Confidence set-membership FIR filter for discrete time-variant systems

In this paper, a confidence set-membership filter based on the finite impulse response (FIR) structure is proposed for time-variant systems that are simultaneously subject to both the unknown but bounded noises and the Gaussian noises. At each step, the filter provides a confidence state set that includes the true state with an adjustable confidence level. The FIR structure improves the robustness and brings more degrees of freedom to the filter design. Multiple recent measurements within a moving horizon are fully utilized to construct and optimize each confidence state set. Under two different size criteria, an analytical solution and an LMI-based numerical solution for the filter gain are derived by minimizing the size of the confidence state set, respectively. Finally, an example is given to illustrate the effectiveness and superiority of the algorithms.