Array processing in practical noise environments

The sonar array processing problem of estimating the bearing and signal strengths of point targets in the far field, has given rise to a number of high resolution parametric algorithms designed to improve accuracy and resolution of arrays beyond that of an FFT beamformer. An important flaw in these techniques however, is that they generally require knowledge of the noise correlation to give a reliable estimate of the spatial spectrum. In practical environments effects such as bottom reflection and limited snapshots, mean that only approximate knowledge of noise covariance exists. To circumvent this difficulty the maximum a posteriori (MAP) estimator was developed to maximise the probability of correct bearing estimates in unknown noise environments. The performance of the MAP algorithm is poor, however, in comparison with high resolution algorithms in known noise. A Bayesian estimator is developed incorporating a prior representing experimental knowledge of noise covariance. This is shown to give a significantly lower mean square error than the MAP estimator. The new algorithm operates in the region between full and no knowledge of the noise covariance, reducing to MAP as a special case of no prior knowledge in the noise correlation.