A new per-sample partitioning filter

Abstract

The partitioning approach essentially constitutes an adaptive framework which is a unifying and powerful setting for optimal linear and nonlinear estimation. In particular, for the class of linear estimation problems, model partitioning has yielded [Lainiotis (1971–1979) and Lainiotis and Andrisani (1979, 1983)] two novel and practically useful estimation algorithms. The first algorithm results by partitioning the initial state vector into the sum of two independent random vectors, arbitrarily chosen by the filter designer. Similarly, the second algorithm results by partitioning both the initial state, and the process-noise vectors, respectively, into the sum of two random vectors. These algorithms were shown to posses several computational advantages, and interesting properties. In this paper, based on the above results, a new linear estimation algorithm is obtained. This constitutes a per-sample partitioning version of the above Lainiotis-Andrisani algorithm. Moreover, a computational analysis of the new algorithm is made with respect to computer time and storage requirements. This is compared to the computational requirements of the Kalman filter, and relevant conclusions are drawn. Finally, to demonstrate the practical usefulness of the new algorithm to signal processing, they are applied to the important class of multi-sensor estimation problems, encountered in geophysical data processing, multi-radar problems, etc.