Classification of four-dimensional estimation algebras

Of central importance in nonlinear filtering theory is the classification of finite-dimensional estimation algebras, through which we can construct recursive filters. We classify all t-dimensional estimation algebras, t/spl les/4, for arbitrary state space dimension.

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

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

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

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

[5]  Rogelio Lozano,et al.  Adaptive control of continuous-time overmodeled plants , 1996, IEEE Trans. Autom. Control..

[6]  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.

[7]  G. Burstein,et al.  Homotopy Theoretic Control Problems in Nonlinear Differential Geometric Control Theory , 1986 .

[8]  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 .

[9]  R. Lozano-Leal Robust Adaptive Regulation without Persistent Excitation , 1989, 1989 American Control Conference.

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

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

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

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

[14]  S. Yau,et al.  Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[15]  D. Ocone Topics in Nonlinear Filtering Theory. , 1980 .

[16]  D. Mayne,et al.  Design issues in adaptive control , 1988 .

[17]  M. M'Saad,et al.  Robust adaptive regulation with minimal prior knowledge , 1990, 29th IEEE Conference on Decision and Control.

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

[19]  Lei Guo Self-convergence of weighted least-squares with applications to stochastic adaptive control , 1996, IEEE Trans. Autom. Control..