Cumulant based approach to harmonic retrieval problem using a state space model

The harmonic retrieval problem considered concerns the estimation of the frequencies in a sum of complex sinusoids in the presence of Gaussian measurement noise. The approach used involves representing this problem as a realization problem in the state space. Fourth-order cumulants are used as a signal processing tool. It is shown that the estimation of the unknown frequencies can be achieved by solving a generalized eigenvalue problem involving a Hankel matrix composed from the fourth-order cumulants of the measured output. Simulation results show the effectiveness of this method when the signals are corrupted by Gaussian noises (white or colored)