Particles resampling scheme using regularized optimal transport for sequential Monte Carlo filters

A resampling method is presented for improving the performance of particle filters by using adaptive numbers of the resampling particles. The proposed method replaces the resampling step of a sequential importance resampling particle filter with regularized optimal transport that makes use of the transport plan to warp a posteriori weights into desired weights. The basis of the method is the same as an ensemble transform particle filter that uses the linear transformation step in the resampling of particles. However, the linear transformation step in ensemble transform particle filter is computationally expensive and needs relaxation matching between the two samples for robust processing. Furthermore, its performance can be degraded if the number of the effective particles becomes below the required number of particles, which represents the needed particle number of importance sampling. Therefore, in this paper, a regularized optimal transport method is used to deal with computational load reduction and relaxation matching in the resampling step by using a modified Sinkhorn-Knopp algorithm that considers the process iteration rate convergence. In order to maintain the proper number of the effective particles for states estimation, Kullback-Leibler distance sampling method is also implemented in the resampling process. The proposed method is evaluated by theoretical analysis including simple simulations compared with the conventional resampling methods. According to the simulations, the proposed method indicates that estimation accuracy is better than conventional methods with small number of the effective particles.