Nonlinear State Estimation Using A Particle Filter with Likelihood Proposal Distributions

State estimation is a central problem in many engineering applications. Traditionally, Kalman filters are widely used for linear systems with additive Gaussian noise. But the many dynamic systems are much more complex, usually involve nonlinear and non-Gaussian elements. Bearing the nature of sequential importance sampling (SIS) and Monte Carlo approach, particle filtering (PF) has emerged as a superior alternative to the traditional nonlinear filtering methods. The basic idea of a particle filter is to approximate the PDF of system states by a set of weighted samples (known as particles) generated from a proposal distribution. The performances of particle filters are strongly influenced by the choice of the proposal distributions, which usually involves complex algorithms and heavy computational load. In real world applications, when compared to dynamic system modeling, the accurate measurement model and measurements are relative easy to obtain. In this case, the system likelihood will provide reliable information of the system state. In this paper, we propose a new PF algorithm which uses the system likelihood as the proposal distribution. In addition, a Metropolis-Hastings algorithm is also integrated into the new algorithm to mitigate the side effect introduced by resampling. As demonstrated by the simulation results, this algorithm can provide good estimations without significantly increase the algorithm complexity.