Bayesian analysis of linear phased-array radar
Andrew G Green and David J C MacKay
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.
postscript.
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