In underwater radiated noise measurement using a vertical linear array, a diagonalization-decorrelation-based diagonal denoising method is proposed to improve the denoising effect for spatially correlated noise. Firstly, the ambient noise cross-spectral matrix is measured without the radiated noise source. Subsequently, the eigenvector matrix of the ambient noise cross-spectral matrix is utilized to implement a unitary transformation for the received data, which eliminates the correlation of the received noise and transforms the received noise cross-spectral matrix into a diagonal matrix, then the noise components are removed by diagonal denoising. Finally, the denoised cross-spectral matrix is used to estimate the power of the radiated noise by beamforming. Consequently, the influence of spatially correlated noise on radiated noise measurement is reduced. The effectiveness of the proposed method is validated and compared with the diagonal denoising method and the whitening-decorrelation-based diagonal denoising method via numerical simulations and experimental data. Under the ideal condition, the noise reduction performances of the proposed method and the whitening-decorrelation-based diagonal denoising method are equal and better than that of the diagonal denoising method. In practice, the number of snapshots is limited, so there is an inevitable mismatch between the ambient noise cross-spectral matrix and the received noise cross-spectral matrix due to the randomness of noise. The mismatch results in imperfect whitening and diagonalization, which reduces the denoising effect. However, the simulation results indicate that the proposed method still reduces more correlated noise and has a better performance on underwater radiated noise measurement compared with the diagonal denoising method and the whitening-decorrelation-based diagonal denoising method even if the number of snapshots is finite.

Underwater radiated noise power estimation is crucial for the quantitative assessment of noise levels emitted by ships and underwater vehicles. This paper therefore proposes a maximum likelihood estimation method for determining the power of underwater radiated noise. The method establishes the probability density function of the hydrophones array received data and derives the minimum variance unbiased estimation of the power through theoretical analysis under the maximum likelihood criterion. Numerical simulations and experimental data demonstrate that this method can significantly reduce the influence of ambient noise on estimation results and improve the estimation accuracy under low signal-to-noise ratio conditions, outperforming commonly used beamforming-based estimation methods. In addition, the estimation variance achieves the Cramér–Rao lower bound, which is consistent with theoretical derivation. When the source position is unknown, this method can simultaneously localize the sound source and estimate its power by searching for the maximum value within a specified region.