AN OVERVIEW OF EFFICIENT NONLINEAR FILTERING - FROM KALMAN FILTER TO PARTICLE FILTERS TO EIS

Generally, in most applied fields, the dynamic state space models are of nonlinearity with non-Gaussian noise. However, as a famous and simple algorithmic filter, Kalman filter can only estimate linear system with Gaussian noise state space models. The Extend Kalman filter and the Unscented Kalman filter still have limitations and therefore are not accurate enough for nonlinear estimation. The Bayesian filtering approach which is based on sequential Monte Carlo sampling is called particle filters. Particle filters were developed and widely applied in various areas because of the ability to process observations represented by nonlinear state-space models where the noise of the models can be non-Gaussian. However, particle filters suffer from two long-standing problems that are referred as sample degeneracy and impoverishment. To fight these problems, resampling step is necessary. In this review work, a variety of resampling of particle filter methods as well as their characteristics and algorithms are introduced and discussed, such as Sampling-Importance resampling, Auxiliary particle filter, Optimal resampling and so on to combat against the sample degeneracy and impoverishment. Finally, efficient importance sampling, as a more accurate method, capable of estimating high-dimensional integration and carrying out global optimization, will be introduced and compared to particle filters