The effect of Doppler rate on small aperture bearing estimation

Abstract

Passive estimation of the angle of arrival using a small aperture array outdoors can be adversely effected by high rates of frequency chirping. This is caused by either rapid change in source frequency and/or rapid change in Doppler frequency due to the motion of the source. Consider two microphone signals simultaneously sampled and analyzed for phase difference via FFT. The time difference of arrival across the small aperture array is small compared to the FFT buffer size, so there are slightly different starting and stopping frequencies for each microphone during the FFT input buffer record. However, the chirp (rate of change in Doppler or source frequency) leads to a significant phase error between the two microphones. An upwards chirp moves the estimated bearing erroneously towards 0 degrees while a downward chirp moves the estimated toward 180 degrees. For tracking aircraft from the ground it is not unusual to experience high rates of change in Doppler frequency near the closest point of approach. This paper shows the extent of the error from practical Doppler and source chirps and how to correct for the bearing error.