Joint DOA Estimation and Distorted Sensor Detection

The exact knowledge of array manifold is vital for finding the direction of arrival (DOA) of targets, while the sensor gain and phase uncertainties can degrade the estimation performance. Focusing on the array uncertainty induced by distorted sensors, we present a robust DOA estimation algorithm for a uniform linear array, where source enumeration and distorted sensor detection are also accomplished. The received array data in the presence of sensor uncertainties are decomposed into a low-rank matrix and a row-sparse component, corresponding to the perfect array observations and errors, respectively. Rather than tackling these two terms in a separate manner, we review their relationship and jointly optimize the perfect array observations and the sparse gain-phase error vector. When formulating the model, variables with the low-rankness or sparsity property are directly regularized by the rank function or ℓ₀-norm, instead of their surrogates. We tackle the resultant problem using a block proximal linear method so that closed-form solutions to the subproblems are derived. The subsequent ℓ₀-norm optimization is solved via the hard-thresholding operator, where the threshold is adaptively determined by our designed scaled quartile scheme. Such an ℓ₀-norm minimization scheme also addresses the tasks of source enumeration and distorted sensor detection. Besides, the convergence of our method is proved. To verify its effectiveness, comprehensive simulations are conducted, demonstrating the superiority of the proposed algorithm over the state-of-the-art methods. © 2025 IEEE.