Array self-calibration via robust steering vector estimation

We present an algorithm for jointly estimating the directions of arrival (DoAs) and array calibration parameters under the assumption of unknown gain and phase errors. We utilize an alternating approach: (1) For a given set of DoAs, we estimate the true array response in each source direction using robust steering vector estimation. The gain and phase errors can then be obtained in closed form from this array response. (2) We then re-estimate the DoAs as the directions most aligned with the updated array response. Alternating between these steps leads to convergence in practice. This approach is not limited in terms of array geometry and succeeds in the presence of limited snapshots. Empirical results from Monte Carlo simulation analysis show that our approach is far more robust to large calibration errors than existing methods. In the high signal-to-noise ratio (SNR) regime, DoA estimates produced by our algorithm obtain a root mean square error of less than one quarter that of competing approaches. In the moderate SNR regime, our error is less than half that of competing approaches. Our algorithm also succeeds when very few snapshots are available due to the use of low-rank projections in steering vector estimation.