Linear Optimal Kalman Estimators for Generalized System with Complex-Colored Noises

This paper addresses the optimal linear estimation problem for a generalized system with complex-colored noises. The complex-colored noises in the generalized system primarily mean that measurement noise and input white noise are all colored noises. By singular value decomposition, and extended state approach, the original system can be transformed into two reduced-order subsystems with augmented uncorrelated noises. Then the problem of optimal Kalman estimation is transformed into estimation problem for augmented systems. Based on Kalman filtering theory, the time-varying Kalman estimators of the original generalized system are presented. The effectiveness of the proposed algorithm is verified by a numerical simulation example.