Aiming at the tracking problem of multiple extended targets under the circumstances with unknown measurement noise covariance, an extension of standard Extended Target Probability Hypothesis Density (ET-PHD) filter and the way to realize its analysis were proposed by using ET-PHD filter and Variational Bayesian (VB) approximation theory. Firstly, on the basis of the target state equations and measurement equations of the standard ET-PHD filter, the augmented state variables of target state and measurement noise covariance as well as the joint transition function of the above variables were defined. Then, the prediction and update equations of the extended ET-PHD filter were established based on the standard ET-PHD filter. And finally, under the condition of linear Gaussian assumptions, the joint posterior intensity function was expressed as the Gaussian and Inverse-Gamma (IG) mixture distribution, and the analysis of the extended ET-PHD filter was realized. Simulation results demonstrate that the proposed algorithm can obtain reliable tracking results, and can effectively track multiple extended targets in the circumstances with unknown measurement noise covariance.

To solve the anomalous smoothing problems caused by the missed detection or target disappearance in the particle Probability Hypothesis Density (PHD) smoother, an improved method based on the modified target survival probability was proposed. Firstly, the prediction and update formulas of forward filtering were modified to obtain the target intensity function of filtering and estimate the number of survival targets in filtering process. On this basis, using the estimated value changes of forward filtering of survival number to judge whether targets disappearance or missed detection occurring, and the survival probability used in backward smoothing calculation was defined. Then, the iterative calculating formula for backward smoothing was improved with the obtained survival probability, and the particle weights were obtained on this basis. The simulation results show that the proposed method can solve the anomalous smoothing problems in PHD smoother effectively, its time averaged Optimal SubPattern Assignment (OSPA) distance error is decreased from 7.75 m to 1.05 m compared with standard algorithm, which indicates that the tracking performance of the proposed method is improved significantly.