Abstract
Ever since the concept of estimation algebra was first introduced by Brockett and Mitter independently, it has been playing a crucial role in the investigation of finite-dimensional nonlinear filters. Researchers have classified all finite-dimensional estimation algebras of maximal rank with state space less than or equal to three. In this paper we study the structure of quadratic forms in a finite-dimensional estimation algebra. In particular, we prove that if the estimation algebra is finite dimensional and of maximal rank, then the Ω=(∂f j /∂x i −∂f i /∂x j )matrix, wheref denotes the drift term, is a linear matrix in the sense that all the entries in Ω are degree one polynomials. This theorem plays a fundamental role in the classification of finite-dimensional estimation algebra of maximal rank.
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This research was supported by Army Research Office Grants DAAH 04-93-0006 and DAAH 04-1-0530.
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Chen, J., Yau, S.S.T. Finite-dimensional filters with nonlinear drift, VI: Linear structure of Ω. Math. Control Signal Systems 9, 370–385 (1996). https://doi.org/10.1007/BF01211857
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DOI: https://doi.org/10.1007/BF01211857