Maximum likelihood estimation of the number, directions and strengths of point radio sources from variable baseline interferometer data

The optimum estimation of the number, directions, and strengths of multiple point radio sources is considered when the mutual coherence function of the sources\´ radiation is spatially sampled at baselines by a variable baseline correlation interferometer. The measurements are corrupted by the effects of additive background noise (including receiver noise) and a finite correlation time. Statistically approached, the problem is considered as a combination of parameter estimation and goodness of fit with the maximum likelihood (ML) principle being the basic criterion used. First the measurements\´ probability density function is derived, assuming the sources\´ number is known. Then the ML estimator (MLE) of the sources\´ parameters is obtained. The MLE\´s asymptotic optimum performance (unbiasedness with minimum variance) is then shown to be achieved when the number of measurements exceeds the number of sources by a threshold that is small (or zero) for most signal-to-noise ratios of interest. Next the number of sources is estimated according to a likelihood probability that measures the tenability of the MLE associated with every possible number of sources with respect to the measurements. The ML number-parameter estimation theory is then put into the form of an efficient algorithm which proves to be superior when compared to other processing methods such as Fourier maps.