A recursive filter for a class of two-dimensional nonlinear stochastic systems

Shulan Kong; Chengbin Wang; Yawen Sun; Shulan Kong; Chengbin Wang; Yawen Sun

doi:10.3934/math.2025079

AIMS Mathematics

2025, Volume 10, Issue 1: 1741-1756. doi: 10.3934/math.2025079

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A recursive filter for a class of two-dimensional nonlinear stochastic systems

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China
2.
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

Received: 24 August 2024 Revised: 12 December 2024 Accepted: 30 December 2024 Published: 24 January 2025

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.
- two-dimensional nonlinear systems,
- filter,
- minimum variance,
- random parameter matrix,
- random nonlinearity
Citation: Shulan Kong, Chengbin Wang, Yawen Sun. A recursive filter for a class of two-dimensional nonlinear stochastic systems[J]. AIMS Mathematics, 2025, 10(1): 1741-1756. doi: 10.3934/math.2025079

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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.

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