Robust Direction-of-Arrival Estimation With Outliers and Partly Calibrated Uniform Linear Array

This article presents a three-step direction-of-arrival estimation method aimed at addressing impulsive noise and array gain-phase errors. Initially, a robustness function combining the logarithmic function with least squares is introduced to address impulsive noise. This robust function is utilized to formulate a low-rank matrix approximation problem for acquiring noise-free received data, which is solved using the alternating-direction method of multipliers. Subsequently, exploiting the obtained noise-free received data, the array gain-phase errors are estimated using the root-rank reduction estimator. Finally, based on the acquired noise-free received data and gain-phase errors, a minimization problem incorporating the logarithmic function is formulated. To efficiently solve this minimization problem, it is transformed into a weighted $l_{2,1}$-norm minimization problem, and the fast-iterative-shrinkage-thresholding algorithm is employed. Compared to existing methods, the proposed approach demonstrates superior estimation accuracy and precision while achieving an attractive tradeoff between performance and computational complexity.