A Bayesian approach to auto-calibration for parametric array signal processing

A number of techniques for parametric (high-resolution) array signal processing have been proposed in the last few decades. With few exceptions, these algorithms require an exact characterization of the array, including knowledge of the sensor positions, sensor gain/phase response, mutual coupling, and receiver equipment effects. Unless all sensors are identical, this information must typically be obtained by experimental measurements (calibration). In practice, of course, all such information is inevitably subject to errors. Several different methods have been proposed for alleviating the inherent sensitivity of parametric methods to such modelling errors. The technique proposed in the present paper is related to the class of so-called auto-calibration procedures, but it is assumed that certain prior knowledge of the array response errors is available. This is a reasonable assumption in most applications, and it allows for more general perturbation models than does pure auto-calibration. The optimal maximum a posteriori (MAP) estimator for the problem at hand is formulated, and a computationally more attractive large-sample approximation is derived. The proposed technique is shown to be statistically efficient, and the achievable performance is illustrated by numerical evaluation and computer simulation