A multiple source direction estimation method based on singular value decomposition and null space combination

To address the issue of degraded direction-of-arrival (DOA) estimation performance caused by covariance matrix calculation errors in the Multiple Signal Classification (MUSIC) algorithm and the Minimum Variance Distortionless Response (MVDR) algorithm under unfavorable conditions such as low signal-to-noise ratio (SNR), the number of sources being close to the array elements, and insufficient snapshots, an angle estimation method combining Singular Value Decomposition (SVD) and Null Space Method (NSM) is proposed. This method performs singular value decomposition on the signal receiving matrix, obtains the dominant information space after rank reduction, and then solves a homogeneous linear system of equations to form the null space. Finally, the null space is used to construct a spectrum for estimating the source direction angle. Theoretical analysis and simulation results demonstrate that, compared with MUSIC and MVDR, the proposed method exhibits lower localization errors under various SNR conditions. These results indicate that the combination of SVD and NSM outperforms traditional algorithms in non-ideal acoustic environments, demonstrating superior direction estimation performance, robustness, and stability.