Research On Star-Convex Set Based Extended Target Tracking Algorithms

In the wake of developments in modern radar systems,the high-resolution radar receives multiple measurements reflected from different scattering points on the surface of the target.These measurements provide more abundant information than the traditional point target tracking,including the dynamic and geometric properties of the target.The information can be fully utilized by the extended target tracking,so the state estimation accuracy and tracking performance are improved.It has been widely used in military fields such as the ballistic missile defense system,maritime reconnaissance and warning system,battlefield situation assessment,and civilian fields such as the air traffic control system,intelligent transportation system,and port monitoring system.However,due to various target shapes and complex tracking environments,extended target modeling,extended state estimation,and multiple extended target tracking become new challenges.The star convex set can model the extended target with a complex shape and has better adaptability to the extended targets with different shapes,which has been widely used in extended target modeling.Due to the highly nonlinear function in the star convex set model and time-varying measurements in extended target tracking,the analytical solution of the posterior state estimate cannot be calculated directly.Therefore,nonlinear filtering methods are used to approximate the extended target states.Based on the nonlinear filtering and label random finite set theories,this dissertation deeply studies the extended target state estimation and multiple extended target tracking framework with complex shapes.The main contributions of the dissertation are given as follows:1.The performance evaluation system of the extended target tracking has been built.The extended target tracking not only estimates the kinematic state but also estimates the extended state compared to point target tracking.In order to introduce the shape error into the performance evaluation system,the target shape parameters are calculated by the Fourier series expansion of the target boundary curve,which can extract the shape parameters effectively.Then,the root mean square error of shape parameters is used to measure the performance of shape estimation,and it is introduced into the optimal sub-pattern assignment(OSPA)distance to propose an improved OSPA distance,which provides a more complete performance evaluation system.2.A nonlinear filtering algorithm based on the measurement transformation is proposed.According to the star convex set model,the relationship between the extended state and scattering point is a nonlinear function.Since the associations between the scattering points and measurements are unknown,the measurement model is a nonlinear hierarchical probability model.Therefore,it is difficult to estimate the first and second moments of the target states directly.Firstly,the measurements are transformed into a high-dimensional space with the Fourier basis functions as unit vectors by the nonlinear function.The measurement model is approximately transformed into a linear model,and the detailed features of the target shape are extracted.Then,a generalized linear minimum mean squared error(GLMMSE)estimator is constructed to estimate the kinematic and extended states.Simulation results demonstrate that the proposed algorithm improves the tracking performance and provides accurate shape estimation compared to the traditional point estimation filters.3.A particle filtering based on the Gaussian-like likelihood function is proposed.In order to further improve the accuracy of shape estimation,it is necessary to increase the dimension of the extended state.However,the traditional point estimation filters will not converge to a stable state due to increasing the dimension of the extended state,thus the particle filtering algorithm is used to solve the problem of high dimensional extended state estimation.Firstly,the extended target is represented by the star convex set model.Then,the distribution of the scattering points in the cartesian coordinate system is derived by the Jacobian determinant,and the likelihood function is constructed in a two-dimensional space using convolution,which retains all the information of the target shape.In order to improve the effectiveness of particles,particle swarm optimization is used to mitigate particle degradation.Simulation results demonstrate that the proposed algorithm can track the extended target stably and accurately in the case of high measurement noise and low measurement rate.4.A generalized labeled multi-Bernoulli(GLMB)filter based on the joint likelihood function is proposed.In multiple extended targets tracking,when multiple extended targets are close to each other,only the distances between the extended targets and measurement cells are used to calculate the likelihood function and construct the association matrix,which may increase the number of the feasible association hypothesis with similar weights and reduce the accuracy and computational efficiency of the data association.This algorithm designs a joint likelihood function based on the distances between the extended targets and measurement cells and the similarities between the shapes of extended targets and extents of measurement cells to solve the multiple extended targets tracking problem with different shapes.Firstly,the Gaussian components in the GLMB filter are updated by the GLMMSE estimator to improve the estimation accuracy of states.Then,the joint likelihood function of the kinematic and extended states is designed by the log-weighted fusion strategy to improve the accuracy of the data association.Moreover,the posterior probability density is approximated by Gibbs sampling to improve the efficiency of the data association.Simulation results demonstrate that the proposed filter can estimate the trajectories of extended targets with different shapes efficiently and accurately.