An optimization model for target tracking of mobile sensor network based on motion state prediction in emerging sensor networks

Abstract

According to the defects of the standard particle filter algorithm in target tracking of mobile sensor networks, such as low accuracy, large network energy consumption and poor anti-noise ability, an optimization model is proposed for target tracking of mobile sensor network based on motion state prediction. First, centroid algorithm was adopted to construct the node localization model, and then the features of the position and the direction of the moving target in the mobile sensor network were as the measurements. The method of integral point assignment was adopted to self-adaptionly optimize the weights of the standard particle filter algorithm, and the introduced modifying factor, the value assignment of integral point was for self-adaption correction, then the difference between the observed and predicted values of the system was provided news residual interest knowledge in the re-sampling phase, to self-adaption modify the sampling particles by measuring the news. And then improve the operation efficiency of the particle filter algorithm with asymmetric kernel function, and provide new residual interest knowledge with the difference between the system current time and forecast values in the re-sampling phase, self-adaptive adjusting of sampling population through measuring the new rates. The simulation experiments show that the proposed improved particle filter algorithm has the higher accuracy and better stability for target tracking, and has lower energy consumption of the network.

Keywords

Emerging sensor networks movement trend prediction parallel optimisation integral point assignment self-adaption correction

1 Introduction

Sensor network is a multiple hops self-organized network formed from a large amount of wireless sensor nodes that with functions of information collection, data processing and wireless communication distributed in the monitoring regions for certain functions [1, 2]. The potential application prospect of mobile network has attracted much attention in the military field, academia and industry all over the world [3]. Target tracking is one of the specific applications in many practical applications of mobile sensor network, and there are limitless applications in many fields, such as in the field of environmental monitoring [4, 5], battlefield target monitoring [6, 7], disaster warning [8, 9], mitigating disasters [10, 11] and so on. Traditional target tracking, such as active or passive detection radar, has the equipment with better data-handling capacity and relative sufficient resources [12, 13]. For mobile sensor network, its single sensor node is limited by energy, time, processing capacity, communication bandwidth and so on. At the same time, it may be interfered by the surrounding and wireless link, network topology changes frequently [14, 15]. Tracking task generally requires real-time, while lots of traditional target track algorithms can’t fit the tracking task based on mobile sensor network for short of high center data processing capability [16]. So there is great significance in researching of target tracking methods based on mobile sensor network.

As an important application of mobile sensor network, target tracking has been researched from several angles. Wang Tian [17] et al. proposed introducing a few mobile nodes to form a heterogeneous WSN with the problems of high energy consumption and coverage hole when track targets for traditional WSN formed with fixed-nodes. The proposal is to reduce the active fixed-nods to save energy consumption. Lou Ke [18] et al. proposed a target tracking algorithm of mobile network based on flocking control. This algorithm detects the target with partial nodes in the network and estimates the states of target with Kalman filter algorithm. It can not only obtain accurate estimates of the states, but also save energy consumption. Then sensor network always maintains topology connected and target network visible under the f control of locking, and collision between nodes can also be avoided. Tian Hao [19] et al. put forward a distributed data fusion object tracking algorithm(WDOT) based on the basis of the existing distributed particle filter (DPF). This algorithm realizes the distributed data fusion of nodes using the Gaussian mixture model and consensus filter. The algorithm improves the stability and decreases the communication overhead. Han Ping [20] et al. proposed a kind of a distributed target tracking algorithm. It can use node guidance to ensure the dynamic connectivity of network. Based on the traditional distributed data fusion architecture, combining consensus filter, it realizes the optimization of distributed data fusion with low communication overhead. Zhu Zhiyu [21] et al. proposed a distributed adaptive particle filter algorithm based on binary WSN. When replace the cluster head, there is no need to transmit a large number of particles, it only needs to transmit the filter values and error variance. Also, the algorithm reduces calculation by adjusting the number of particle online according to the filtering variance.

Peng Yuanfang [22] et al. introduce particle filter which is not limited by the nonlinear and non-Gaussian problems to target tracking applications of WSN. They also improve the defects of basic particle filter algorithm. Yao Xianlian [23] et al. used Cricket of MIT as the hardware verification system, ranging with time difference of arrival(TDOA), and use maximum likelihood estimation based on the measured distance for node-positioning. Target tracking model is established according to the characteristics of moving targets. Finally, it tracks the moving target with measuring tracking algorithm of Kalman filter. Zheng Juanyi [24] analyzed the principle of objects tracing in WSN and researches on the main technology of particle filter algorithm. Finally, she presents a method to improve the accuracy of tracking precision of basic particle filter algorithm after improving the importance function and resampling technology of basic particle filter. Yue Juan [25] et al. presented an improved distributed dynamic clustering particle filter (DDCPF) algorithm. Distributed tracking cluster is established dynamically. Cluster members combine with their latest optimal estimation and variance to generate particles. According to algorithms like Kalman, get the resulting value that combing the predicted and measured value of particle filter, as a predictive value. This algorithm can improve the tracking accuracy. Xu Xiaoliang [26] et al. researched on the target tracking fusion algorithm that based on the measurement information quantitative strategy and cubature particle filter. It aims at the low accuracy and poor practicability of the existing nonlinear networked target tracking fusion algorithm, targeting a kind of nonlinear networked target tracking system with noise related. Gu Jing [27] et al. present an improved distributed particle filter algorithm. This algorithm maintains the diversity of particles by adjusting the likelihood distribution of filter. It improves the tracking mechanism of WSN and adopts the tracking precision to adjusting the number of sensor nodes in dynamic cluster adaptively. Tang Xianfeng [28] et al. present three target tracking algorithms based on the quantitative information in the centralized fusion framework. It mainly aims at the non-cooperative target tracking problem, solving the problem that caused by limited bandwidth and wireless sensor network and correlated noise of WSN. To Improve the accuracy of WSN target tracking, Dong Yue Jun [29] et al. proposed a kind of target tracking algorithm of WSN based on quantum genetic algorithm to optimize the particle filter. The quantum genetic algorithm can not only increase the particle variability, preventing particle degradation, but also shorten computing time and improve particle tracking ability. Jiang Peng [30] et al. proposed a kind of target tracking method of WSN based on particle awarm optimization and M-H sampling particle filter. The method adopts distributed architecture and makes filter in the sampling process come true by the technology of particle swarm optimization and M-H sampling particle filter, curbing particle degeneracy. It makes each particle convergence to the optimal distribution quickly by sharing their historical information to lower the correlation between single particle’s history states. Finally, it can achieve high-precision target tracking. Guo Shaoming [31] et al. proposed a Grey-Markov model target tracking (GMMTT) algorithm. It introduces Markov model that contains shock consciousness to segmented gray prediction. In this way, it can make the target location not only achieve better precision but also adapt to the change of the target motion mode. Zhou Fan [32] et al. propose particle filter based target localization and a sampling aware tracking cluster formation based on the coverage problem in sensor networks. The basic idea is adopting a series of weighted particles to predict the distribution of moving object’s location. At each moment, it determines the location by the measured data of sensors.

According to the defects of the standard particle filter algorithm in target tracking of mobile sensor networks, a tracking model for mobile sensor network target is proposed based on motion state prediction. The simulation results show the effectiveness of the improved strategy. The rest of this paper is organized as follows: A target tracking model for particle filter algorithm in mobile sensor network is in Section 2. The particle filter algorithm based on self-adaption weight is proposed in Section 3 and performance optimization of antinoise based on motion prediction method is proposed in Section 4. In Section 5, Simulation results are discussed and the simulation experiments show that the proposed algorithm has the higher accuracy and better stability for target tracking. Finally, conclusions are made in Section 6.

2 A target tracking model for particle filter algorithm in mobile sensor network

In target tracking of mobile sensor network, we need to position every node in the network first, and the Centroid algorithm is used to establish position model [33, 34], and its locating equation can be expressed as:

$\begin{matrix} (X_{est}, Y_{est}) \\ = (\frac{X_{1} + X_{2} + \dots + X_{n}}{n} + \frac{Y_{1} + Y_{2} + \dots + Y_{n}}{n}) \end{matrix}$ (1)

Centroid algorithm usually uses the location error to indicate the location accuracy, and is divided into Absolute error (Absolute error, AE) and the relative error (relative error, RE), shown as follows: $AE = \sqrt{(X_{est} - X_{a})^{2} + (Y_{est} - Y_{a})^{2}}$ (2) $\begin{matrix} RE & = & \frac{AE}{R} \\ = & \frac{\sqrt{(X_{est} - X_{a})^{2} + (Y_{est} - Y_{a})^{2}}}{R} \end{matrix}$ (3)

In which, (X_est, Y_est) denotes the estimate location of the unknown nodes, (X_i, Y_i) denotes coordinates of the No. i beacon node, n denotes the number of beacon nodes, (X_a, Y_a) denotes the real position of unknown nodes, and R denotes communication radius. In order to improve the accuracy of positioning, the number of beacon nodes that need positioning can be set a threshold value, for example, beacon nodes are locating when the value is greater than m.

According to the node positioning model, assuming that target tracking in a two-dimensional plane, the state model of target tracking system in mobile sensor network is as follows: $x_{k + 1} = {Fx}_{k} + {Gw}_{k}$ (4)

In which, x_k represents the state of moving targets in the moment k, [l_k,x, l_k,y, v_k,x, v_k,y] represents vectors, l_k,xl_k,y respectively represents the coordinates of x axis and y axis of the target at the moment k, v_k,x and v_k,y respectively represents the speed value of x axis and y axis of the target at the moment k, F represents the state transition matrix, G represents the noise transfer matrix, T represents the sampling period, and w_k represents process noise. Measurement equation is as follows: $Z_{k} = A_{k} x_{k} + e_{k}$ (5)

In which, Z_k represents the observation vectors, A_k represents the observation matrix, e_k represents the observation noise, w_k and e_k are for the zero mean Gaussian white noise, and FG can be expressed as follows: $F = [\begin{matrix} 1 & T & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & T \\ 0 & 0 & 0 & 1 \end{matrix}]$ (6) $G = [\begin{matrix} \frac{T^{2}}{2} & 0 \\ T & 0 \\ 0 & \frac{T^{2}}{2} \\ 0 & T \end{matrix}]$ (7)

In which, T is for the sampling period among it.

The particle filter algorithm is for estimating the target state mobile in moving sensor network to achieve the purpose of target tracking. Particle filter is a kind of the optimal regression Bayesian filtering algorithm based on MONTE CARLO simulation [35, 36].

Set the space model of dynamic system state as follows: ${\begin{matrix} x_{k} = f_{k} (x_{k - 1}, v_{k}) \\ y_{k} = h_{k} (x_{k}, v_{k}) \end{matrix}$ (8)

In which, x_k ∈ Rⁿ represents the system status, y_k ∈ Rⁿ represents measured values, v_k ∈ Rⁿ and w_k ∈ Rⁿ respectively represents independent identically distributed system noise sequences and measurement noise sequences.

Bayesian filtering principle is to estimate the posterior probability density of the system state variables with all the known information. First, predict prior probability density of states with the system model, and then modify with the latest measurement value, finally get a posterior probability density. So that by the observation data y_1:k to inference the confidence coefficient p (x_k|y_1:k) of calculation state x_k with different values; thus gain the optimal estimates of the status. Therefore, the Bayesian filter including the two steps as prediction and updating.

Step 1. Prediction:

Assume that the probability density of system initial state as p (x₀|y₀)= p (x₀) and the probability density is p (x_k-1|y_k-1) at the moment k - 1, for the first-order Markov process (the state of the moment k - 1 is only associated with the state of moment k - 2), the prediction equation of the moment k can be known by Chapman-Kolmogorov equation. $p (x_{k} | y_{1 : k - 1}) = \int p (x_{k} | y_{k - 1}) p (x_{k - 1} | y_{1 : k - 1}) {dx}_{k - 1}$ (9)

Namely get the prior probability without observed value at the moment k, and is calculated by the system state transition probability p (x_k|x_k-1).

Step 2. Updating:

This step is a process of correction, with using the latest observations y_k and the prior probability p (x_k-1|y_1:k-1) at the moment k derived by p (x_k|y_1:k).

After getting the latest observations, using the Bayes formula $p (a | b) = \frac{p (b | a) p (a)}{p (b)}$ we can get is as follows: $p (x_{k} | y_{1 : k}) = \frac{p (y_{1 : k} | x_{k}) p (x_{k})}{p (y_{1 : k})}$ (10)

In order to independent the y_k above, p (y_1:k|x_k) and p (y_1:k) can be expressed as: $p (y_{1 : k} | x_{k}) = p (y_{k}, y_{1 : k - 1} | x_{k})$ (11) $p (y_{1 : k}) = p (y_{k}, y_{1 : k - 1})$ (12) $p (x_{k} | y_{1 : k}) = \frac{p (y_{k}, y_{1 : k - 1} | x_{k}) p (x_{k})}{p (y_{k}, y_{1 : k - 1})}$ (13)

Form the conditional probability density formula p (a|b)= p (b|a)p (a), we can get follows: $p (y_{k}, y_{1 : k - 1}) = p (y_{k} | y_{1 : k - 1}) p (y_{1 : k - 1})$ (14)

By the joint probability density formula p (a, b|c)= p (a|b , c) p (b|c), we can get Equation (15). $p (y_{k}, y_{1 : k - 1} | x_{k}) = p (y_{k} | y_{1 : k - 1}, x_{k}) p (y_{1 : k - 1} | x_{k})$ (15)

By the Bayes formula, Equation (16). $p (y_{1 : k - 1} | x_{k}) = \frac{p (y_{k} | y_{1 : k - 1}) p (y_{1 : k - 1})}{p (x_{k})}$ (16)

The Equations (13–15) are substituted into Equation (12), which can be defined as:

$\begin{matrix} p (x_{k} | y_{1 : k}) \\ = \frac{p (y_{k} | y_{1 : k - 1}) p (x_{k} | y_{1 : k - 1}) p (y_{1 : k - 1}) p (x_{k})}{p (y_{k} | y_{1 : k - 1}) p (y_{1 : k - 1} | x_{k})} \end{matrix}$ (17)

The observed value is independent, which can be defined as: $p (y_{k} | y_{1 : k - 1}, x_{k}) = p (y_{k} | x_{k})$ (18)

The Equation (17) is substituted into Equation (16), and then we get Equation (19). $p (x_{k} | y_{1 : k}) = \frac{p (y_{k} | x_{k}) p (x_{k} | y_{1 : k - 1})}{p (y_{k} | y_{1 : k - 1})}$ (19)

Equations (9 to 19) realizes the recursive process form the prior probability density to posterior probability density.

Particle filter algorithm is almost like a Bayesian method that introduce into the discrete time recursive filtering [37 –40]. The core of the algorithm is to construct a posterior probability density function based on sample [41]. Here we are sampling particles from the posterior probability density function p (x_0:k|z_1:k), ${x_{0 : k}^{i}, ω_{k}^{i}}_{i = 1}^{N}$ denotes particle swarm collection. ${x_{0 : k}^{i}, i = 1, \dots, N}$ denotes support for the sample set, and ${ω_{k}^{i}, i = 1, \dots, N}$ for the corresponding weights of particles, and satisfy $\underset{i = 0}{Σ} ω_{k}^{j} = 1$ , the posterior density can be represented as follows: $p (x_{0 : k} | z_{1 : k}) \approx Σ_{i = 0}^{N} ω_{k}^{j} δ (x_{0 : k} - x_{0 : k}^{i})$ (20)

So the discrete weighted approximate representation [42] can be used to represent the true posterior density p (x_0:k|z_1:k), so the questions about mathematical expectation also can be calculated. $E (g (x_{0 : k})) = \int g (x_{0 : k}) p (x_{0 : k} | z_{1 : k}) {dx}_{0 : k}$ (21)

It can be approximate by Equation (22). $E (g (x_{0 : k})) = Σ_{i = 0}^{N} ω_{k}^{j} δ (x_{0 : k}^{i})$ (22)

To test the performance of target tracking of the particle filter algorithm in mobile sensor network, simulation experiment is carried out on the experimental platform of Matlab. The Bayesian algorithm and the particle filter algorithm is respectively adopting for the filtering effect of the system equations and compared in experiments, the Equation (4) as an estimation model for system in the experiment.

Detailed experimental results are shown in Figs. 1 and 2. Figure 1 is given estimation results of the posterior probability density that the Bayesian algorithm and the particle filter estimate for the system status at the moment k = 20, sampling particle beam is N = 80 in experiment. It can be seen clearly in the Fig. 1, particle filter has better estimation performance, the estimate of the Posterior Probability Density Function (Posterior Probability Density Function, PDF) accounted for about 80% of the real Probability Density Function, and the Bayesian estimation results is less than 50% of the algorithm.

Fig.1

The estimate of the Posterior Probability Density Function at moment k = 20.

Fig.2

The filtering estimation results after 50 iterations.

According to the current mobile sensor target tracking model, we do comparative experiment of Bayesian algorithm in common use, the experimental results as shown in Figs. 1, 2. It can be seen clearly from the Figure, the error of Bayesian algorithm is bigger, especially between k = 10 to k = 20, because of Bayesian algorithm by Taylor series approximation processing, leading to a sharp change in the status when filtering divergence, and offset is larger. And the particle filter method still keeps higher tracking accuracy and the better filtering stability, so it has higher filtering precision and adaptability.

Then place 10 wireless sensor network nodes with the function of obtaining its location randomly in the selected 100 m × 100 m field, and the maximum communication range of all the nodes is 20 m. The movement speed of nodes is v = 20 m/s, and mobile nodes choose the goal position randomly, and the residence time at a particular location is determined randomly.

Add Gaussian white noise in the simulation experiment [43], and it increases from 0 dB to 10 dB, and particle filter algorithm tracking precision of the change is shown in Fig. 3.

Fig.3

The effect of noise on tracking accuracy.

Figure 3 showns the tracking accuracy of particle algorithm reduces greatly after Gaussian white noise reaches 2 db.

From the above experiment analysis, it can be seen that for target tracking in mobile sensor networks, the particle filter algorithm has better estimation accuracy and stability, but it has a poor antinoise performance and iterative late weight degradation.

3 The particle filter algorithm based on self-adaption weight

3.1 The weights self-adaption optimization based on the integral point assignment

For weight degradation of the standard particle filter algorithm, we consider complementary of characteristics both static and dynamic. The target location features and movement direction observation quantity of the standard particle filter algorithm are as the optimization weights for the self-adaption fusion. And then the features of the position and the direction of the moving target as the measurements are self-adaption optimizing for the weight of the particle filter algorithm.

Consider a random variable x of the scalar, assume that it is satisfying the Gaussian probability distribution, and then the expectation of the function g (x) can be approximate to as follows:

$\begin{matrix} E (g (x)) & = & \int_{R} g (x) N (x, 0, 1) dx \\ \approx \sum_{i = 1}^{m} ω_{i} g (ξ_{i}) \end{matrix}$ (23)

Assume that J is a symmetric triangular matrix, the diagonal elements is zero, which can be defined as: $J_{i, i + 1} = \sqrt{i / 2}, 1 \leq i \leq m - 1$ (24)

In which, m is integral points, choose 3 integral points in this paper, then m = 3^{n
_x}, n_x denotes the dimensions of the state, set λ_i as the No. i eigenvalues of J, η_i is the standardized feature vector of corresponding λ_i, then the value of integral points ξ_i is $ξ_{i} = \sqrt{2} λ_{i}$ , the corresponding weights is ω_i = ((η_i) ₁) ², (η_i) ₁ is the first element of No. i standardized characteristic vectors of J and the first element of η_i.

In order to make the integral point can obtain accurate and effective weight assignment, and the weight assignment of integral point can do online self-adaption correction, we can introduce correction factor, and by setting the integral initial weights threshold, guarantee the integral points with lower weight assignment is discarded in the calculation, only the integral points with higher weights are reserved. Suppose there are m integral points, the corresponding threshold value can be calculated as follows: $θ_{m} = \frac{ω_{1} ω_{(m + 1) / 2}}{m}$ (25)

In the equation, if integral point weights assignment is ω_i ≥ θ_m, then keep the integral point ξ_i; if integral point weights assignment is ω_i < θ_m, then discard integral point, and the integral of the revised point do normalized processing again.

Target tracking for mobile sensor network model, because of its randomness, the number of sampling particles of fixed value is difficult to ensure the effectiveness and accuracy of the sample particles, so we use the differences between current moment observation and prediction of system to provide residual knowledge in re-sampling phase [44], the sampling population is for online self-adaption adjustment by measuring the new rates.

Assuming at moment k, the state estimate and prediction of the system is respectively as y_k and ${\tilde{x}}_{k}$ , then the corresponding new coupon residual error estimation can be expressed as follows: $e^{k} = y_{k} - {\tilde{x}}_{k}$ (26)

There is correlation between the number of particles and residual of the system in the process of sampling. When the residual is small, a small amount of sample particles can approximate distribution system effectively, so that ensure the sampling efficiency; When the residual is bigger, it needs to expand the scope of the particle sampling, and to increase the number of particles sampled at the same time, to ensure the accuracy of sampling.

The Sigmoid function is adopted to express the relationship between the particle number and the deviation [45]. $N_{k} = N_{min} + (N_{max} - N_{min}) (\frac{2}{1 + exp (- β e^{k})} - 1)$ (27)

In which, N_min and N_max respectively denotes the minimum and maximum number of particles, e^k is the system residual at the moment k.

The concrete implementation steps of the particle filter algorithm based on the integral point with self-adaption optimization weights (IP-PF) are as follows:

Step 1. The initialization of particles

At the moment k = 0, extract particles from the prior distribution p (x₀). ${\hat{x}}_{0}^{i} = E (x_{0}^{i})$ (28) $P_{0}^{i} = E [(x_{0}^{i} - {\hat{x}}_{0}^{i}) (x_{0}^{i} - {\hat{x}}_{0}^{i})^{T}]$ (29)

Initialized weights are set as follows: $ω_{0}^{i} = 1 / N$ (30)

Step 2. The updates of each status

IP-PF is to calculate the integral point, and adjust the number of integral particle by the self-adaption, update particle. $X_{(1, \dots, m), k | k - 1}^{i} = P_{k - 1}^{i} ξ_{j} + {\hat{x}}_{k - 1}^{i}$ (31)

Then to update the time, which can be expressed as:

$\begin{matrix} P_{k | k - 1}^{i} & = & Q_{k} + \sum_{j = 1}^{m} ω_{j} (X_{j, k | k - 1}^{i} - {\hat{x}}_{k | k - 1}^{i}) \\ (X_{j, k | k - 1}^{i} - {\hat{x}}_{k | k - 1}^{i})^{T} \end{matrix}$ (32)

And then to update the measurement, which can be expressed as: $P_{k}^{i} = P_{k | k - 1}^{i} - K_{k}^{i} P_{k | k - 1}^{i} (K_{k}^{i})^{T}$ (33)

The specific sampling is implemented as follows: $x_{k}^{i} \sim q (x_{k}^{i} | x_{0 : k - 1}^{i}, z_{1 : k}) \approx N (x_{k}^{i}, {\hat{x}}_{k}^{i}, P_{k}^{i})$ (34)

The corresponding weights can be expressed as: $ω_{k}^{i} = ω_{k - 1}^{i} \frac{p (z_{k} | x_{k}^{i}) p (x_{k}^{i} | x_{k - 1}^{i})}{q (x_{k}^{i} | x_{0 : k - 1}^{i}, z_{1 : k})}$ (35)

$p (z_{k} | x_{k}^{i})$ is the likelihood function of the measurement value, and then the normalized weight is as follow: ${\bar{ω}}_{k}^{i} = \frac{ω_{k}^{i}}{\sum_{i = 1}^{N} ω_{k}^{i}}$ (36)

Step 3. Calculate the number of sampling particles

Given the initial threshold of resampling, if there is N_eff < N_th, then made ${\bar{ω}}_{k}^{i} = 1 / N$ , particles sets are used to resampling, calculate noise variance of system at the moment k + 1 according to the Equation (35), and calculate the number N_m of sampling particles by Equation (36).

Step 4. Estimate the system state

After the iterations of algorithms above, the experienced probability distribution of the filter distribution, system state estimation and output value of the error covariance is as follows: $P_{k} = \frac{1}{N_{m}} \sum_{i = 1}^{N} ({\hat{x}}_{k} - x_{k}^{i}) ({\hat{x}}_{k} - x_{k}^{i})^{T}$ (37)

3.2 Operation efficiency optimization based on asymmetric nuclear function

After adaptive optimization in using integral point assignment of weight of the particle filter algorithm, considering the obvious slower operation efficiency of improved algorithm, this paper gets improved IPS-PF algorithm with asymmetric kernel function optimization [46].

The goal of statistical characteristic got from the cooperation of the target area and its corresponding kernel functions is often called kernel density estimation function. Define the area for tracking as E = {x, y, a, b}, (x, y) is the target center position, (a, b) represents the width and height of the target area. Target area space kernel density estimation is $H_{x} = {h_{i}}_{i = 1}^{B}$ , and the channel number is B = 8 ×8 × 8, namely there are eight isometric channels in every selected space. The corresponding kernel density estimate of channel i is as follows: $h_{i} = f_{h} \sum_{u \in E} K (u) \cdot δ_{i} (b (u))$ (38)

In which, u = (x, y) denotes it’s in the target area E, b (u) ∈ {1, 2, …, B} is the corresponding channel index of u, δ_i is the response Dirac function of channel i, K (·) is as the kernel function, and f_h is kernel density estimation normalized constant. $\sum_{i = 1}^{B} h_{i} = 1$ (39)

One of the most important drawbacks of symmetric kernel function is that it is hard to avoid the introduction of noise in the target area description, which affects the tracking accuracy, so asymmetric optimization comes first.

After obtaining the target information υ, internal area is the target area R, definition is as the follow three-dimensional function K (x, y): the kernel function value at every point in the inner regions R of the contour is proportional to the point to the outline of the Euler distance d, and the value in the external points of nuclear function is 0. ${\begin{matrix} K (x, y) \propto d, (x, y) \in R \\ K (x, y) = 0, (x, y) \notin R \end{matrix}$ (40)

Normalize the function K (x, y) into asymmetric nuclear function K_n (x, y): $K_{n} (x, y) = \frac{K (x, y)}{\sum_{(a, b) \in R} K (a, b)}$ (41)

In the process of target tracking in wireless sensor network, the target reference template H_m is known, and if you want to know the possibility of a target located in a certain position x_k, you need to know the corresponding characteristic of target at x_k and the similarity with the template features H_m, and the function describe the similar degree is called similarity function, or Distance function.

Fig.4

Asymmetric nuclear function diagram.

Figure 4 shows the asymmetric nuclear function diagram. This paper sets the asymmetric kernel density estimation as the target characteristics, Bhattacharyya coefficient as a similarity function: $D (x_{k}) = D (H (x_{k}), H_{m}) = \sum_{i = 1}^{B} \sqrt{h_{i} (x_{k}) \cdot h_{i} (m)}$ (42)

H (x_k) is the asymmetric kernel density estimation when target is in the position of x_k, and among which H_m is the target template, B is the total number of channels, h_i (x_k) is the value of H (x_k) in the channel i, and h_i (m) is the value of a template H_m in the channel i.

The observation model p (Y_k|X_k) in particle filter algorithm decides the particle weight update process. After obtaining the node information Y_k of current time of k, the location of particle X_k is the probability of the current position of target. p (Y_k|X_k) is proportional to the similarity function: $p (Y_{k} | X_{k}^{i}) = ω_{k}^{i} = \frac{D (x_{k}^{i})}{\sum_{j = 0}^{N} D (x_{k}^{j})}$ (43)

In which, $ω_{k}^{i}$ is the updated weights of particle $X_{k}^{i}$ , and $x_{k}^{i}$ is the location of the particle $X_{k}^{i}$ .

In the target tracking in wireless sensor networks, the morphology of target changes gradually, so a template updating strategy is needed to be designed. Define the update threshold as θ_ut, and calculate the similarity $D ({\hat{o}}_{k})$ of eventually track position ${\hat{o}}_{k}$ after outputting tracking results of each frame. If $D ({\hat{o}}_{k}) < θ_{ut}$ , then set the current target location as the initial position, have the Snake position evolution, and update the current target position and reestablish target asymmetric nuclear function, and obtain kernel density estimation template H_m for target. Considering the target location gradient in practical engineering, the update process the Snake iterations period N_it is inversely proportional to the similarity and efficiency of no more than 3 times in order to meet the requirements: $N_{it} = min {\frac{c}{D ({\hat{o}}_{k})}, 3}$ (44)

Among which, c is the proportional coefficient. The improved particle filter algorithm is based on asymmetric kernel density estimation characteristics observed of Snake, and the corresponding template updating strategy, always grabs the target location in the process of tracking, and the observation model set up can eliminate noise as far as possible, has faster computing efficiency compared with the traditional particle filter algorithm.

3.3 The performance analysis of the improved algorithm

To verify the effectiveness of the improvement strategy, we test the precision of filtering algorithm by a kind of weak nonlinear system state model, which is shown as: ${\begin{matrix} x_{t} = 1 + sin (0.4 π t) + 0.5 x_{t - 1} + v_{t - 1} \\ y_{t} = {\begin{matrix} 0.2 x_{t}^{2} + n_{t}, t \leq 30 \\ 0.5 x_{t} - 2 + n_{t}, t > 30 \end{matrix} \end{matrix}$ (45)

The process noise is v_t-1 ∼ Gamma (3, 2) and measurement noise is n_t ∼ N (0, 0.0001), the initial state is set as ${\hat{x}}_{0} = 1$ in the experiment system, to produce the corresponding observational data y_1:T, the initial sampling particles are all set to N = 100, the observation time is set to T = 60, the state estimation results of the standard algorithm and the proposed improved algorithm are shown in Fig. 5.

Fig.5

The state estimation results of two algorithms.

At some points, Fig. 5 show the standard particle filter is relatively serious deviation from the estimate of real data, and the state is estimated by theproposed improved algorithm can better in conformity with the real condition with higher filtering precision and stronger stability.

4 Performance optimization of antinoise based on motion prediction

4.1 Motion prediction based on the Kalman

Particle filter algorithm is for the adaptive assignment by integral point, improves the accuracy of the original algorithm, but in the target tracking of mobile sensor network, the improved algorithm has the defects of poor antinoise. For this defect, we use Gaussian distribution [47] as the importance density function, and Kalman filtering method [48, 49] is for predicting about the linear part of the state transition and update.

Assume that a group of random sample ${x_{k - 1}^{i}, i = 1, 2, \dots, N}$ , and k - 1 always obeys the probability density function p (x_k-1|z^k-1) for the distribution, and Kalman algorithm is for predicting and updating samples, making its approximation to the distribution of p (x_k|z^k), and finally get the approximate posterior probability density as the importance density function, as shown: $q (x_{k} | x_{0 : k - 1}, z_{1 : k}) \approx N ({\hat{x}}_{k}, P_{k})$ (46)

In Gaussian distribution, due to the superposition of the real distribution x_k-1 and the latest measurements z_k, making the prior distribution move toward high likelihood area and the measured values of particle weight increase accordingly. After resampling, the proportion of particles is increased in the total particle, and particles will be abandoned without observation information, so that computation cost will not be wasted.

The approximation of the second order regression model is for the above methods to construct a system model, and there is a deviation in the actual system inevitably. So the method of artificial weight gain filter is adopted to improve the real divergence of algorithm. Increase the weight of current observation data by the method of weighted, and reduces the weight of the old data to overcome filtering divergence.

In the process of filtering, artificially increase the error covariance matrix of filtering by the method of weighted, thus indirectly increase the gain matrix K_k. The specific method is: in computing P_k|k-1, P_k-1|k-1 will be artificially increased by s times, can be expressed as:

$\begin{matrix} P_{k | k - 1} & = & s Φ_{k, k - 1} P_{k - 1 | k - 1} Φ_{k, k - 1}^{T} \\ + Γ_{k, k - 1} Q_{k - 1} Γ_{k, k - 1}^{T} \end{matrix}$ (47)

With the increase of P_k|k-1, the filtering gain K_k increases indirectly, which at the k→ ∞, under the condition of the system model is not accurate, gain K_k will not rapidly approaching zero, so as to avoid the filter divergence.

Then second order autoregressive model is established, the model assumes that in addition to a random noise, the target speed is constant between adjacent nodes.

$\begin{matrix} x_{k} - x_{k - 1} & = & x_{k - 1} - x_{k - 2} + U_{k} \Rightarrow x_{k} \\ = & 2 x_{k - 1} - x_{k - 2} + U_{k} \end{matrix}$ (48)

If extension of the system state variables is defined as x_k = [x_k, y_k, x_k-1, y_k-1] ^T, then the transition matrix of the system state is shown as: $A = [\begin{matrix} 2 & 0 & - 1 & 0 \\ 0 & 2 & 0 & - 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{matrix}]$ (49)

In the Equation (49), observed value Z_k is defined as the target position in mobile sensor networks, namely Z_k = [x_k, y_k] ^T, and the coefficient matrix of observation equation can be expressed as: $C = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{matrix}]$ (50)

For the realization of the Kalman importance sampling, Z_k which is for updating the observed value may be defined as the prediction ${\bar{x}}_{k | k - 1}^{i}$ of the biggest weight was shown as follows: $Z_{k} = arg max {\bar{w}}_{k | k - 1}^{i}$ (51)

In the Equation (51), ${\bar{w}}_{k | k - 1}^{i}$ is the importance weight of predict particles ${\bar{x}}_{k | k - 1}^{i}$ .

Finally, estimate the mean ${\bar{x}}_{k}^{i}$ and covariance matrix $P_{k}^{i}$ with Kalman algorithm.

4.2 Construct the model of target tracking

In target tracking algorithm in mobile sensor networks, the likelihood model p (z_i|x_i) is set up based on the functional relationship between observation z and state vector x.

The method is to divide the motion state component of node x into k equal interval blocks, and x ∈ E^d, to form k^d blocks, then count the numbers q_i of samples in each block, the probability density of corresponding blocks is as follows: q_i (N × V), N as the total number of samples, V as the volume of the block.

So, the specific process of the construction of the observation likelihood model is as follows:

Step 1. The expression of target model

Quantitative function of motion state is defined as b (l_m) : R² → {l, …, B}, which denotes to quantify the motion state of the position the location l_m. So the state of target is given as x, then the kernel function motion state distribution is defined as: ${\hat{q}}_{u} = C \sum_{i = 1}^{n} k ({∥ \frac{x_{i} - x_{0}}{h} ∥}^{2}) δ [b (x_{i}) - u]$ (52)

In the equation, k () denotes the kernel function, and h denotes its bandwidth.

Step 2. Expression of the candidate model

According to the state transition model to predict the position of particles, the area of the prediction location of particles is named as the candidate area in the subsequent nodes, and is a rectangular area commonly, the center coordinates as y. Moving state in the region is set as {x_i} _i=1,…,n, the kernel function of the candidate regions is defined as: ${\hat{p}}_{u} (y) = C_{h} \sum_{i = 1}^{n} k ({∥ \frac{y - x_{i}}{h} ∥}^{2}) δ [b (x_{i}) - u]$ (53)

Step 3. The similarity function

Similarity function is describing the similarity between the target model and candidate model. We use Bhattacharyya coefficient as the similarity function, as greater as the value, the higher similarity, limiting cases ρ = 1 denotes two models match exactly. Bhattacharyya coefficient is defined as:

$\begin{matrix} \hat{ρ} (y) & = & ρ [p (y), q] \\ = & \sum_{u = 1}^{m} \sqrt{{\hat{p}}_{u} (y), {\hat{q}}_{u}} \end{matrix}$ (54)

From above equation, it can get the similarity measure function of the candidate area x and the target template x₀ as follows: $D (p, q) = \sqrt{1 - ρ [p^{u}, q^{u}]}$ (55)

Based on the definition of similarity measure function described before, we can define the likelihood model of the target as follows: $p (z | k) = \frac{1}{\sqrt{2 π} δ_{c}} exp {- D^{2} (p, q) / 2 δ_{c}^{2}}$ (56)

In which, δ_c is the variance of nodes motion information Gaussian distribution in mobile sensor network.

4.3 Optimize network energy consumption based on parallel processing

The hot spots of program can be parallelized in particle filter to reduce the network energy consumption of mobile sensor network target tracking. Sampling algorithm of particle filter can be described as follows:

Step 1. $[{x_{k}^{i}, w_{k}^{i}}_{i = 1}^{N_{s}}] = SIS [{x_{k - 1}^{i}, w_{k - 1}^{i}}_{i = 1}^{N_{s}}, Z_{k}]$

Step 2. For i = 1, 2, ⋯ , N_s, calculate the sampling particles $x_{k}^{i} \cdot q (x_{k} | x_{k - 1}^{i}, Z_{k})$ ,

Step 3. Make the normalized weights as $\sum_{i = 1}^{N_{s}} w_{k}^{i} = 1$ .

And the pseudo-code of resampling algorithm is described as follows:

Step 1. $[{x_{k}^{i}, w_{k}^{i}, i^{j}}_{j = 1}^{N_{s}}] = Re sample [{x_{k}^{i}, w_{k}^{i}}_{i = 1}^{N_{s}}]$ ,

Step 2. Initializes the probability cumulative distribution function C₁ = 0,

Step 3. For i = 2 : N_s, calculate probability cumulative distribution function: $C_{1} = C_{i = 1} + w_{k}^{i}$ ,

Step 4. Make i = 1 in the probability cumulative distribution function,

Step 5. Take a starting point $u_{1} \cdot U [0 . N_{s}^{- 1}]$ to obey uniform distribution,

Step 6. For j = 1 : N_s, on the movement of probability cumulative distribution function, when u_j > c_i *i = i + 1, assign to sample: $x_{k}^{j^{*}} = x_{k}^{i}$ , assign to weight: $w_{k}^{j} = N_{s}^{- 1}$ , assign to index i^j = i.

Namely when k = 0, sample No. N Particles set S_k-1 with uniform distribution, and establish a target model. $\hat{q} = f \sum_{i = 1}^{I} k ({∥ \frac{x_{0} - x_{i}}{a} ∥}^{2}) δ [h (x_{i}) - u]$ (57)

As known the tracking results S_k-1 (E) at the moment k - 1, the particle set as S_k-1 (i), the weight of each particle as w_k-1 (i), the cumulative probability as C_k-1 (i) i = 1 . ⋯ , N_k-1, and the number of the particles as N_k-1, the motion template as $q_{N}^{k}$ at the moment k.

Perform the following steps:

Step 1. According to the sampling weights $w_{k - 1}^{(n)}$ to re-sampling particles S_k-1.

First calculate the normalized cumulative probability function C_k-1; then produce uniformly distributed random number r ∈ [0, 1]; and then find the minimum j to meet $C_{k - 1}^{(j)} \geq r$ ; generate $S_{k - 1}^{(n)} = S_{k - 1}^{(j)}$ at last.

Step 2. By dynamic equation from k - 1 the particle set $S_{k - 1}^{(n)}$ , calculate the particle set $S_{k}^{(n)} = {AS}_{k - 1}^{(n)} + v_{k - 1}^{(n)}$ at moment k, $v_{k - 1}^{(n)} \cdot N (0, σ^{2})$ .

Step 3. Estimate the state

Calculate the weighted average condition $S_{k} (E) = \sum_{n = 1}^{N} w_{k}^{(n)} S_{k}^{(n)}$ .

5 Simulations of algorithm performance

To verify the effectiveness of the improved algorithm in the paper, a simulation experiment was carried out. First of all, adopt weak nonlinear system state model as Equation (38) to validate the accuracy of the improved algorithm (K-IPS-PF). The state estimates of the standard algorithm, IPS-PF algorithm and K-IPS-PF algorithm is shown in Fig. 6. The curve of mean square error from sixty independent testing is shown in Fig. 7.

Fig.6

Three algorithms’ state estimates.

Fig.7

The curve of mean square error from sixty independent testing.

However, in a practical application of a mobile sensor network, in a 100 m × 100 m simulation area, all nodes and beacon nodes are generated at random. The tracking accuracy is mainly described by root-mean-square error (RMS): $RMS = \sqrt{\frac{1}{N_{p}} (\sum {| x_{i} - {\hat{x}}_{i} |}^{2})}$ (58)

In which, x_i is actual coordinates, ${\hat{x}}_{i}$ is an unknown estimated coordinates, N_p is total volume of error sample for every tests.

Above three algorithms are adopted for target tracking test. Figure 8 shows their efficiency of target tracking under the condition of non-noise. Figure 9 shows their RMS error comparison results under the condition of non-noise.

Fig.8

Three algorithms’ efficiency of target tracking under the condition of non-noise.

Fig.9

Three algorithms’ RMS error comparison results under the condition of non-noise.

Then, adding gauss white noise in Equations (4 and 5) to be e (k) and w (k) ∼ (0, Q (k, T)).

Adopting above three algorithms for target tracking test, Fig. 10 shows their efficiency of target tracking under the condition of noise. Figure 11 shows their RMS error comparison results under the condition of noise.

Fig.10

Three algorithms’ efficiency of target tracking’s under the condition of noise.

Fig.11

Three algorithms’ RMS error comparison results under the condition of noise.

Finally, in the area of simulations, 100 nodes were placed randomly. Their primary energy was 50 units. A convergent node was generated randomly. We performed three algorithms respectively when the total nodes are 20, 30, 40, 50, 60, 70 and 80 for 100 times. Finally, the mean value which was chosen as the results is shown in Table 1 and Fig. 12.

Table 1

The performance comparison of three algorithms’ network energy consumption

Total node number	Average energy consumption
	PF	IPS-PF	K-IPS-PF
20	4.1	3.7	2.3
30	3.5	3.9	1.8
40	3.2	4.0	2.6
50	3.9	3.6	2.1
60	4.2	3.9	2.5
70	4.4	4.2	2.4
80	3.7	4.0	2.0

Fig.12

The comparison of network energy consumption between three algorithms.

As Shown in Table 1 and Fig. 12, the network energy consumption of K-IPS-PF is lower than the other two algorithms.

In conclusion, the improved algorithm proposed in this paper has excellent performance. It has better application in the target tracking of mobile sensor network.

6 Discussion

As shown in Figs. 7, 8, after forecasting the movement trend by Kalman algorithm, the filter accuracy has improved significantly, and the statistic results of the absolute error with the real trajectories are shown in Table 2 and Fig. 13.

Table 2
The absolute error between the algorithm and real trajectory

Times/s PF IPS-PF K-IPS-PF

10 0.231 0.103 0.041

20 0.041 0.025 0.012

30 0.282 0.124 0.038

40 0.315 0.145 0.089

50 0.472 0.168 0.104

60 0.158 0.092 0.054

70 0.102 0.081 0.045

80 0.134 0.062 0.032

Average Error 0.218 0.168 0.073

Times/s	PF	IPS-PF	K-IPS-PF
10	0.231	0.103	0.041
20	0.041	0.025	0.012
30	0.282	0.124	0.038
40	0.315	0.145	0.089
50	0.472	0.168	0.104
60	0.158	0.092	0.054
70	0.102	0.081	0.045
80	0.134	0.062	0.032
Average Error	0.218	0.168	0.073

Fig.13

Comparison of state evaluated error for three algorithms.

As shown in Fig. 13, after forecasting the movement trend by improved Kalman algorithm, average of sates evaluated error of algorithm is 0.073, much lower than the other two algorithms.

The simulations show that in the absence of noise, target tracking accuracy of K-IPS-PF algorithm is higher than other two algorithms as shown in Figs. 8, 9. Count the accuracy error, the results as shown in Table 3.

Table 3

Statistical results of Absolute error of target tracking in the absence of noise

Time/s	Absolute error/m
	PF	IPS-PF	K-IPS-PF
5	2.21	1.06	0.71
10	3.65	1.46	0.86
15	3.68	1.25	0.73
20	3.52	1.02	0.62
25	4.23	0.83	0.58
30	3.02	1.68	0.93
35	2.89	1.21	0.81
40	3.72	1.13	0.73
45	3.48	1.46	0.89
50	3.16	2.51	1.15
Average Error	3.51	1.38	0.94

The simulations show that target tracking accuracy of K-IPS-PF algorithm is higher than other two algorithms in the absence of noisy as shown in Figs. 10, 11. Count the accuracy error, the results as shown in Table 4.

Table 4

Statistical results of average error of target tracking wit noisy

Time/s	Absolute error/m
	PF	IPS-PF	K-IPS-PF
5	2.68	1.37	0.271
10	2.51	1.63	0.492
15	3.21	1.51	0.491
20	3.74	1.43	0.87
25	3.53	1.81	1.29
30	3.59	2.23	1.35
35	3.04	2.36	1.38
40	4.18	1.87	0.492
45	3.47	2.31	1.36
50	3.23	2.51	1.42
Average Error	3.24	1.84	1.16

As shown in Tables 3, 4, in the absence of noise, the average absolute error of target tracking of K-IPS-PF algorithm is 0.94 m, far less than PF algorithm and IPS-PF algorithm; In noisy case, the average absolute error of target tracking of K-IPS-PF algorithm is 1.16 m, are also far less than PF algorithm and IPS-PF algorithm. The simulations show that the network energy consumption of K-IPS-PF is far lower than other two algorithms.

7 Conclusions

With the development of micro-electro-mechanical systems and communication technology, the falling cost of computing, the miniaturization of MPU and the continuous decreasing of power dissipation, mobile sensor network shows more significant scientific research value and wide application prospects in the field as network manufacture and device monitoring, dynamic targets locating and tracking. According to the defects of the standard particle filter algorithm in target tracking of mobile sensor networks, a tracking model for mobile sensor network target is proposed based on motion state prediction. The simulation results show that compared with the standard algorithm, the improved model has higher accuracy and stability, and has lower network energy consumption.

Author contributions

Fengjun Hu and Chun Tu conceived and designed the experiments; Chun Tu performed the experiments; Fengjun Hu analyzed the data; Fengjun Hu and Chun Tu contributed reagents/materials/analysis tools; Fengjun Hu wrote the paper.

Conflicts of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51675490), the Department of Science and Technology of Zhejiang Province (Grant No. 2015C31091), and the Department of Science and Technology of Zhejiang Province (Grant No. 2016C31116), the Department of Science and Technology of Zhejiang Province (Grant No. 2017C31050), the Department of Science and Technology of Zhejiang Province (Grant No. 2017C31063), and the Department of Science and Technology of Zhejiang Province (Grant No. 2017C33018).

References

Aziz

, Fitzpatrick

, et al., A survey on distributed topology control techniques for extending the lifetime of battery powered wireless sensor networks, IEEE Communication Surveys Tuts (99) (2012), 1–24.

Liu

and Liu

S.Y.

Mobile data collecting algorithm based on mixed sink strategy in WSNs, Journal of Jilin University: Eng and Technol Ed (5) (2015), 1680–1687.

J.W.

and Xu

J.B.

New routing algorithm for mobile wireless sensor network, Application Research of Computers32(3) (2015), 866–868.

Chen

, Wang

Z.J.

, et al., Gaussian process modeling and multi-step prediction for time series data in wireless sensor network environmental monitoring, Journal on Communications36(10) (2015), 252–262.

Z.J.

, Yin

L.X.

, Zhang

and Mi

L.H.

RF signal estimation algorithm for mobile sensor networks in urban environment, Computer Science41(1) (2014), 183–186.

F.X.

, Zhang

J.C.

, et al., The acoustic target in battlefield intelligent classification and identification with multi-features in WSN, Science Technology and Engineering (35) (2013), 10713–10721.

Zhu

S.C.

, Wang

H.T.

, Chen

and Yan

Survivable routing protocol based on cluster for wireless sensor network applied to battlefield environment, Journal of Transduction Technology26(10) (2013), 1426–1431.

Jia

Z.X.

, Vcu

C.D.

, et al., A target tracking method of rescue system for buildings during disaster, Journal of Northeastern University (Natural Science)31(3) (2010), 334–337.

Cao

L.J.

, Guo

and Jin

Y.F.

Marine water quality monitoring and design of a red tide forecasting system based on sensor network, Journal of Dalian Fisheries University29(6) (2014), 334–337.

10.

Huang

, Wang

Q.P.

, et al., Analysis and design of wireless sensor network nodes for mine monitoring, Computer Applications and Software25(10) (2008), 72–74.

11.

Wang

W.T.

, Locating nodes three-dimensional deployment in emergency salvage, Journal of Inner Mongolia Normal University (Natural Science Edition)43(2) (2014), 180–185.

12.

Bachir

, Dohler

, et al., MAC essentials for wireless sensor networks, IEEE Commun Surveys Tuts12(2) (2010), 222–248.

13.

Cui

Y.F.

and Shi

J.F.

Target tracking based on adaptive dynamic clusters and prediction mechanism in WSN, Journal of Transduction Technology28(7) (2015), 1046–1050.

14.

Teng

, Snoussi

and Richard

Decentralized variational filtering for target tracking in binary sensor networks, IEEE Trans Mobile Computing9(10) (2010), 1465–1477.

15.

Chen

Y.J.

, Pan

and Wang

Performance optimization and simulation based on target tracking in wireless sensor networks, Journal of Transduction Technology28(4) (2015), 544–550.

16.

Ling

, Fu

and Tian

Localized sensor management for multitarget tracking in wireless sensor networks, Information Fusion29(5) (2011), 194–200.

17.

Wang

, Peng

, et al., Heterogeneous wireless sensor networks for continuously tracking mobile targets, Mini-micro Systems36(3) (2015), 503–507.

18.

Lou

, Cui

B.T.

and Li

Target tracking algorithm of mobile sensor networks based on flocking control, Control and Decision28(11) (2013), 1637–1642.

19.

Tian

and Han

Objects tracking algorithm for WMSN based on distributed data fusion, Application Research of Computers28(7) (2011), 2664–2666.

20.

Han

, Li

F.M.

and Luo

Distributed target tracking algorithm for wireless mobile sensor networks, Journal of Beijing University of Posts and Telecommunications32(1) (2014), 90–94.

21.

Zhu

Z.Y.

and Su

L.D.

Target tracking based distribute adaptive particle filter in binary wireless sensor networks, Computer Science40(8) (2013), 43–45.

22.

Peng

Y.F.

and Huang

X.F.

Research target tracking algorithm of wireless sensor networks, Computer Simulation29(5) (2011), 122–125.

23.

Yao

X.L.

, Hu

and Lv

X.L.

Kalman filtering research in the tracking of moving target in WSN, Journal of Changchun University of Science and Technology34(3) (2011), 88–92.

24.

Zheng

J.Y.

, Improved particle filtering algorithm for target tracking in WMSN, Computer Engineering and Applications47(15) (2011), 83–85.

25.

Yue

, Wang

, Min

J.M.

, Xie

Y.T.

and Si

G.J.

Improved distributed dynamic clustering particle filter algorithm, Application Research of Computers32(10) (2015), 3091–3095.

26.

X.L.

, Tang

X.F.

, Ge

Q.B.

and Guan

B.L.

Target tracking algorithm based on cubature particle filtering fusion with quantized innovation, Acta Automatica Sinica40(9) (2014), 1867–1874.

27.

and Shi

J.F.

Application of distributed particle filtering algorithm in target tracking, Transducer and Microsystem Technology33(8) (2014), 158–160.

28.

Tang

X.F.

, Guang

B.L.

, Ge

Q.B.

and Xu

X.L.

Multi-sensor Quantized Fusion Tracking Algorithm for Non-cooperative Target, Application Research of Computers31(10) (2014), 2902–2906.

29.

Dong

Y.J.

and Li

G.W.

Wireless sensor networks target tracking based on particle filtering optimized by quantum genetic algorithm, Science Technology and Engineering (12) (2013), 3305–3309.

30.

Jiang

, Song

H.H.

and Lin

Target tracking algorithm for wireless sensor networks based on particle swarm optimization and metropolis-hasting sampling particle filter, Journal on Communications34(11) (2013), 8–17.

31.

Guo

S.M.

, Zheng

, Md

, Alam

, Wang

G.J.

and Lu

P.P.

Grey markov model-based target tracking algorithm for wireless sensor networks, Transducer and Microsystem Technology32(11) (2013), 128–131.

32.

Zhou

, Jiang

, et al., Moving target localization and tracking algorithms: A particle filter based method, Journal of Software24(9) (2011), 2196–2213.

33.

Zha

D.L.

, Bai

F.S.

, Dong

S.Y.

and Li

H.S.

An improved triangle centroid location algorithm based on kalman filtering and linear interpolation, Journal of Transduction Technology28(7) (2015), 1086–1090.

34.

Cui

F.Y.

and Shao

G.L.

Weighted centroid localization algorithm based on multilateral localization error of received signal strength indicator, Infrared and Laser Engineering44(7) (2015), 2162–2168.

35.

Shen

, Xu

G.H.

and Sang

Adaptive variational bayesian cubature kalman filtering, Electric Machines and Control19(4) (2015), 94–99.

36.

Zhao

, Li

W.Y.

and Sun

RSS-based localization via bayesian ranging and iterative least squares positioning, Journal of Southwest China Normal University (Natural Science)40(9) (2015), 23–29.

37.

Yoon

, Cheon

and Park

Object tracking from image sequences using adaptive models in fuzzy particle filter[J], Information Sciences: An International Journal253(18) (2013), 74–99.

38.

Forte

and Srivastava

Resource-aware architectures for adaptive particle filter based visual target tracking[J], ACM Transactions on Design Automation of Electronic Systems18(2) (2013), 949–958.

39.

, Wang

, Bu

, Jiang

and Liu

A novel method based on least squares support vector regression combing with strong tracking particle filter for machinery condition prognosis[J], Proceedings of the Institution of Mechanical Engineers, Part C Journal of Mechanical Engineering Science228(6) (2013), 1048–1062.

40.

Luo

and Mori

Robust endoscope motion estimation via an animated particle filter for electromagnetically navigated endoscopy[J], IEEE Transactions on Biomedical Engineering61(1) (2014), 85–95.

41.

Dal Moro

, Pipan

and Gabrielli

, Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation[J], Journal of Applied Geophysics61(1) (2007), 39–55.

42.

Zhongxing

, Haibin

and Jingcui

A trapezoidal approximation of left right fuzzy numbers[J], Journal of Guangxi University (Natural Science Edition)35(6) (2010), 1063–1068.

43.

Yiting

, Shiqi

, Hongxia

and Daizhi

An improved detection method for hyperspectral imagery based on white gaussian noise[J], Applied Spectroscopy: Society for Applied Spectroscopy (69) (2015), 23–29.

44.

Zhang

X.C.

, Xu

B.S.

, Wang

H.D.

and Wu

Y.X.

Optimum designs for multi-layered film structures based on the knowledge on residual stresses[J], Applied Surface Science: A Journal Devoted to the Properties of Interfaces in Relation to the Synthesis and Behavior of Materials253(253) (2007), 5529–5535.

45.

Yong

P.C.

, Nordholm

and Dam

H.H.

Optimization and evaluation of sigmoid function with a priori SNR estimate for real-time speech enhancement[J], Speech Communication: An International Journal55(2) (2013), 358–376.

46.

, Asymmetric kernel density estimation based on grouped data with applications to loss model[J], Communications in Statistics, B Simulation and Computation43(43) (2014), 657–672.

47.

Kalke

and Richter

W.D.

Simulation of the P-generalized gaussian distribution[J], Journal of Statistical Computation and Simulation83(4) (2013), 1–27.

48.

Chang

, Hu

, Li

and Qin

Transformed unscented kalman filter[J], IEEE Transactions on Automatic Control58(1) (2013), 252–257.

49.

Myrseth

, Sastrom

and Omre

Resampling the ensemble kalman filter[J], Computers & Geosciences55(2) (2013), 44–53.

An optimization model for target tracking of mobile sensor network based on motion state prediction in emerging sensor networks

Abstract

Keywords

1 Introduction

2 A target tracking model for particle filter algorithm in mobile sensor network

3.1 The weights self-adaption optimization based on the integral point assignment

4.1 Motion prediction based on the Kalman

Table 2 The absolute error between the algorithm and real trajectory Times/s PF IPS-PF K-IPS-PF 10 0.231 0.103 0.041 20 0.041 0.025 0.012 30 0.282 0.124 0.038 40 0.315 0.145 0.089 50 0.472 0.168 0.104 60 0.158 0.092 0.054 70 0.102 0.081 0.045 80 0.134 0.062 0.032 Average Error 0.218 0.168 0.073

Author contributions

Conflicts of interest

Footnotes

Acknowledgments

References