Harmonic retrieval in multiplicative and additive noise based on the generalized covariance matrix

For the harmonic retrieval in nonzero mean multiplicative noise, we propose a new method to estimate the number of harmonics and frequencies of the harmonics in multiplicative noise based on the generalized covariance matrix. We first define a generalized covariance, and then construct a covariance matrix using the defined generalized covariance. Analyzed the eigenvalues of the covariance matrix, we get the inherent relation between the number of harmonics and the eigenvalues of the covariance matrix. This relation can be used to estimate the number of harmonics in multiplicative noise. Meanwhile, the frequencies of harmonics can be estimated via subspace rotational invariance. The proposed method does need to assume the color and distribution of the multiplicative and additive noise, and it can be applied to harmonic retrieval in multiplicative and additive noise with any color and any distribution. The simulation results demonstrated that the proposed method is high-resolution.