Relative velocity measurement from the spectral phase of a match-filtered linear frequency modulated pulse

Linear frequency modulated signals are commonly used to perform underwater acoustic measurements since they can achieve high signal-to-noise ratios with relatively low source levels. However, such signals present a drawback if the source or receiver or target is moving. The Doppler effect affects signal amplitude, delay, and resolution. To perform a correct match filtering that includes the Doppler shift requires prior knowledge of the relative velocity. In this paper, the relative velocity is extracted directly from the Doppler cross-power spectrum. More precisely, the quadratic coefficient of the Doppler cross-power-spectrum phase is proportional to the relative velocity. The proposed method achieves velocity estimates that compare favorably with Global Positioning System ground truth and the ambiguity method.