Abstract:The fixed-lag smoothing problem is investigated for linear time-delay systems with multiplicative noise. The problem can be transformed into an estimate of stochastic system with unknown noises through compensation of fictitious noises. The smoother is presented by solving Riccati-type equations with the same dimension as the original systems based on the reorganized innovation approach and projection theory in Hilbert space. Therefore, there is computational advantage over traditional approaches. Simulation results show the effectiveness of the algorithm.