Identical maximum likelihood state estimation based on incremental finite mixture model in PHD filter

The incremental finite mixture model is proposed for the multiple target state estimation in sequential Monte Carlo implementation of probability hypothesis density filter. The model is constructed in incremental way. It consists of two steps, the step of inserting new component into model and the step of estimating mixing parameters. The maximum likelihood criterion is adopted for both steps. At the inserting step, the inserted component is selected from the candidate set of new mixture components by maximum likelihood, while the mixing parameters of existing components remain unchanged. Expectation maximization algorithm is adopted at the step of mixing parameters estimation by maximum likelihood. The step of inserting new component into mixture model, and the step of estimating mixing parameters by expectation maximization algorithm, are alternately applied until component number is equal to the estimate of target number. The candidate set of new mixture components for inserting into mixture model is generated by k-dimensional tree. The incremental finite mixture model unifies the increasing tendency of component number and that of likelihood function so that it contributes to search maximum likelihood solution of mixture parameters step by step. Simulation results show that the proposed state estimation algorithm based on incremental finite mixture model is slight superior to the existing two algorithms in sequential Monte Carlo implementation of probability hypothesis density filter.