Classification of all finite-dimensional nonlinear filters from Lie algebraic point of view: State dimension 2

In this paper, we give a complete classification of all finite dimensional estimation algebras with state space dimension 2. It is shown that a finite-dimensional estimation algebra with state dimension 2 can only have dimension less than or equal to 6. We then use the Wei-Norman approach to construct all finite-dimensional nonlinear filters with state space dimension 2 from the Lie algebraic point of view.

[1]  Daniel Ocone.  Finite Dimensional Estimation Algebras in Nonlinear Filtering , 1981 .

[2]  Stephen S.-T. Yau,et al.  Classification of four-dimensional estimation algebras , 1999, IEEE Trans. Autom. Control..

[3]  Amid Rasoulian,et al.  Finite dimensional filters with non-linear drift IX: construction of finite dimensional estimation algebras of non-maximal rank , 1997 .

[4]  R. Bucy,et al.  A priori error bounds for the cubic sensor problem , 1978 .

[5]  G.-G. Hu.  Finite-dimensional filters with nonlinear drift. , 1997 .

[6]  Michael Hazewinkel.  Lectures on linear and nonlinear filtering , 1988 .

[7]  D. Michel,et al.  Des resultats de non existence de filtre de dimension finie , 1984 .

[8]  S. Marcus,et al.  Nonexistence of finite dimensional filters for conditional statistics of the cubic sensor problem , 1983 .

[9]  Wing Shing Wong.  On a new class of finite dimensional estimation algebras , 1987 .

[10]  Mitter.  On the analogy between mathematical problems of non-linear filtering and quantum physics. Interim report , 1980 .

[11]  V. Benes.  Exact finite-dimensional filters for certain diffusions with nonlinear drift , 1981 .

[12]  Wing Shing Wong,et al.  Structure and classification theorems of finite-dimensional exact estimation algebras , 1991 .

[13]  Wing Shing Wong.  Theorems on the structure of finite dimensional estimation algebras , 1987 .

[14]  Roger Brockett.  Classification and equivalence in estimation theory , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[15]  Wen-Lin Chiou,et al.  Finite-Dimensional Filters with Nonlinear Drift II: Brockett's Problem on Classification of Finite-Dimensional Estimation Algebras , 1994 .

[16]  Stephen S.-T. Yau,et al.  Complete classification of finite-dimensional estimation algebras of maximal rank , 2003 .

[17]  Stephen S.-T. Yau,et al.  Recent results on classification of finite dimensional estimation algebras: dimension of state space >or=2 , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[18]  W. Wong,et al.  The estimation algebra of nonlinear filtering systems , 1998 .

[19]  Wing Shing Wong,et al.  On a necessary and sufficient condition for finite dimensionality of estimation , 1990 .

[20]  Roger W. Brockett,et al.  Nonlinear Systems and Nonlinear Estimation Theory , 1981 .

[21]  S. Marcus.  Algebraic and Geometric Methods in Nonlinear Filtering , 1984 .

[22]  W. Wong.  New classes of finite-dimensional nonlinear filters , 1983 .