Phase wrapping & velocity ambiguity

​In pulse-coherent Doppler systems, phase wrapping and velocity ambiguities are critical challenges that can affect the accuracy of velocity measurements. Phase-wrapped velocities appear as sudden discontinuities in the recorded velocity time series, typically showing abrupt jumps between maximum and minimum values. In coordinate transformations, phase wrapping can be more evident in XYZ or ENU coordinate systems when velocities are converted from the beam coordinate system.

Phase wrapping occurs when the phase difference between successive pulses exceeds ±π radians, causing the measured phase to "wrap around" and leading to incorrect velocity estimations. This typically happens when the actual velocity surpasses the system's configured velocity range, known as the ambiguity velocity. In such cases, a sine wave with phase -π appears identical to one with phase +π, resulting in ambiguous measurements.

Velocity ambiguity refers to the inability to distinguish between true and aliased velocities when the measured phase shift exceeds the unambiguous range. This is particularly problematic in pure coherent systems due to large pulse separations. The phase difference between two reflected pulses directly measures velocity; however, if this difference goes beyond ±π, the measurement uniqueness is lost, leading to velocity ambiguity.

 

Figure: Coordinate systems. From left: Beam coordinates, XYZ coordinates and ENU coordinates. An example of phase wrapping showing an abrupt change from negative to positive velocity. The nominal velocity range was set to 30 cm/s, yielding a horizontal velocity range of 142 cm/s. The plotted velocity is from the X component of the recorded data for a Vector.

 

Phase wrapping is most prevalent in highly turbulent environments, such as surf zones and rivers, where rapid velocity fluctuations increase the likelihood of exceeding the instrument's ambiguity velocity. However, it can also occur if the instrument is not properly configured for the deployment conditions, leading to phase aliasing even in moderate flow environments. To minimize phase wrapping, it is essential to assess expected flow conditions and configure the instrument accordingly. Increasing the velocity range above the anticipated maximum flow speed helps prevent wrapping by reducing pulse separation, which in turn raises the ambiguity velocity, allowing the system to measure higher speeds before aliasing occurs.

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