  In this paper we present a data analysis approach applicable to the potential
saddle-point fly-by mission extension of LISA Pathfinder (LPF). At the peak of
its sensitivity, LPF will sample the gravitational field in our Solar System
with a precision of several $\text{fm/s}^2/\sqrt{\text{Hz}}$ at frequencies
around $1\,\text{mHz}$. Such an accurate accelerometer will allow us to test
alternative theories of gravity that predict deviations from Newtonian dynamics
in the non-relativistic limit. As an example, we consider the case of the
Tensor-Vector-Scalar theory of gravity and calculate, within the
non-relativistic limit of this theory, the signals that anomalous tidal
stresses generate in LPF. We study the parameter space of these signals and
divide it into two subgroups, one related to the mission parameters and the
other to the theory parameters that are determined by the gravity model. We
investigate how the mission parameters affect the signal detectability
concluding that these parameters can be determined with the sufficient
precision from the navigation of the spacecraft and fixed during our analysis.
Further, we apply Bayesian parameter estimation and determine the accuracy to
which the gravity theory parameters may be inferred. We evaluate the portion of
parameter space that may be eliminated in case of no signal detection and
estimate the detectability of signals as a function of parameter space
location. We also perform a first investigation of non-Gaussian
"noise-glitches" that may occur in the data. The analysis we develop is
universal and may be applied to anomalous tidal stress induced signals
predicted by any theory of gravity.
