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

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.