Dual algorithms for optimal guaranteed estimation and a truncated least squares method.

Computer Science

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Orbits: Numerical Methods, Orbits: Artificial Satellites

Scientific paper

The problem of calculating optimal guaranteed estimates has been reduced in previous works (1990, 1992, 1993) to that of unconstrained minimization of a differentiable convex function which can be solved by gradient methods and a mimimax least squares method. In the present paper, the author describes an application of the Newton method to solve the dual problem which turned out to be closely connected with the weighted least squares method on truncated measurement samples. To compare the efficiency of the three methods, the author applies them to the problem of estimating parameters of satellite motion in the near vicinity of a circular orbit. Numerical examples show that the new method is preferable for estimation problems with not a large number of parameters.

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