Structure theorem for six-dimensional estimation algebras

The problem of classification of finite-dimensional estimation algebras was formally proposed by Brockett in his lecture at International Congress of Mathematicians in 1983. Due to the difficulty of the problem, in the early 1990s Brockett suggested that one should understand the low-dimensional estimation algebras first. In this paper, We extend Yau and his coauthors' work of the Mitter conjecture for low dimensional estimation algebras in nonlinear filtering problem. And we apply the results to give classification of estimation algebras of dimension six.

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

[2]  Jie Chen,et al.  Finite-Dimensional Filters with Nonlinear Drift VII: Mitter Conjecture and Structure of $\eta$ , 1997 .

[3]  Jie Chen,et al.  Finite-dimensional filters with nonlinear drift, VI: Linear structure of Ω , 1996, Math. Control. Signals Syst..

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

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

[6]  Jie Chen,et al.  Finite-Dimensional Filters with Nonlinear Drift VIII: Classification of Finite-Dimensional Estimation Algebras of Maximal Rank with State-Space Dimension 4 , 1996 .

[7]  Xi Wu,et al.  Classification of Estimation Algebras with State Dimension 2 , 2006, SIAM J. Control. Optim..

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

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

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

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

[12]  Stephen S.-T. Yau,et al.  Mitter conjecture for low dimensional estimation algebras in non-linear filtering , 2008, Int. J. Control.

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

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

[15]  S. Yau,et al.  Finite-dimensional filters with nonlinear drift. III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for the linear filtering system and the Benes filtering system , 1997, IEEE Transactions on Aerospace and Electronic Systems.

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

[17]  Stephen S.-T. Yau,et al.  Structure theorem for five-dimensional estimation algebras , 2006, Syst. Control. Lett..