Extended Object Tracking Based on Distributed Sensor Network

In this paper, an extended Kalman filtering algorithm based on coupled velocity model (CVM) is proposed for extended object tracking under distributed sensor networks. This algorithm tracks an object using measurements collected by multiple sensor nodes, and then obtains a global solution based on weighted Kullback-Leibler divergence. Simulation results display that the improved method can effectively track the extended object.


Introduction
Recently, with the increase of sensor resolution, many measurements can be received from each time step of object, so we call such object as extended object.Extended object tracking is significant in some domains, for instance autonomous driving [1], maritime surveillance [2], because it can track position, size, and direction.
Researches have proposed many measurement models, e.g., the random matrix model (RMM) [3]- [4], random hypersurface model (RHM) [5], gaussian process (GP) [6]- [7] model, multiplicative noise error model (MEM) [8]- [9], and coupled velocity model (CVM) [10], etc.The CVM introduces a method to construct correlations between direction and velocity compared to the MEM model.CVM introduces a sideslip angle to focus on the direction and direction of target motion in a more intuitive way.
Wireless sensor networks are very important in target tracking, so two multisensor fusion architectures are proposed, including centralized and distributed [11].Centralized architecture has only one fusion center which causes a huge computational burden.Whereas distributed architecture has each node as a fusion center and the breakdown of any node does not affect the overall work, therefore it has gained a lot of attention.li et al. modeled the extended object as a random matrix and completed fusion based on the weighted Kullback-Leibler divergence [12].Ren et al. modeled the extended object as a multiplicative noise error model(MEM) and proposed a diffusion strategy [13]- [14] to obtain the state of the object by the extended Kalman filter algorithm proposed by Baum [9].Liu et al. considered the asynchronous measurement problem in a distributed network [15] and derived a distributed Bayesian estimation scheme for asynchronous measurements based on a random matrix framework to reduce the communication cost.
In this paper, we use coupled velocity model (CVM) to establish velocity-direction linkage and estimate the state of object by the extended Kalman filter under a collaborative diffusion approach.We assume that each node can exchange information with any other node in the network, and every node has multiple measurements.The state of the object will be obtained by processing measurements of neighboring nodes, and a distributed fusion rule based on weighted Kullback-Leibler divergence [16] is utilized for this purpose.

Problem stereotypes
In a distributed network Ν, s represents sensor node, and , represent the domain of the node s and the quantity of the node, respectively.We consider an We consider an elliptical object, and obtain its shape parameterization, measurement process, and dynamics process.

Shape parameterization
Kinematic state at time t is expressed as follows: where indicates the center position of the object, , ⊤ : = indicates the velocity along x-axis and y-axis direction, and then some other parameters(acceleration, etc.).extension of the object is expressed as follows: ,1 , ,2 represent the semi-lengths, and the side-slip angle = arctan − is defined as a drift between orientation and velocity direction [10].

Measurement models
The Measurement , of node s at time t are expressed as follows: = 1 0 0 0 0 1 0 0 is a measurement matrix at node s, it represents the position extracted from the kinematic state at time t. is a coefficient matrix, and it denotes extent and kinematics.The multiplicative noise t with a covariance ℎ = 1 4 2 of the zero-mean Gaussian distribution denotes the location(local or boundary) of scattering source J and is independent of the kinematic state, coefficient matrix, and measurement noise., is a Gaussian measurement noise with covariance and has no relevance to other nodes.
In distributed network, the number of measurements received at node s is , , and all measurements received by node s at time t are as below: , (2) , (3) …… , Similarly, the set of measured values is as follows: , = , 1 , 2 , 3 …… , (5) where 1 , 2 , ...... represents the neighbor indices of node s, and the measurement model is shown in Figure 1.Where and represent the center, orientation respectively, and β is the side slip angle. is the angle of rotation along the x-axis.The scattering source J consists of multiplicative noise and shape parameters, and y is the measurement.= , ⊤ is the velocity on the x and y axes, and v is the measurement noise.

Dynamical model
where , denote the transition matrices, and and denote the zero-mean Gaussian noises with covariance of and .

Distributed Extended Target Tracking
Every node uses the EKF algorithm and diffusion strategy to obtain local estimates including kinematic state and extension for the same object in this part.According to [9], [13], [14], the motion and extention of local nodes after completing estimation are , , , , and their covariances are , , , respectively.Following [9], it is important to obtain the closed solution by converting the nonlinear measurement of the true measurement , into a pseudo-linear measurement , to estimate extension.Let , (−1) , , (−1) , , (−1) and , (−1) denote the motion and extent of the priori estimations and their corresponding covariances at the i-1-th iteration., () , , () , , () and , () are obtained by processing and updating measurements from neighboring nodes of node s at the i-th iteration.Finally those nodes fused their estimates to get , , , , , and , through weight coefficients at time t.
The i-th iteration pseudo-measurements are calculated by introducing a vect-operator: Simultaneous updating of the covariance , () of the pseudo-measurements: it can be seen that CVM has a higher tracking effect than MEM at the turn, while the distributed tracking effect does not differ much from the centralized one.In Figure 3, it can be seen that CVM based on distributed network has a higher estimation accuracy for the shape than MEM.But overall, the distinction is not significant and the fluctuation range is small.Figure 4 shows the error in velocity, and it can be seen that distributed tracking algorithm based on CVM is a little better than others.Similarly, none of the four tracking methods have significant difference.In general, it can be concluded from these results that these algorithms all have good performance in extended object tracking.Overall, there is not much difference in the simulation results mentioned above.Based on this, we analyze that this simulation was implemented in a fully connected network and did not consider issues such as loss during transmission.Therefore, to ensure the effectiveness of this method, we will continue to explore experiments conducted in not fully connected situations to better optimize the proposed method.

Conclusion
In this paper, an extended Kalman filter tracking algorithm based on coupled velocity model (CVM)   is proposed under distributed network with six nodes, and the fusion steps after tracking of extended object is accomplished by weighted Kullback-Leibler divergence distributed fusion rules.We evaluated the performance of several algorithms using CVM and MEM in both centralized and distributed architectures by simulation experiments.The results show that our proposed algorithm has good tracking effect in both centralized and distributed case.In the future, We can consider tracking a single extended object or multiple extended objects under asynchronous measurement conditions.In addition, the impact of noise on this method can also be explored.