Immune adaptive Gaussian mixture particle filter for state estimation

The particle filter (PF) is a flexible and powerful sequential Monte Carlo (SMC) technique capable of modeling nonlinear, non-Gaussian, and nonstationary dynamical systems. However, the generic PF suffers from particle degeneracy and sample impoverishment, which greatly affects its performance for nonlinear, non-Gaussian tracking problems. To deal with those issues, an improved PF is proposed. The algorithm consists of a PF that uses an immune adaptive Gaussian mixture model (IAGM) based immune algorithm to re-approximate the posterior density. At the same time, three immune antibody operators are embed in the new filter. Instead of using a resample strategy, the newest observation and conditional likelihood are integrated into those immune antibody operators to update the particles, which can further improve the diversity of particles, and drive particles toward their close local maximum of the posterior probability. The improved PF algorithm can produce a closed-form expression for the posterior state distribution. Simulation results show the proposed algorithm can maintain the effectiveness and diversity of particles and avoid sample impoverishment, and its performance is superior to several PFs and Kalman filters.