Multiple Imputations Particle Filters: Convergence and Performance Analyses for Nonlinear State Estimation With Missing Data

In this paper, we present a multiple imputations particle filter (MIPF) to deal with non-linear state estimation when part of the observations are missing. The MIPF uses randomly drawn values called imputations to provide a replacement for the missing data and then uses the particle filter to estimate non-linear state with the data. Unlike the existing techniques, we do not assume a linear system and also take into account the time-varying transition matrix when accounting for missing data. We present the convergence analysis of the MIPF and show that it is almost surely convergent. We present examples with a non-linear time-varying model, which demonstrate that the MIPF can effectively deal with missing data in nonlinear problems. Comparison with existing techniques further validates the improvement offered by the proposed MIPF.