Radio source parameter estimation by maximum likelihood processing of variable baseline correlation interferometer data

The accurate joint determination of the direction and strength of a point noise source when the mutual coherence function of its radiated field is spatially sampled at
M
baselines by a correlation interferometer is considered. The measurements are corrupted by the combined effects of a) the additive background and receiver noises at the interferometer antennas and b) the finite integration time of a practical correlator. The problem is approached from a statistical point of view (as contrasted with beam forming techniques). First the probability density function of the measurements is derived. The source's two parameters (direction and strength) are then jointly estimated using the maximum likelihood (ML) method. Investigation of the estimates' properties shows that they are virtually unbiased with variances that effectively attain the standard Cramer-Rao (C-R) lower bound when the number of measurements exceeds a "threshold" which is a decreasing function of the measurements' signal-to-noise ratio (SNR). The empirically observed fact that such a threshold is quite small, even at low SNR's, as well as the unbiasedness of the estimates, makes the performance of these (ML) estimates optimum for most practical applications.