Likelihood particle filter and its proposed modifications

In this paper, three methods, namely: Hybrid Kalman Filter, Hybrid Kalman Particle Filter, and Likelihood Particle Filter for state estimation have been presented. These algorithms have been applied to three nonlinear objects and one linear object (one- and multivariable systems) and have been compared with Bootstrap Particle Filter. Moreover, authors proposed three modifications of Likelihood Particle Filter, intended for different types of objects. Operation of three particle Filter algorithms, namely Bootstrap Particle Filter, Hybrid Kalman Particle Filter and Likelihood Particle Filter, have been compared for a different number of particles, and the results have been presented together with Extended Kalman Filter, Unscented Kalman Filter and Hybrid Kalman Filter algorithm. It has been shown that Hybrid Kalman Particle Filter gives better results than Bootstrap Particle Filter for a low number of particles. Furthermore, Likelihood Particle Filter provides better than other examined methods output match (through suitable choice of estimated state variables). For the linear object, Kalman Filter algorithm is the best.