Fractionally Delayed Bayesian Approximation Filtering under Non-Gaussian Noisy Environment

Gaussian filtering traditionally suffers from two major drawbacks: i) Gaussian approximation of the intrinsic non-Gaussian measurement noises and ii) ignoring delay in measurements. This paper designs an advanced Gaussian filtering algorithm for addressing the two drawbacks and improving the accuracy. The proposed method is abbreviated as GFMCFD, indicating Gaussian filtering under maximum correntropy (MC) criterion for fractionally delayed measurements. The MC criterion-based design enables the proposed GFMCFD to handle the non-Gaussian noises. Moreover, to deal with the delay, the proposed GFMCFD stochastically identifies the delay and uses the current measurement to estimate the desired state at a past instant, depending on the preidentified delay. Thereafter, it later updates the estimated state till the current time instant using state dynamics to perform real-time estimation. Interestingly, the proposed GFMCFD considers the delay as a fractional multiple of sampling interval. The improved accuracy of the proposed GFMCFD is validated for two nonlinear filtering problems.