A Gaussian-Mixture-Based Bayesian Filter With Unknown Fading Measurements

In this research, a novel Bayesian filter is constructed to address the state estimation problem for non-Gaussian systems with multiple fading measurements and unknown parameters. Specifically, the non-Gaussian property arises from the non-linear dynamics and fading measurements. The multiple fading phenomenon is modeled by a diagonal matrix whose entries are independently Gaussian-distributed with distinct unknown means and variances. Then the prior distribution is approximated by the moment matching technique and the non-Gaussian statistics are transformed into a tractable form. For handling nonlinearity, the cubature rule is utilized to compute nonlinear integrals. Given the combined challenges of unknown parameters and non-Gaussian characteristics, a weighted linear combination of two Gaussian distributions is proposed to approximate the measurement likelihood function. Within this framework, the means and covariances of the aforementioned distributions are treated as unknown variables and jointly estimated alongside system states via the variational Bayesian approach. To validate the proposed method, a target tracking simulation is conducted under scenarios with unknown fading measurements.