Notices of the International Consortium of Chinese Mathematicians

Volume 10 (2022)

Number 2

Recent progresses on two suboptimal methods for nonlinear filtering problems

Pages: 44 – 52



Xue Luo (School of Mathematical Sciences, Beihang University, Beijing, China; and Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China)

Huimin Miao (School of Mathematical Sciences, Beihang University, Beijing, China)


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.


This work is financially supported by the National Key R&D Program of China (grant no. 2022YFA100503), by the National Natural Science Foundation of China (grant no. 12271019, 11871003, 11961141005), and by the Fundamental Research Funds for the Central Universities (grant no. YWF-22-L-640).

Published 6 February 2023