE of 23.5cm from the EKF. For the classical Bayesian algorithm, the tracking RMSE is 14.9cm, nearly equal compared to the proposed algorithm. On the other hand, we compare the mean time consumption of the tracking from Bayesian algorithm, proposed algorithm and EKF, as shown in Fig.16. The average time consumption from proposed algorithm is 10.8ms, an 82.8 percent improvement compared to the average time consumption of 0.0627s from Bayesian algorithm. For EKF,

   !"  #$





















 

















Figure 14: Estimated errors of tracking in classical Bayesian algorithm, proposed algorithm, and EKF.

the average time consumption is 10.1cm, nearly equal compared to the proposed algorithm. Meanwhile, we calculate the RMSEs of three algorithms based on 30 trajectories for better illustrate the performance of the proposed algorithm, as shown in Fig.17. In conclusion, the proposed algorithm improves the accuracy of target tracking in compared with the EKF, and reduces the time consumption in compared to Bayesian algorithm. Next, in order to further illustrate the performance of the proposed algorithm, we compare the proposed algorithm with WKNN, PKF, FKF [10, 49], VBAKF, Dual-factor EVBAKF [56], and VBEM [57]. The localization error is still as the evaluation index. As shown in Fig. 18. In the aspect of localization error, the proposed algorithm calculates better results than the other three algorithms. Fig. 19 exhibits the CDFs of the tracking errors generated by the WKNN, PKF, FKF, VBAKF, Dual-factor EVBAKF, VBEM, and proposed algorithm. Because the FKF has no ability to perceive the noise, its refinement effect on the WKNN is very limited. Compared with FKF, the PKF uses the position estimated by the fingerprint matching algorithm as the system meaPage 14 of 18

Target Localization and Tracking Based on IBELS Algorithm in WSN 5

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surement instead of the measurement data, which does not directly filter the noise of sensors, but only indirectly reduces the fluctuation in the position estimates caused by the noise [10]. However, the proposed algorithm has a good ability to judge noise and can better match the characteristics of the current noise. Variational Bayesian inference is mainly used to approximate the posterior probability of unobservable variables, which can approximate the calculation of complex posterior distribution. However, the randomness of the approximation results will also affect the performance of the variational Bayesian algorithm. The posterior distribution calculated by the proposed algorithm after the prior training is better than the approximate posterior distribution calculated by the algorithm based on the variational Bayesian inference. Hence, the proposed algorithm always maintains a higher and more stable positioning precision compared to the other algorithms. The average RMSEs obtained from the WKNN, PKF, FKF, VBAKF, Dual-factor EVBAKF, VBEM, and proposed algorithm are revealed in Fig. 20. Compared to the WKNN, PKF, FKF, VBAKF, Tao Wang et al.: Preprint submitted to Elsevier

5

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Figure 19: CDFs of tracking errors in WKNN, PKF, FKF, VBAKF, Dual-factor EVBAKF, VBEM, and proposed algorithm.

Dual-factor EVBAKF, and VBEM algorithms, the proposed algorithm reduces their errors by 32%, 18%, 13%, 9%, 6%, and 0.4% respectively. Similarly, we calculate the RMSEs of four algorithms based on 30 trajectories for better illustrate the performance of the proposed algorithm, as shown in Fig. 21. In conclusion, the proposed algorithm improves the accuracy of target tracking in compared with the WKNN, PKF, FKF, VBAKF, Dual-factor EVBAKF, and VBEM algorithms.

6.5. Discuss

In this paper, the Star-Topology is used on the WSN Testbed. The scalability of the Star-Topology is another important research content of the WSN, that is, the research on the top-level topology control based on Sink node. Our future research direction will consider the top-level topology control based on Sink node. In the real world application, the proposed algorithm and the testbed in this paper has the advantages of accurate positioning and simple deployment, but in terms of resource consumption, the survival time of the sensor is short. Therefore, the testbed can only meet some specific occasions for Page 15 of 18

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short use time, such as the positioning and navigation of the exhibition visitors in the indoor exhibition, and the positioning and navigation of escape personnel after the mine is in danger and power is cut off. In addition, the target of tracking in this paper is human. After the training is completed in the experiment, the parameters can be used all the time. After the thresholds and the joint probability matrix in the calculation are obtained based on the previous training, it can be micro-adjusted when the system is in hibernation through the measurement data onto previously normal operation. However, the disadvantage of the proposed method is that when the external characteristics of the target change dramatically (for example, replacing the human with truck), all parameters have to be retrained and set.

7. Conclusion

The main work of the paper can be concluded as follows: 1) an improved Bayesian method was developed for moving target localization and tracking in WSNs. We apply an improved Bayesian algorithm to obtain a set of sub-range probability based on target predictive location, and forming a range probability matrix. The region probability matrix is only automatically updated when the WSN testbed is asleep. Then, the true probability of every measurement Tao Wang et al.: Preprint submitted to Elsevier

data is calculated based on the region joint probability matrix, and the false measurement data was deleted. 2) The weight values of each effective measurement data are optimized by using the true probability information calculated in the previous steps, and the optimized weights are applied to the weighted least-squares algorithm; 3) the proposed algorithm was validated in experiments carried out in the WSN Testbed. The experimental results show that the proposed algorithm can reduce localization RMSE by more than 35 percent compared with EKF-CMAC. Besides, the proposed algorithm reduces computational time consumption compared to Bayesian algorithm. Our future research directions will focus on improving the proposed algorithm to further optimize the performance of our WSN-based trajectory estimation algorithm. Meanwhile, we further consider image factors into existing range-based multi-target localization and tracking, and to improve and optimize the corresponding image recognition algorithm.

Acknowledgements

This work was supported by the National Science Foundation of China (Grant No. 60973106 and 81571142), the Key Project of National Science Foundation of China(Grant No. 61232009), Astronautic Support Fund (Grand No.377054), and National 863 Project of China (Grant No. 2011A A010404).

References

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Zhenxue He received the Ph.D. degree in computer architecture from Beihang University, Beijing, China, in 2018. He is currently a Full Associate Professor with Hebei Agricultural University. He has authored or coauthored over 20 papers in peer-reviewed journals, and proceedings. His research interests include low power integrated circuit design and optimization, multiple-valued logic circuits and intelligent algorithm. He is a member of China Computer Federation.

Tongsheng Xia received the B.S. and M.Sc. degrees from University of Science and Technology of China, Hefei, in 1997 and 2000, respectively, and the Ph.D. degree in microelectronics from University of Texas at Austin, USA, in 2005. He is currently an Associate Professor with the School of Electronic and Information Engineering, Beihang University.

Tao Wang was born in Qianjin Village, Heyang County, Shaanxi Province, in 1986. He is currently a Ph.D. candidate in microelectronics and solid electronics from Beihang University, Beijing, China. He has been with the School of Electronic and Information Engineering, Beihang University, since 2014. His current research interests include data fusion, target localization and tracking, and spacesky information network. Xiang Wang received Ph.D. degrees from Huazhong University of Science and Technology, Wuhan, China, in 2001. He is currently a Professor with the School of Electronic and Information Engineering, Beihang University. His current research interests include space-sky information network, ultra large scale integration, and System on Chip.

Wei Shi was born in Hefei, Anhui Province, in 1995. He is currently a B.Eng. candidate in electronic and communication engineering from Beihang University, Beijing, China, in 2014. His current research interests mainly include data fusion, big data analysis and machine learning.

Zongmin Zhao received the B.S. degree in electronics technology from Nanchang Hangkong University, Nanchang, China, in 2004 and M.S. degree in microelectronics and solid electronics from Tianjin University, Tianjin, China, in 2007. He is a Ph.D candidate in the School of Electronic and Information Engineering, Beihang University, China, in 2015. His current research mainly interests include integrated circuit design with security.

Tao Wang et al.: Preprint submitted to Elsevier

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: