Bayesian Analysis of Linear Phased-array Radar

A number of methods have been developed to analyze the response of the linear phased array radar. These perform remarkably well when the number of sources is known, but in cases where a determination of this number is required, problems are often encountered. These problems can be resolved by a Bayesian approach. Here, a linear phased-array consisting of equally spaced elements is considered. Analytic expressions for the posterior probability distribution over source positions and amplitudes, and the corresponding Hessians are derived. These are integrated to give the evidence for each model order. Tests using model data showed that performance at the second level of inference is critically determined by the accuracy of position estimation. If adequate parameter optimization is available, the Bayesian approach is demonstrated to work well, even in extreme circumstances. A commonly employed method of source location, noise subspace eigenanalysis of the correlation matrix, was tried and found to be inadequate. A Newton-Raphson optimization was then used starting from the positions predicted by eigenanalysis.