Research On Filtering And Smoothing Algorithms Based On Random Finite Set

The study on the techniques for multi-target tracking(MTT)is an important research direction in the field of signal processing.Under the complex tracking conditions,the main research content of the MTT problems,whose key components are filtering and smoothing algorithms,is how to get the target information such as position and velocity from the received measurements.The multi-target filtering and smoothing algorithms based on the random finite set(RFS)are very suitable for tracking multiple targets in real time under complex situations due to their filtering frameworks incorporating all of the possible uncertainties in the process of tracking.Unlike the traditional approaches for tracking multiple targets,the multi-target filtering and smoothing algorithms,based on RFS,do not require the complex data association process to determine the explicit connections between the targets and measurements,thus avoiding the computation requirements caused by the data association process,so they are simple and efficient algorithms and also with good promising applications.In this paper,the multi-target filtering and smoothing algorithms based on RFS are studied,and the corresponding solutions are proposed for some problems presented in applications.The main works and contributions of this thesis are stated as follows:(1)The sequential Monte Carlo cardinality balanced multi-target multi-Bernoulli(SMC-CBMe MBer)filter is the multi-target filtering algorithm which is used to handle to the MTT problems under the condition of the nonlinear tracking models.However,the problem of the SMC-CBMe MBer filter is that plenty of time is spent to compute the updated multi-target density and complete the resampling step.In this paper,an improved SMC-CBMe MBer filtering algorithm is proposed for solving the problems of large computation and long running time.Based on the predicted state estimation and measurement likelihood,by using only the sensor measurements with likelihoods greater than or equal to a preset likelihood threshold to update the predicted multi-target density,the proposed algorithm can effectively reduce the computation of SMC-CBMe MBer filter,and thus improves the running speed of the SMC-CBMe MBer filter.(2)The CBMe MBer filter is an improved algorithm which is used to solve the target number over-estimation problem presented in the multi-target multi-Bernoulli(Me MBer) filter.However,tracking multiple targets in the scenarios where the measurement biases exist with the standard CBMe MBer filter will generate significant deviation.In order to solve the application problem of the CBMe MBer filter in the clutter environment with measurement biases,a CBMe MBer filtering algorithm with error compensation is proposed and its Gaussian mixture(GM)implementation are also presented for linear tracking models.With the real-time estimation and compensation of the measurement biases,the proposed algorithm can effectively eliminate the adverse effects of the measurement biases on the filtering results,and also achieve good tracking performance.(3)The Gaussian mixture probability hypothesis density(GM-PHD)smoother is the closed-form solution to the forward-backward PHD smoother under the condition of the linear Gaussian tracking models,tracking multiple targets with the GM-PHD smoother can yield better state estimates.However,the target disappearance in tracking process will lead to the smoothed PHD function being estimated incorrectly in the backward smoothing,thus resulting in the misestimation problems of the smoothed target number and state.In this paper,an improved GM-PHD multi-target smoothing algorithm is proposed for the misestimation problems caused by the disappeared targets.Based on the filtering results obtained by the forward GM-PHD filter,the proposed algorithm defines the target survival probability used in the backward smoothing process,and modifies the backward smoothing recursion equations of the GM-PHD smoother.The proposed algorithm can effectively eliminate the misestimation problems caused by the disappeared targets in the tracking process,and also improve the tracking performance of the GM-PHD smoother.(4)The extended target probability hypothesis density(ET-PHD)filter is a multi-target filtering algorithm for handling the extended target tracking(ETT)problems in the RFS theory framework.For the purpose of addressing ETT problems with measurement biases and on the basis of the mechanism of the ET-PHD filter,this paper proposes a ET-PHD filter with bias compensation by defining the augmented state which consists of extended target state and measurement bias.By using the weighted sum of Gaussian functions to represent the initial PHD function and the PHD function at each time step,the analytic implementation of the proposed filter is derived for the linear Gaussian multi-target model.The simulated results show that the proposed algorithm can effectively handle the ETT problems in the clutter environment with measurement biases,compared with the standard ET-GM-PHD filter,the proposed algorithm can achieve satisfactory tracking results in the process of tracking,and also with a good tracking performance and a strong robustness.