Steady-State Optimal Filtering for Continuous Systems With Time-Delay

This paper is concerned with the steady-state optimal filtering problem for continuous-time systems with l delayed measurements. The design of the filter involves in solving one spectral factorization with time-delays, which is the key problem to be solved. A novel approach for the spectral factorization is proposed based on reorganized innovation analysis. The calculation of spectral factor comes down to solving l+1 standard Riccati equations with the same dimension as the original systems.