Recent Progresses on Two Suboptimal Methods for Nonlinear Filtering Problems

The nonlinear filtering (NLF) aims to yield a good estimation of the signal/state corrupted with noise, based on the noisy observations. In 2014’s survey paper [31], the NLF methods are classified into two categories, the local and global approaches, by examining whether it approximates the posterior distribution of the states or only a finite number of the statistical quantities. Compared with the global approaches, the local ones are more computational friendly. In this survey, we shall discuss two recently developed suboptimal local methods for solving NLF problems, with emphasis on their reasonableness from a mathematical point of view.