Finite-dimensional filters with nonlinear drift. VI: Linear structure of \(\Omega\) (Q1356631)

[For reviews of Part I, II and IV see Zbl 0811.93059, Zbl 0809.93060 and Zbl 0847.93062, respectively.] The authors study the structure of quadratic forms in a finite-dimensional nonlinear filter by estimation algebra. They prove that if the estimation algebra is finite-dimensional and of maximal rank, then the \(\Omega=(\partial f_j/\partial x_i-\partial f_i/\partial x_j)\) matrix, where \(f\) denotes the drift term, is a linear matrix in the sense that all the entries in \(\Omega\) are degree one polynomials. This theorem plays a fundamental role in the classification of finite-dimensional estimation algebra of maximal rank.