Optimal Algorithm to Estimate Signal Arrival Angles and Number of Signals under Parametrical a priori Uncertainty

An optimal algorithm to estimate signal arrival angles and a number of signals under the parametrical a priori uncertainty based on the maximum likelihood method is considered. The algorithm involves obtaining the maximum likelihood function to estimate simultaneously the signal arrival angles (both elevation and azimuth) on the basis of combined amplitude data for case of plane wave, correlated noise and arbitrarily spaced antenna elements. It also involves solving the nonlinear multidimensional multimodal optimization problem to find arrival angles estimates with the a priori known number of signals. If there is no data on the number of signals, multi-alternative test of elaborate hypotheses is carried out and the decisive rule on the number of signals is derived. The statistical simulation has been conducted using the derived algorithm. The relationship between the probability of decision-making on the number of signals and signal-to-noise ratio in multi signal situation is obtained.