Bearing Accuracies for Arctan Processing of Crossed Dipole Arrays

Crossed dipole arrays are often used for bearing estimation in simple radio direction finders and in acoustic systems. A common bearing estimation algorithm requires that the output of each dipole be multiplied by the output of a collocated omnidirectional sensor and temporally averaged. The estimate of the source bearing is the arctan of the ratio of the pair of products; the quadrant of the target bearing may be deduced from the signs of the numerator and denominator. In this paper, both numerical simulation and mathematical modelling are used to study the performance of such a bearing estimator. For large time-bandwidth products, the bearing estimate approximates a Gaussian random variable. As the time-bandwidth product is decreased, the probability density function begins to deviate significantly from Normality, and, at very small time-bandwidth products, the density becomes bimodal with an additional peak displaced by from the actual source direction. The performance of the estimator is presented for both two and three dimensionally isotropic noise.