Partitioning: The multi-model framework for estimation and control, I: Estimation

Abstract

Partitioning, the multi-model framework for estimation, and control introduced by Lainiotis [1–26], constitutes the unifying and powerful framework for optimal estimation and control, for linear as well as nonlinear problems. Partitioning is the natural setting for estimation problems, since it decomposes the original estimation problem into a set of estimation problems of considerably reduced complexity, the optimal or suboptimal estimators of which are far easier to derive and, most importantly, they are far easier to implement. Using the partitioning approach, estimation problems are treated from a global viewpoint that readily yields and unifies previous, seemingly unrelated, results, and most importantly, yields fundamentally new classes of optimal and suboptimal estimation formulas in a naturally decoupled, parallel-realization form. The partitioning estimation formulas are of considerable theoretical significance. They provide insight into the nature of estimation problems, and the structure of the resulting estimators. Most importantly, the partitioning estimation formulas yield realizations of optimal and suboptimal estimators, both filters and smoothers, that have significantly reduced complexity, that are computationally attractive, and numerically robust, and whose practical implementation may be done in a pipeline or parallel-processing mode. Indeed, the flexible structure of the partitioning estimation algorithms affords a wide variety of serial-parallel processing combinations that can meet the computational and storage constraints of a large class of practical applications, especially realtime ones.