Performance analysis and robust DOA estimation using acoustic vector sensor array under non-orthogonal deviation

In this paper, the problem of direction of arrival (DOA) estimation under the non-orthogonal deviation (NOD) in an acoustic vector sensor array (AVSA) is systematically addressed. First, by incorporating NOD information into the ideal AVSA model, two AVSA models with NOD are established. Subsequently, closed-form expressions for DOA estimation bias, the Cramér-Rao lower bound (CRLB), and the root mean square error (RMSE) are analytically derived for scenarios where each AVS exhibits NOD to illustrate the degrading influence of NOD on DOA estimation accuracy. To mitigate the effect of NOD, an innovative optimal modification matrix construction (OMMC) method is proposed. The NOD range of each AVS is initially coarsely estimated using prior information from a known auxiliary source and the theoretical RMSE. Based on the estimated deviation range, an overcomplete redundant correction matrix is constructed, which is used to calibrate the measurement data of each AVS. The optimal correction matrix is selected by minimizing the deviation between the estimated and true DOAs, and a global correction matrix for the entire array is formed by extracting the optimal correction sub-matrix for each AVS, thereby enabling accurate array calibration. A comprehensive performance evaluation is conducted through extensive simulations, where the proposed OMMC method is demonstrated to significantly outperform existing techniques, especially in challenging environments with large NOD or limited snapshot.