  The core of every orbit determination process is the comparison between the
measured observables and their predicted values, computed using the adopted
mathematical models, and the minimization, in a least square sense, of their
differences, known as residuals. In interplanetary orbit determination, Doppler
observables, obtained by measuring the average frequency shift of the received
carrier signal over a certain count time, are compared against their predicted
values, usually computed by differencing two round-trip light-times. This
formulation is known to be sensitive to round-off errors, caused by the use of
finite arithmetic in the computation, giving rise to an additional noise in the
residuals, called numerical noise, that degrades the accuracy of the orbit
determination solution. This paper presents a mathematical model for the
expected numerical errors in two-way and three-way Doppler observables,
computed using the differenced light-time formulation. The model was validated
by comparing its prediction to the actual noise in the computed observables,
obtained by NASA/Jet Propulsion Laboratory's Orbit Determination Program. The
model proved to be accurate within $3 \times 10^{-3} \,\text{mm/s}$ at $60
\,\text{s}$ integration time. Then it was applied to the case studies of
Cassini's and Juno's nominal trajectories, proving that numerical errors can
assume values up to $6 \times 10^{-2} \,\text{mm/s}$ at $60 \,\text{s}$
integration time, and consequently that they are an important noise source in
the Doppler-based orbit determination processes. Three alternative strategies
are proposed and discussed in the paper to mitigate the effects of numerical
noise.
