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A numerical algorithm for stable 2D autoregressive filter design. (English) Zbl 1144.94316

Summary: Based on previous theoretical results we present in this paper a global estimation scheme for solving the stable 2D autoregressive filter problem. The different algorithms are based on the traditional Newton method and on the log barrier method that is employed in semi-definite programming. The Newton method is the faster one but the barrier method ensures that the iterates stay in the cone of positive semidefinites. In addition, a numerical test for the existence of a stable factorization of a two-variable squared magnitude response function is presented.

MSC:

94A11 Application of orthogonal and other special functions
93E11 Filtering in stochastic control theory
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
15B48 Positive matrices and their generalizations; cones of matrices
42B05 Fourier series and coefficients in several variables
47A57 Linear operator methods in interpolation, moment and extension problems
47A20 Dilations, extensions, compressions of linear operators
60G25 Prediction theory (aspects of stochastic processes)
60G10 Stationary stochastic processes

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