conditioned matrices. Singularities are automatically detected and cor-
rected, and the problem parameters are identified. In essence, if the algo-
rithm encounters an ill-conditioned matrix, it safely steps around the prob-
lem point(s) and proceeds in such a way as to mine the matrix for the
maximum amount of information. When a singularity (rare in practice) or
degenerate column (not rare!) is encountered, the combination of parame-
ters that led to the fault is easily extracted. Thus, not only are singularities
safely handled, but -- more importantly -- parameter combinations to
which the data are insensitive are automatically identified.
It is unusual to encounter a computational method that is this reliable
and blowup-proof. I have already developed and tested matrix inversion
using
SVD
and incorporated it into the Matrix utility class. With regard to
Newcomb,
SVD
is a "plug'n'play" capability.
2.7. The Observations Module
Perhaps the most difficult section of the program is the module that
processes input observations and reduces them to a form suitable for pas-
sage to the O-C section of the parameter adjustment module (see Figure
10). In essence, the observations are sent to the O-C section in the form of
apparent positions, corrected for various biases, including (but not limited
to):
catalog corrections
delay/doppler bias corrections
coordinate frame fiducialization
aberration corrections
nutation and precession
Integral to this section are the specific types of observational datasets
and the specific types of observational platforms. The data and platform
types vary widely.
2.7.1. Observing Platforms
One must consider the various observing platforms presently available in
the solar system. They are
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