So far we have assumed that exact ensemble averages of the array output covariances (or mean values) are available, and based on this assumption, several conventional and high resolution techniques have been developed to resolve the directions of arrival of incoming signals. In this chapter we analyze the performance of these methods based on finite observations, from a statistical point of view, and establish several results. When the ensemble averages are not available, they usually are estimated from the available array output data. In general, a finite data sample is available and estimation is carried out for the unknown covariances of interest such that the resulting estimators represent their “most likely” values. The principle of maximum likelihood (ML) is often chosen in various estimation and hypothesis testing problems for this purpose . As the name implies, the unknowns are selected so as to maximize (the logarithm of) the likelihood function, which is (the logarithm of) the joint probability density function of observations.
KeywordsAngular Separation Joint Probability Density Function Signal Subspace Arrival Angle Favorable Configuration
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