Estimating the frequencies of harmonics in additive colored noise based on the rotational invariance of subspace

The harmonic retrieval in noise is the classic problem in the signal processing, and it has been applied to many signal processing areas. This paper studies the estimation of frequencies in additive colored noise, and proposes a method to estimate the frequencies of the harmonics based on the rotational invariance of subspace. A covariance matrix is constructed using the self-covariance of observed harmonic signals. The inherent relation between the frequencies of harmonics in additive colored noise and the covariance matrix is derived, and it can be used to estimate the frequencies of harmonics in additive colored noise. The proposed method does need to assume the model of the noise and can be implemented without the knowledge of the distribution of the noise. It can be applied to harmonic retrieval in Gaussian and non-Gaussian colored noise. The simulation results demonstrated the effectiveness of the proposed method.