The structure of Ω-matrix in nonlinear filters

The structure of Ω=(ω_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=(f₁, f₂, …, f_n) is a C^∞ function, the entries of Ω, ω_ij =∂f_i/∂x_i-∂f_i /∂x_j, are polynomials