A Key Conditional Quotient Filter for Nonlinear, non-Gaussian and non-Markovian System

TL;DR

This paper introduces a new key conditional quotient filter (KCQF) for estimating states in complex nonlinear systems, improving accuracy by focusing on key measurement conditions and utilizing Monte Carlo methods.

Contribution

The paper presents a novel KCQF that selectively uses key measurement conditions for state estimation in nonlinear, non-Gaussian, and non-Markovian systems, enhancing estimation accuracy.

Findings

KCQF outperforms seven existing filters in accuracy

Uses Monte Carlo for calculating conditional PDFs, means, and variances

Effective for both Gaussian and non-Gaussian, Markovian and non-Markovian systems

Abstract

This paper proposes a novel and 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 are derived by using the principle of probability conservation, and are calculated by using the Monte Carlo method, which thereby constructs the KCQF. Two nonlinear numerical examples were given to demonstrate the superior estimation accuracy of KCQF, compared to seven existing filters.