@article{Kong2025, 
author = {Shulan Kong and Chengbin Wang and Yawen Sun},
title = {A recursive filter for a class of two-dimensional nonlinear stochastic systems},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1741-1756},
keywords = {filter, two-dimensional nonlinear systems, minimum variance, random parameter matrix, random nonlinearity},
url = {https://www.sciopen.com/article/10.3934/math.2025079},
doi = {10.3934/math.2025079},
abstract = {A recursive filtering problem on minimum variance is investigated for a type of two-dimensional systems incorporating noise and a random parameter matrix in the measurement equation, along with random nonlinearity. It methodically describes random variables using statistical characteristics, placing a strong emphasis on the application of random multivariate analysis and computational techniques. A bidirectional time-sequence recursive filter is designed to achieve unbiasedness and reduce error variance effectively. This involves deriving the gain matrix through a completion of squares method and solving a complex difference equation with two independent variances. To facilitate the online implementation of this filter, various formulations and an algorithm are proposed. A numerical study demonstrates the effectiveness of the design in practical applications.}
}