Asymptotically Singular Differential Correction Matrices.

This paper contains the results of a study to determine the maximum time arc that can be spanned in a differential correction program as limited by the choice of the orbit parameters used in reducing the observation residuals. The paper proves that the differential correction matrices used in conventional iteration techniques become asymptotically singular in time in the event that more than one parameter affecting the energy of the orbit is used as a correction variable. The key result is that the loss of numerical accuracy is proportional to s = (2r- 1) logio(t), where r is the number of variables affecting the energy of the orbit.