Theoretical accuracy of Doppler navigation sonars and acoustic Doppler current profilers

This paper addresses the problem of Doppler shift estimation in Doppler sonar systems. The analysis focuses on the single-beam geometry formed by a circular planar array and considers both narrow-band (or so-called incoherent) and wide-band (or coherent) Doppler sonars, transmitting, respectively, one long continuous-wave pulse and a train of short continuous-wave pulses. The correlation function of the reverberation signal at the beam output is derived for volume reverberation. Directive transmission or reception and a combination of both is considered. Estimation theory is applied to derive the Cramer-Rao bound of the Doppler parameter estimate. The effect of pulse duration, sonar geometry, beamwidth, and signal-to-noise ratio are discussed. The accuracy of coherent and incoherent systems is compared for a specific case.