Nonlinear and Non-Gaussian State-Space Modeling with Monte Carlo Techniques: A Survey and Comparative Study

Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or non-Gaussian state estimation problems have been developed. Numerical integration becomes extremely computer-intensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integration with importance sampling, resampling, rejection sampling, Markov chain Monte Carlo and so on are utilized, which can be easily applied to multi-dimensional cases. Thus, in the last decade, several kinds of nonlinear and non-Gaussian filters and smoothers have been proposed using various computational techniques. The objective of this paper is to introduce the nonlinear and non-Gaussian filters and smoothers which can be applied to any nonlinear and/or non-Gaussian cases. Moreover, by Monte Carlo studies, each procedure is compared by the root mean square error criterion.