For pulse coherent measurements the precision is highly dependent on the correlation value which is not known up front. You could use a model where you do the calculation at for example 90% correlation. The topic is described in the following paper and the resulting expression can be found in the end of the article.

https://support.nortekgroup.com/hc/en-us/articles/360013114780-Observing-Finescale-Oceanic-Velocity-Structure-with-an-Autonomous-Nortek-Acoustic-Doppler-Current-Profiler-2018-