Toeplitz and Hankel matrix approximation using structured approach

Algorithms are presented for least-squares approximation of Toeplitz and Hankel matrices from noise corrupted or ill-composed matrices, which may not have correct structural or rank properties. Utilizing Caratheodery 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.