An Estimation Procedure for Orbit Determination, Using the K.S. Transformation
Initially the orbit estimation problem is formulated. Assuming a perturbed two body physical model, the equations of motion in the mathematical model are treated by using the Kustaanheimo-Stiefel transformation in order to get an analytical solution in parametric space; this solution is explicit in parametric time and the only numerical approximation needed in the propagation of the state is the one to relate parametric to physical time. The observation relationships, at each step of estimation, are expressed in terms of variables of the parametric state so that the problem of determining the orbit is transferred to parametric space. Once the problem of orbit determination is formulated in terms of parametric variables, a procedure is given, making use of the sequential extended Kalman filter. It is expected that the procedure proposed will provide a gain in accuracy as well as a saving in computer work, since no numerical integration of the state is involved.
KeywordsParametric Space Extended Kalman Filter Orbit Determination Physical Time Nominal State
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