A learning drift homotopy particle filter

In this paper, we design a learning drift homotopy particle filter algorithm. We employ the drift homotopy technique in the extra Markov Chain Monte Carlo move after the resampling step of the generic particle filter algorithm to efficiently resolve the degeneracy of the algorithm. In this work, we use the effective sample size as a learning parameter to control the levels of drift homotopy which need to be considered in each time step. The proposed algorithm adjusts the number of levels of drift homotopy and reduces its computational time without undermining the accuracy of estimation. We test the algorithm on two synthetic problems, a partially observed diffusion in a double well potential and a multi-target tracking setting.