On-line harmonic signal denoising from the measurement with non-stationary and non-Gaussian noise

• An online algorithm based on the Bayesian Maximum a Posteriori (MAP) is proposed. • The Gaussian Mixture Model (GMM) is adopted to fit the non-Gaussian noise. • The online Expectation Maximization (EM) algorithm is derived Harmonic denoising is one of the important preprocessing steps before extracting harmonic signal characteristics. Several signal processing techniques have been developed and applied for denoising the harmonics, which assume that the noise follows a Gaussian distribution and is stationary. However, the noise is often not so simple as a Gaussian distribution, and it could be non-Gaussian and non-stationary in most practical scenarios. A novel online denoising method for the harmonic signal with non-stationary complex noises based on the Bayesian Maximum a Posteriori (MAP) framework is proposed in this paper. The measured signal is divided equally into several frames. Then these frames are transformed into the time-frequency domain by the Short-Time Fourier transform (STFT) and are assumed to be the sum of a low-rank matrix and a noise matrix. The online model of the low-rank matrix and the noise matrix is then constructed between the frames. The online Gaussian mixture model (GMM) and low-rank matrix factorization are performed on the measurement matrix in the complex number domain to reconstruct the harmonic signal. The performance of the proposed method is validated in the simulations. The non-Gaussian and non-stationary noise can be removed more effectively, and the proposed algorithm can improve the frequency estimation accuracy.