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3. Problems with the linear theory
The linear theory for orbit identification provides the most rigorous
mathematical setting to solve this problem. A mathematical theorem,
however, is not at all a rigorous tool unless all the hypothesis are
applicable to the concrete problem to be solved. The hypothesis needed
to apply the formalism of Section 2 are the following:
- 1.
- The normal matrices C1, C2 and
C0=C1+C2 are invertible and
positive-definite.
- 2.
- The map between the space of the residuals
and the space
of estimated parameters X is in the linear regime, that is the
linearized map
is a good approximation in
a region including both orbits.
- 3.
- The observation errors are of a size consistent with the
residual normalization adopted.
In this Section we shall discuss the applicability of these three
hypothesis to the problem of orbit identification.
Andrea Milani
2000-06-21