New Optimal Smoothing Algorithm for Linear Time-varying System with Correlative Noises

The design problem of state optimal smoothers for a class of linear time-varying system with correlative noises is studied in this paper. A new state smoothing algorithm is designed on the basis of minimum mean square error estimation to the limitations of the conventional method, which are the complexity of computing and the call for state transition matrix to be nonsingular. The new algorithm is simpler and easier to implement than the traditional method. It also provides a new tool for solving the signal and state estimation problem in practice. A simulation example also shows its effectiveness.