Robust Filtering and Smoothing Based on Mixture Similarity Measure with Correlated Noises under Random Disturbance

In this article, we propose the robust recursive Kalman filter along with its Rauch-Tung-Striebel smoother designed for systems with correlated noises at the same epoch, where the control inputs and measurements are subjected to hybrid random disturbances. Given the challenge of correlated noises coupled with unknown disturbance signals in practical applications, we utilize the correlation coefficient between noises to reconstruct the process equation for decorrelation. To tackle the potential disturbances introduced during the decorrelation process and further enhance the estimate accuracy under complicated noise scenarios, a mixture similarity measure (MSM) is proposed to suppress the unexpected random disturbances and noises. Within the MSM framework, we derive the proposed robust filtering and fixed-internal smoothing algorithms through fixed-point iterations and Jensen's inequality. Furthermore, we demonstrate the optimality and convergence of the proposed algorithms by leveraging properties of the Hessian matrix and the Banach theorem. Simulations on target tracking examples illustrate the superiority of the proposed algorithms over related methods, even in scenarios involving non-Gaussian correlated noise.