Spurious peak-resistant frequency-difference DOA estimation via sparse Bayesian learning

Frequency-difference methods reduce the processing frequency by conjugate multiplication of high-frequency signals, and can effectively mitigate spatial aliasing in direction-of-arrival estimation for underwater targets using sparse arrays. However, frequency-difference processing also broadens the main lobe of the spatial spectrum and results in relatively high sidelobe levels. To address these issues, this paper applies sparse Bayesian learning (SBL) to frequency-difference beamforming, exploiting the high-resolution capability of SBL to improve the direction estimation accuracy of frequency-difference methods. In addition, to suppress spurious peaks caused by cross terms introduced by conjugate multiplication, an iterative refined dictionary frequency-difference sparse Bayesian learning (IRD-FDSBL) method is proposed. The proposed method dynamically removes interference vectors from the dictionary matrix by quantifying the stability of spectral peaks at different frequency points, and eliminates spurious peaks through multiple iterations of dictionary updating. Simulation and sea-trial experimental results demonstrate that, compared with conventional frequency-difference beamforming, the proposed method achieves higher resolution and direction estimation accuracy. In underwater multi-target direction estimation scenarios, it can effectively suppress spurious peaks, prevent weak target peaks from being masked by high sidelobes in the spatial spectrum, and improve the accuracy of direction estimation.