Linear Optimal Estimation for Discrete-Time Measurement Delay Systems With Multichannel Multiplicative Noise

This brief investigates the estimation problem for multiplicative noise systems with measurement delay. Multiplicative noise is usually assumed to be a scalar in existing literature works. We consider multichannel multiplicative noise represented by a diagonal matrix in this brief. First, based on the reorganized innovation approach, the finite-horizon filter is derived in terms of two Riccati difference equations of the same dimension as that of the given system and one Lyapunov difference equation. Then, a sufficient condition for the existence of the steady filter is presented. Finally, we provide a numerical example to demonstrate the efficiency of the proposed approach.