Bootstrap and High-Degree Cubature Particle Filters for Nonlinear Systems With Correlated Noise and Missing Measurements

In this article, the particle filtering problem is investigated for nonlinear systems with correlated noise and missing measurements (MMs). By accounting for both correlated noise and MMs, a novel explicit weighting expression is presented. Based on this weighting scheme, a new bootstrap particle filtering algorithm is designed to address such influence. Furthermore, to limit the particle degradation suffered by the bootstrap particle filter (PF), a novel importance function based on the Gaussian optimal filter is presented. To perform the numerical integration required by the Gaussian optimal filter, the fifth-degree spherical-radial cubature rule (FSRCR) is used to acquire a novel importance function. Consequently, a novel high-degree cubature particle filtering algorithm is developed for these systems. Simulation experiments show that the two proposed algorithms significantly improve estimation accuracy, with notable performance gains over the existing unscented Kalman filter (KF), especially as the sample size increases.