Generalized weight function selection criteria for the compressive sensing based robust DOA estimation methods

The performances of the conventional direction-of-arrival (DOA) estimation algorithms degrade significantly when some sensors in the array are miscalibrated. Inspired by a maximum correntropy criterion (MCC) based robust DOA estimation algorithm, this paper proposes a series of weight function selection criteria for the compressive sensing (CS) based DOA estimation algorithm to suppress the effect of the sensor miscalibrations under the half-quadratic (HQ) optimization framework. Based on the analysis of how the MCC works under the HQ framework, four weight function selection criteria are proposed to diminish the contribution of the observations received by the miscalibrated sensors. The analytical relationship between constraint function and weight function is then derived, based on which another selection criterion is supplemented to ensure that the selected weight function can be applied to the HQ framework. A generalized framework for the CS based robust DOA estimation methods is thus established, where the specific form of the constraint functions does not need to be known. Examples are presented to verify the effectiveness and generality of the proposed selection criteria.