A unifying approach to linear estimation via the partitioned algorithms, II: Discrete models

In a radically new approach to linear estimation, Lainiotis [9-11] obtained fundamentally new discrete filtering and smoothing algorithms in a "partitioned" or decomposed form. The partitioned algorithms were shown to have several theoretically interesting and computationally attractive properties. In this paper, a companion to part I on continuous models [13], the fundamental nature of the partitioned algorithms is demonstrated by showing that the discrete partitioned algorithms serve as the basis of a unifying approach to discrete linear filtering and smoothing. Specifically, generalized discrete partitioned algorithms are presented that are theoretically interesting, computationally attractive, and all encompassing. The all encompassing nature of the generalized partitioned algorithms is demonstrated by showing that they contain as special cases all previous major filtering and smoothing algorithms. More importantly, they yield important generalizations, of past well-known algorithms, as well as whole families of such algorithms.