Single-shot Doppler Velocity Estimation using double chirp pulse compression

Coherent ultrasonic Doppler velocimeters provide precise and accurate measurements of velocity profiles in many applications. However, these instruments suffer from the well known range-velocity ambiguity, making this kind of instruments not well suited for velocity measurements in channels of several meters depth and water velocities of some meters per second. On the other side, incoherent ultrasonic Doppler velocimeters don't have such limitations but suffer from reduced spatial and temporal resolution. The known actual solutions to this compromise consist in using phase-coded repeated pulses composing one excitation ping. The performance of such a solution is mainly conditioned by the appropriate choice of the binary coding sequence. While longer codes reduce the variance of the velocity estimate, they limit both spatial resolution and measurable velocity range. We present in this paper an alternative pulse compression scheme using overlapping linear chirps. This method makes it possible to improve the estimation variance with respect to phase coding using minimum peak sidelobe level binary codes. The performances in term of both bias and variance with respect to various parameters including noise level, length of range-gated signal, velocity dispersion within a considered volume and number of particles will be addressed based on a model taking into account the Doppler effect on wideband transmitted pulses. These results will be discussed and compared with experimental measurements and theoretical predictions of performance limits (The Cramér-Rao lower bounds) for both wideband and narrow-band Doppler velocimeters. Furthermore, we will show that it is possible to extend the measurable velocity range without affecting spatial resolution and precision, all parameters otherwise unchanged.