Robust algorithms for spherical angle-of-arrival source localization

The performance of traditional algorithms for spherical angle-of-arrival (AOA) source localization will be significantly degraded when there are outliers in the angle measurements. By using the symmetric $\alpha$-stable ($S\alpha S$) distribution to describe the measurement noise containing outliers and constructing the cost function using the $l_p$-norm, we propose a robust algorithm for spherical AOA source localization: the spherical iteratively reweighted pseudolinear estimator (SIRPLE). The SIRPLE is similar to the iteratively reweighted least squares (IRLS), with the difference that a homogeneous least squares (HLS) problem is solved in each iteration. The SIRPLE suffers from bias problems owing to the nature of the pseudolinear estimators. To overcome this problem, the instrumental variable (IV) method is introduced and the spherical iteratively reweighted instrumental variable estimator (SIRIVE) is proposed. Theoretical analysis shows that the SIRIVE is asymptotically unbiased and it can achieve the theoretical error covariance of the constrained least $l_p$-norm estimation. Extensive simulation analyses demonstrate the better performance of the SIRIVE compared to the conventional spherical AOA source localization methods and the SIRPLE under $S\alpha S$ noise environment. The performance of the SIRIVE is similar to that of the Nelder–Mead algorithm (NM), but the SIRIVE are computationally more efficient. In addition, the SIRIVE is nearly unbiased and the root mean square error (RMSE) performance is close to the Cramér–Rao lower bound (CRLB).