Astronomical Applications Department, U.S. Naval Observatory NAO 150 Page 15
2.6. The Parameter Adjust-
ment Module
The parameter adjustment
module is relatively straight-
forward. The processed obser-
vations from the Observations
Module and the calculated
ephemeris data from the Inte-
gration Module are compared,
thus forming the O-C
residuals. First, coordinate
frame compatibility between
the observations and the syn-
thetic ephemeris is reconciled.
The calculated ephemeris
must be transformed to appar-
ent positions in order to match
the observations. The residu-
als are characterized, with sta-
tistical and descriptive output
going to disk as well as to an
output window on-screen. At
this point, outlying data points
can be automatically -- or
manually -- detected and
removed.
The core of the module fol-
lows with the determination of
parameters via a nonlinear
maximum likelihood estimator
(e.g., Levenberg-Marquardt). The normal equations are formed and
solved, and the parameters and associated formal error estimates are saved.
Finally, the residuals are evaluated, and the module exits with a solution
"acceptability" code. Figure 10 illustrates the process.
Matrix inversion is accomplished via singular value decomposition
(
SVD
), which is very robust and offers useful diagnostics for ill-
MURISON: MODELING PLANETARY MOTIONS
15 of 20
Figure 10 -- The Parameter Adjustment Module.
Parameter
Adjustment
retrieve
massaged
observations
retrieve
calculated
ephemeris
calculate O-C
quantities
statistical
characterization
of residuals
statistics
form the
normal
equations
solve the
normal
equations
output
parameters
correlations
determine
parameters
evaluate
residuals
exit TRUE
exit FALSE
removal of
outliers
calculate
apparent
positions
