  The Earth-Moon-Sun system has traditionally provided the best laboratory for
testing the strong equivalence principle. For a decade, the Apache Point
Observatory Lunar Laser-ranging Operation (APOLLO) has been producing the
world's best lunar laser ranging data. At present, a single observing session
of about an hour yields a distance measurement with uncertainty of about 2~mm,
an order of magnitude advance over the best pre-APOLLO lunar laser ranging
data. However, these superb data have not yet yielded scientific results
commensurate with their accuracy, number, and temporal distribution. There are
two reasons for this. First, even in the relatively clean environment of the
Earth-Moon system, a large number of effects modify the measured distance
importantly and thus need to be included in the analysis model. The second
reason is more complicated. The traditional problem with the analysis of
solar-system metric data is that the physical model must be truncated to avoid
extra parameters that would increase the condition number of the estimator.
Even in a typical APOLLO analysis that does not include parameters of gravity
physics, the condition number is very high: $8 \times 10^{10}$.
