Classification of Finite Dimensional Filters from Lie Algebraic Point of View,
Abstract
Ever since the technique of the Kalman-Bucy filter was popularized, there has been an intense interest in finding new classes of finite dimensional recursive filters. In the late seventies, the concept of the estimation algebra of a filtering system was introduced. It has proven to be an invaluable tool in the study of nonlinear filtering problems. In 1990, the present author considered a general class of nonlinear filtering systems which include both Kalman-Bucy filtering systems and Benes filtering systems as special cases. A simple algebraic necessary and sufficient condition was established for an estimation algebra of this class of filtering systems to be finite dimensional. Consequently the present author has rigorously constructed a new class of finite dimensional filters which include both Kalman-Bucy filters and Bene's filters as special cases. In 1991, Chiou and the present author have shown that the above new class of finite dimensional filters are the most general filters from Lie algebraic point of view.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1992
- Accession Number
- ADP006626
Entities
People
- Stephen S. T. Yau
Organizations
- University of Illinois at Chicago