Harmonic retrieval via state space and fourth-order cumulants

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 method developed for solving this problem relies on the use of a diagonal form state space model representation of the harmonic retrieval problem. Fourth-order cumulants are employed as the signal processing technique. It is shown that using this approach the unknown frequencies can be estimated by finding the eigenvalues of a symmetric matrix made up from the cumulants of the data. Simulation results show the effectiveness of this method when the signals are corrupted by Gaussian noise (white or colored)