DCACT hybrid method inWSN-based target tracking

- The use of Bayesian location estimation methods (a subset of consensus average tracking methods) is one of the most commonly used tracking methods in Wireless Sensor Networks (WSN) due to high error tolerance, tracking accuracy and scalability. In these networks, due to Quasi-spherical of the transmitting radiation pattern (sensing), it is only possible to estimate the target distance from the received signal level. In this paper, a hybrid method called DCACT based on dynamic clustering and baysian estimation methods (IMMKF and MMPF), will be presented that tracks the maneuvering target with very good accuracy. The simulation results show DCACT method based on multi-mode particle filter (DCMMPF), with a 50% reduction in active sensors, track the target well only with increasing the location estimation error and velocity estimation error up to 26 and 16 percent respectively .

In recent years, much attention has been paid to the use of WSN in target tracking.Common networks are mostly based on radar networks but the advantages and excellence of WSN such as the possibility of sampling within the scope of the operation, lacking LOS, Low cost and low interference have made these systems more effective on the battlefield [1].Tracking the target in a wireless sensor network is one of the research topics that have been gaining interest in recent years [2][3][4][5].The most important thing in target tracking in a wireless sensor network is to estimate the position and direction of the target(or extracting the target velocity vector) using observed measurements (based on the received signal level).This estimate is used to determine the next header and to wake up sensor nodes that are effective in target tracing.Given that the transmitted radiation pattern (sensing) of the nodes are quasi-spherical and practically it is only possible to estimate the distance from the received signal level, the prediction of the signal direction is not possible andthe distance detection method of a single node is limited to this method.In many articles, writers assume that the sensor node can extract the target position [6][7][8].But, due to the limitations of the wireless sensor network; this is only possible to measure the distance (range only).
Several papers and research have been conducted in the field of tracing the passive object. Wenjun Tanget al. [7]have been working on a distributed consensus-based distributed particle filter in a wireless sparse sensor network.The main objective of this plan is to provide an optimal way to limit the consensus average error in sparseWSN.In this method, the information is weighted from local particle filters and finally, a consensus of these sensors is considered as an optimal output consensus.
Wang, Xingbo et al. [9]in order to compensate for the sub-optimality of the EKF tracking method, provide an algorithm based on the combination of the ML method and the standard Kalman filter. In this paper, in which additiveandmultiplicative noises and nonlinear target motion are the purposes of input assumptions, the ML method is used to estimate the initial location of the target and to eliminate nonlinear effects in the distance measurement and then uses the standard Kalman filter algorithm to estimate the target path. This paper then compares the tracking error using the proposed method and the developed Kalman filter in the conclusion section.
Ziyia Jia et al. [10] have tried to provide a distributed algorithm to obtain target path in a binary networkwith the same distributed sensors.In this paper, the estimation of the moving target velocity (in purely progressive motion) is determined by the time the target is detected by each network sensor.In this method, target tracking is based on the sensing node tracking, which involves several problems, such as fading and Multipath, so this method can be used in high density nodes.
In [11]Atieh Mohammadian Keshavarz and their colleagues have presented a method for tracking Maneuvering target in 3D in WSN.In this method, in a three-dimensional space with scalable and multiplicative noise, sensor clusters based on Posterior Cramer-Rao Lower Band(PCRLB) is selected and then object tracking is performed based on IMMPF.
Many references in this field, such as [6,[12][13][14][15][16]often do not include two fundamental points: 1) All consensus-based methods, such as the Kalman filter and derivatives, require the initial positioning of the target.As mentioned,each sensor node alone cannot extract the target location without the help of its neighbors.In many of these articles, it is assumed that each node can estimate the position of the target, which is not based on the limitations of the present article.
2) In practice, considering the limited battery and computational power, it is not possible to implement consensus average filtering filters in each sensor node (based on the state-vector combination method).
To fix these problems, an algorithm is selected for this researchwhich combines dynamic clustering based on PCRLB, Multi-laterationand average consensus filters (two different methods, IMMKF and particle filtering). In this algorithm, after sensor selection and forming a PCRLB-based dynamic cluster in the context of the target, by using the multilaterationmethod, the position of the target is extracted from the object observation and the result is sent to the data integration center (Figure 1). At this center, with the implementation of average consensus tracking algorithm,the future position and trajectory of the target are foreseen.The corresponding new dynamic cluster is determined to awaken the nodes that the target moves towards them.This algorithm will be repeated until the end of the tracking mission ( Figure  2). The content of this article is organized as follow.In Section 2, the WSN and target dynamics are introduced. In the third section, the formation of the dynamic cluster and the selection of active sensors are described.In Section 4, the target observation and positioning model (which is used as input for the tracker filter) is expressed and the tracking algorithm is described in Section 5.In the final section by simulating the proposed method, the accuracy of the estimation of the target location and targetvelocity is extracted.Scalability of the DCACT method in the tracking of the target with high percentage variationof active sensors is investigated and the results are presented.

Problem formulation 2.1 Network architecture
In WSN, sensors are usually distributed randomly in a uniformdistribution due to the lack of access to the sensor trace environment.Based on the principle of WSN, the geographic location of the sensors is determined at the beginning of the network configuration, and the position of each sensor in the network is determined.Due to the fact that the sensors are completely randomly distributed in the network structure, the method of tracking the target in this structure will have the ability to extend and generalize in the same networks (with regular or Gaussian distribution)

TargetDynamic
The state equations are expressed in the following general form: As a result, jth is the element of the vector of observations k z , which means that j z is the equivalent of the received signal from the sensor jth, and it is modeled as follows. (2) is the noise of the received observations in the jthsensor at k time. To get enoughobservations for tracking, at least, the top 3 sensors are selected based on the PCRLB benchmark to estimate the target position [17].

Sensor selection and dynamics clustering
One of the major challenges encountered in WSN is the high telecom load because all sensors need to send their observations to a sink.Given the bandwidth and power constraints, the size of sent observations should be minimal.In this regard, the issue of power consumption is important because it determines the life span of the network.As shown in [12], the power consumption level per each transmitted byte 10 times the calculation byte.These values are 400 nJ for each byte of transmission and 40 nJ for each byte of calculations in this reference.Also, broad bandwidth is required to prevent interference between observations from the requirements of sending all observations which it is almost impossiblein WSNs.To solve these problems, only the sensors that have better quality observations can be selected. Here, according to event base structures of WSNs, observations can be limited to the scope of the target.In this case, at least 3 sensors should be selected using the Cramer-Rao lower bandfrom the total numbers of sensors that can see the target.Since this band is the low limit of the variance of the non-bias estimation error to estimate the state of an uncertain target [18],wecan select the best sensors for providing observations with the least possible error. The Cramer-Raolower band for the covariance matrix of thestate vector errorx is equal to the inverse of the Fisher information matrix k J .
In which ˆk x is the estimator of the vector k x .The calculation of the Fisher information matrix requires high computations.However, it can be calculated recursively [18,19]: x in the following condition applies.
Since the objective of tracking the target in order to minimize the target location error, a suitable criterion for sensor selection is considered as follows: are the CRLBs of x and y respectively.If the prior distribution of state p(x 0 )isGaussian with covariance C 0 , then J 0 = C 0 -1 .
Choosing the best sensor with the above criterion is a hybrid problem that requires high volume computing. According to this issue,in order to reduce the computational volume, the following algorithm is proposed.

Observation and positioning model
As noted above, in WSN, since these sensors only have the ability to calculate their distance from the target, they cannot alone extract the position of the target position.Therefore, the target position could be extracted only with the combination of sensors observations.For this subject, at least 3 observations of the sensor should be shared so that the multilateration method can extract the target's Cartesian position.Here, 3 sensors in a dynamic cluster are selected based on the PCRLB criteria participate in the initial positioning process.  Suppose that 3 sensor nodes with specific coordinates. A target with uncertain coordinates in the field of view of these sensors is introduced.The distances are measurable to each of the sensor nodes as follows: To do this, it's best to write a set of linear equations based on u u (x ,y ) . Here we need to delete the values of 2 2 u u x and y . To do this, it suffices to deduce the third equation from the two previous equations: The above equations can easily be expressed as a linear matrix: Which can be written as the following linear equation: The above equation is anoverdetermined equation. In this type of linear equation, when the average value of the square error is minimized, the pair u u (x ,y ) will minimize 2 2 Ax-b (which is equal to the Euclidean norm).Since 2 2 T 2 v = v vexists for each matrix v, we will have: Minimizing this value will be the minimization of the average squares.By putting this Polynomial equal to zero, we have: By solving the above equations, the value of the x vector, which is the approximate location of the target, is obtained.

Tracking algorithm
In practical scenarios, common goals are similar to those of your own (speed, location, and acceleration) with time.For example, a target that is moving at a steady pace may suddenly enter into its own mode of maneuver.It is impossible to model this kind of behavior in a constant way.Therefore, in addition to estimating the target state, it is also necessary to estimate its fashion.

5.1.Multi-Mode Kalman filtering method
One of the most widely used algorithms for intercepting modes which modalities can be changed by the Markov random variable sequence is the IMM [20].
The current state of the system is assumed to be one of the n possible modes of the   1 ,..., n M M M  set.Furthermore, by default, the initial probability is that the target is in j M mode specifies and is equal to .Also, the probability of a change from one mode to another is modeled in the form of the firstorder Markov process with the transmission matrix with the following subdivisions: The transport mode matrix is defined as follows.
And also the received data is as follows.
Hx v Figure 3 shows the general schema of the IMM algorithm.In general, the IMM consists of three steps: 1. Interaction, 2. Filtering and 3. Combination

1) Interaction
At this stage, for the mode   The goal change is usually modeled based on the Markov process, which is likely to transfer a mode to another mode as follows

2) Filtering
In this step, the Kalman filter equations with the appropriate model are used to update the hybrid mode in (18) using current data. In order to update, it is necessary to calculate the probabilities of different modes, which are obtained from the following equation.
is the innovation vector, n is the dimension and j S is the covariance matrix.After this mode has been updated by using  

3) Combination
Estimated modes   Regarding the nonlinear state of state equations, we can use UKF and EKF. The UKF is rarely used in a multimode approach because the covariance matrix cannot be positive Semi-definite by increasing the covariance matrix of non-conformal filters and computational errors [21]. In this case, UKF loses tracking capability.So, the report will only be used by EKF.

Multi-Mode Particle Filter (MMPF)
In this section we study the conventional particle filter algorithm in tracking the maneuverable target.Consider the dynamic equation of a generalized maneuvering target as follows. (29) , the prediction stage is performed in two steps.
Step 1 -A random sample of indexes   1 and exit

End End
Step 2 -The system mode vector is predicted to be in accordance with the system dynamics. In other words, the particle n of the n k x vector is obtained as follows.
In this case, the set of predicted particles is    

2) Updating
At this stage, a new set of particles is sampled and the estimated latent density function is updated below. (34)

Simulation
Effectiveness of the proposed tracking approach is validated through some Monte Carlo simulations in terms of trackingaccuracy and energy consumption. In these simulations, 800 sensors in 35 hectares (1400 m in 250 m) were distributed randomly with a uniform distribution.Based on the principles of WSN, the geographic location of the sensors is determined at the beginning of the network configuration. Each sensor's visibility is limited and can only see the target in a range of 30 meters radius.In this system, it is assumed that at any moment, up to 10 sensors can be selected.We consider the multi-mode dynamics model in the below form: it assumes that the matrix   m F is identical for all modes and is equal to [19]: The matrix G is also defined as: The state It is also the proba (ω = 0.00 The mea independ

Conclusion
The simulation results show the DCACT tracking sustainability (based ondynamic clustering and the use of multi-mode Kalman filtering methods and multi-mode particle filtering).The DCMMPF tracking method has better results in RMSE of location and speed.TheRMSE of location and velocity with Multi-Mode extended Kalman filter (DCIMMEKF) is 2.5 times greaterthan the multi-mode particle filter (DCMMPF) method. Also, the scalability was tested and the results showed that the DCMMPF method, with a 50 percent decrease in active sensors,present steadily tracking the target with an increase up to 30% in RMSE of location and speed.Also, the RMSE of location and velocity in the DCMMPF method remainsabout 40% of DCIMMEKF, so it is considered as the preferred method.