The error probability of estimating the number of two closely located sources

The basic concept of direction finding of narrowband signals is reviewed. The validity of applying Taylor series approximations to the error probabilities in the estimation of the number of sources impinging on an array in a direction-finding problem that uses eigenspace methods is studied, particularly for the case of two sources close to each other. It is shown that these approximations are very sensitive to the number of sensors, but also to the signal-to-noise ratio (SNR), and are satisfactory only at very low SNR and for sources very close to each other. These approximations lead to results that are increasingly optimistic if either the SNR or the angle of separation between the signal is increased