Parameter Estimation of Two-Dimensional Linear Differential Systems Via Fourier Based Modulation Function

Abstract: In this paper, parameter identification of two-dimensional (2-D) linear differential systems via two-dimensional modulating functions is proposed. In this method, a partial differential equation on the finite time intervals converts into an algebraic equation linear in parameters. Then the parameters of the system can be estimated using the least squares algorithm. The underlying computations utilize a 2-D fast Fourier transform algorithm on polynomials of the data without the need for estimating unknown initial or/and boundary conditions at the beginning of each finite time interval. Numerical simulations are presented to confirm the theoretical results.