Multipartitioning in distributed parameter adaptive estimation

Abstract

In this paper the generalized partitioned algorithm (GPA) similar to the one applicable to lumped parameter systems is derived first for the case of distributed parameter systems and subsequently used as the basis for studying multi-partitioning estimation problems. The fundamental nature of this algorithm is demonstrated by showing that this approach contains as special cases important generalizations of well established distributed-parameter filtering and smoothing approaches. The structure of GPA is also appropriate for studying estimation problems the initial conditions of which may be partitioned into a sum of jointly gaussian random variables which may also be statistically dependent. The form of the resulting algorithm consists of an imbedded distributed parameter Kalman filter and hence the multi-partitioning structure. This multi-partitioning structure can in many cases be used as the mathematical tool in studying parameter identification problems.