Discrete-time complementary models and smoothing algorithms: The correlated noise case

The concept of complementary models for discrete-time linear finite dimensional systems with correlated observation and process noise is developed. 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 ??o. Next, using the framework developed in Sections II and III, a new and a simple derivation of the two-filter smoother is presented. Furthermore the relationship between the new smoothing algorithm, the two-filter 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.