  Compact autonomous marine vehicles, both surface and submersible, are now
commonly used to conduct observations of ocean velocities using Acoustic
Doppler Current Profilers (ADCPs). However, in the inevitable presence of
surface waves, ADCP measurements conducted by these platforms are susceptible
to biases stemming from wave-coherent orbital motion and platform tilting. In
typical ocean conditions, the magnitude of the bias can reach tens of
centimeters per second. This paper presents analytical derivation of the
depth-dependent bias formulas for a variety of scenarios, encompassing surface
and subsurface platforms, upward- and downward-looking ADCPs, free-drifting and
self-propelled vehicles. The bias is shown to be a function of the wave field
properties, platform response dynamics, and the ADCP configuration
(particularly, orientation and beam angle). In all cases, the wave-induced
biases show parametric scaling similar to that of the Stokes drift, albeit with
a number of critical nuances. Analytical derivations are validated with a
semi-analytical model, which can also be used to estimate the biases for more
complex measurement configurations. Further analysis reveals unexpected
fundamental differences between the upward- and downward-looking ADCP
configurations, offering insights for experimental design aimed at minimizing
and mitigating wave-induced biases in autonomous oceanographic observations.
