The application of the frequency domain LMS adaptive filter to split array bearing estimation with a sinusoidal signal

This paper considers the use of the frequency domain LMS adaptive filter in a split array sonar to estimate the bearing of a plane wave acoustic source radiating a sinusoidal signal. For such a signal, the bearing can be determined from the relative signal phase between split array outputs at the signal frequency. In this paper, the split array outputs are fast Fourier transformed and used as the primary and reference inputs to the frequency domain LMS adaptive filter configured as a canceller. The signal frequency is estimated based upon the magnitude of the weights, and the relative signal phase between split array outputs is estimated as the phase of the frequency domain weight with the largest magnitude. The statistics of the magnitude and phase of the frequency domain weights are determined and then mapped to the variance of the bearing estimate. Computer simulations of the adaptive tracker which verify the analytical results are included.