The structure of Omega-matrix in nonlinear filters

The structure of Omega = (w(ij)), a matrix related to the estimation algebras in nonlinear filtering theory, plays a major role in determining the finite dimensionality of these algebras. In this paper we give a simple view of this important matrix, i.e. although the drift term f = (f(1.) f(2.) ..., f(n)) is a C-infinity function, the entries of Omega, w(ij) = partial derivative f(j)/partial derivative x(i) - partial derivative f(i)/partial derivative x(i) are polynomials.