FA4 9:4§ DISCRETE-TIME COEPLEMENTARY MODELS and SMOOTYING ALGORITHMS :
B. Desai, Howard L. Weinert, Gene J. Yusypchuk · 1981
The concept of complementary models for discrete-time linear finite dimensional systems with correlated observation and process noise is devel:, oped. Using this concept a new algorithm for the fixed interval smoothing problem is obtained. The new algorithm offers great flexibility with respect to changes in the initial state variance no. Next, using the framework developed in Sections I1 and 111, a new and a simple derivation of the two-filter smoother is presented. Furthermore the relationship betwcen the new smoothing algorithm, the twofilter smoother and the reversed-time Kalman filter is explored. It is shown that a similarity transformation on the Hamiltonian system simultaneously produces the new smoothing algorithm as well as the reversed-time Kalman filter.