The use of phase difference trace functions for bearing estimation with small circular arrays

A geometric interpretation of the space-time data from an array of elements called the "trace function" by the authors is used to form an estimate of the bearing of a plane wave sinusoidal signal impinging upon a circular array of small diameter compared to a wavelength. A minimum mean-square error (MMSE) bearing estimator is derived using phase differences between pairs of elements. An estimator is also derived for wave propagation speed. The processor was simulated on a digital computer and the standard deviation of bearing error as a function of variance of phase difference and diameter of array is compared to the Cramér-Rao lower bound.