A key conditional quotient filter for nonlinear, non-Gaussian, and non-Markovian systems

Yue Zeng; Yuelin Zhao; Feng Wu; Li Zhu; Yue Zeng; Yuelin Zhao; Feng Wu; Li Zhu

doi:10.3934/math.2026366

AIMS Mathematics

2026, Volume 11, Issue 4: 8879-8902. doi: 10.3934/math.2026366

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Research article

A key conditional quotient filter for nonlinear, non-Gaussian, and non-Markovian systems

Dalian University of Technology, Dalian 116024, China

Received: 23 January 2026 Revised: 19 March 2026 Accepted: 24 March 2026 Published: 01 April 2026
MSC : 93E10

In this paper, we propose a novel efficient key conditional quotient filter (KCQF) for the estimation of state in the nonlinear system, which can be either Gaussian or non-Gaussian, and either Markovian or non-Markovian. The core idea of the proposed KCQF is that only the key measurement conditions, rather than all measurement conditions, should be used to estimate the state. Based on key measurement conditions, the quotient-form analytical integral expressions for the conditional probability density function, mean, and variance of state were derived using the principle of probability conservation, and were calculated using the Monte Carlo method, which thereby constructed the KCQF. Three numerical examples were given to demonstrate the superior estimation accuracy of KCQF, compared to ten filters. The experimental results demonstrated that the KCQF algorithm not only accurately addresses nonlinear problems with high precision but also directly handles navigation issues under time-varying noise conditions.
- estimation,
- filtering,
- nonlinear systems,
- stochastic systems,
- key conditional quotient
Citation: Yue Zeng, Yuelin Zhao, Feng Wu, Li Zhu. A key conditional quotient filter for nonlinear, non-Gaussian, and non-Markovian systems[J]. AIMS Mathematics, 2026, 11(4): 8879-8902. doi: 10.3934/math.2026366

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Abstract

In this paper, we propose a novel efficient key conditional quotient filter (KCQF) for the estimation of state in the nonlinear system, which can be either Gaussian or non-Gaussian, and either Markovian or non-Markovian. The core idea of the proposed KCQF is that only the key measurement conditions, rather than all measurement conditions, should be used to estimate the state. Based on key measurement conditions, the quotient-form analytical integral expressions for the conditional probability density function, mean, and variance of state were derived using the principle of probability conservation, and were calculated using the Monte Carlo method, which thereby constructed the KCQF. Three numerical examples were given to demonstrate the superior estimation accuracy of KCQF, compared to ten filters. The experimental results demonstrated that the KCQF algorithm not only accurately addresses nonlinear problems with high precision but also directly handles navigation issues under time-varying noise conditions.

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