Abstract: In order to avoid the use of complex transform and correlation techniques for estimating the velocity of a target from which ultrasonic RF bursts are received as return echoes, the time of occurrence of successive returns are compared with a plurality of delay trajectories each representing a different target velocity. The trajectory with which the returns match with minimum variance, or maximum likelihood of being in time coincidence, provides an estimate of the velocity of the target. In different embodiments the RF return, the envelope of the return or the quadrature components thereof are processed to determine to which delay trajectory they are most proximal. The search for the delay trajectory is called a "butterfly search" in two dimensions (slow time or transmitted pulse repetition periods and fast time or range). Each butterfly line corresponds to a distinct linear velocity.