Error analysis of autocorrelation-based velocity vector estimation in the aperture domain

Velocity vector estimation using aperture domain data involves a linear curve fitting to the Doppler shift measured at the individual receiving channel. Its superiority over conventional axial velocity estimation performed after beamforming and speckle tracking techniques has been previously demonstrated. This paper further investigates its statistical properties when the autocorrelation function is applied to estimate the Doppler shift. In particular, the analysis is performed using a k-space approach. With this technique, variances of velocity estimation for both the conventional and aperture-domain methods are derived. The theoretical values were verified by constant-flow simulations where a 5-MHz array with an f-number of 1.56 was used. Simulation results demonstrate the validity of the error analysis when the signal-to-noise ratio (SNR) is above 0 dB. It is shown that accuracy of the axial velocity estimation using aperture domain data is not only better than the lateral velocity estimation by a factor of 9.1 times the f-number in the absence of noise, but improved maximally by 1.6 over conventional axial velocity estimation when the SNR is above 0 dB.