Toeplitz and Hankel matrix approximation using structured approach

structures on a model based on available prior informaAlgorithms are presented for least-squares approximation. Earlier work on these problems has primarily contion of Toeplitz and Hankel matrices from noise corsisted of using Singular Value Decomposition [4, 5, 81, rupted or ill-composed matrices, which may not have where only the rank information of the underlying sigcorrect structural or rank properties. Utilizing CarathCodervYl is used. Theorem on complex number representation to model the Toeplitz and Hankel matrices, it is shown that these matrices possess specific row and column structures. The inherent structures of the matrices are exploited to develop a computational algorithm for estimation of the matrices that are closest, in the Frobenius norm sense, to the given noisy or rank-excessive matrices. Simulation studies bear out the effectiveness of the proposed algorithms providing significantly better results than the state-space methods. We use a theorem due to Caratheodery in complex analysis [3], in addition to the rank information of the underlying signal to form a model which imposes certain row and column structures on the Toeplitz and Hankel matrices. This facilitates the development of algorithms, along the lines of [7], for minimization of the Frobenius norm between the noisy and the model matrices, and a consequent reconstruction of the matrices.