Recent results on finite dimensional exact estimation algebras

In a series of papers by W.S. Wong (1987), new results were announced giving necessary and sufficient conditions for a certain class of estimation algebras to be finite dimensional. Building on these results, the authors presented in a recent paper (to appear in SIAM J. Control and Optimization) a simple algebraic necessary and sufficient condition for the estimation algebra of a certain class of filtering systems to be finite dimensional. This result makes it possible to derive a rigorous proof of the Wei-Norman program, leading the authors to reexamine certain partial differential equations first associated with the Benes filters. The goal of this study is to provide a brief summary of these results