Chebyshev collocation methods for fast orbit determination

摘要

We apply some Chebyshev collocation methods for fast and accurate determination of ephemeris of artificial satellites. This formulation is based on the approximation of the differential system by means of Chebyshev polynomials. In order to assess the convergence of the iterative process and to reduce the number of operations, the special formulation of Dziobek—Brouwer is used. From several numerical tests we conclude that the method presents very good behaviour for geostationary and low eccentric orbits (the most frequent cases). The number of operations with this method, in some cases, is 20 times less than that with a standard integrator. Besides, a typical dense output in a polynomial form is obtained.