In quantitative ultrasonic flow measurements, the beam-to-flow angle (i.e., Doppler angle) is an important parameter. An autoregressive (AR) spectral analysis technique in combination with the Doppler spectrum broadening effect was previously proposed to estimate the Doppler angle. Since only a limited number of flow samples are used, real-time two-dimensional Doppler angle estimation is possible. The method was validated for laminar flows with constant velocities. In clinical applications, the flow pulsation needs to be considered. For pulsatile flows, the flow velocity is time-varying and the accuracy of Doppler angle estimation may be affected. In this paper, the AR method using only a limited number of flow samples was applied to Doppler angle estimation of pulsatile flows. The flow samples were properly selected to derive the AR coefficients and then more samples were extrapolated based on the AR model. The proposed method was verified by both simulations and in vitro experiments. A wide range of Doppler angles (from 30° to 78°) and different flow rates were considered. The experimental data for the Doppler angle showed that the AR method using eight flow samples had an average estimation error of 3.50° compared to an average error of 7.08° for the Fast Fourier Transform (FFT) method using 64 flow samples. Results indicated that the AR method not only provided accurate Doppler angle estimates, but also outperformed the conventional FFT method in pulsatile flows. This is because the short data acquisition time is less affected by the temporal velocity changes. It is concluded that real-time two-dimensional estimation of the Doppler angle is possible using the AR method in the presence of pulsatile flows. In addition, Doppler angle estimation with turbulent flows is also discussed. Results show that both the AR and FFT methods are not adequate due to the spectral broadening effects from the turbulence.
Simple and Accurate Two-Dimensional Angle Estimation for a Single Source With Uniform Circular Array