Ephemeris Compression Using Multiple Fourier Series
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Ephemeris Compression Using Multiple Fourier Series 1 A. M. Segerman! and S. L. Coffey' Abstract An ephemeris compression method has been developed which uses multiple Fourier series. The compression itself is performed upon the Cartesian residuals which result from differencing a numerically integrated ephemeris with an ephemeris generated by a widelyused analytical propagator, such as PPT. An accurate estimate of the ephemeris may then be generated by reconstructing the residuals from the Fourier coefficients and superposing these with the analytical propagator's ephemeris. Statistical results from testing the method with the satellite catalog are presented.
Introduction The task of making orbital ephemerides available to remote sites has always involved a trade-off between simplicity and accuracy. The most accurate and straightforward method, performing a high-order numerical integration on-site, is also the most computationally intensive, often requiring more time and equipment than is available, especially when a large satellite catalog is to be maintained. Performing the integration at a central location and then transmitting the ephemerides to the sites can be just as accurate, but is the most voluminous to transmit. Analytical propagators are less demanding from a computational standpoint, and only require the transmission of initial conditions, but are less accurate. One alternative to these choices is the representation of ephemerides in a compressed form, using some reduced set of coefficients to describe the orbits. In this way, the time consuming computations can take place at a central location and only the coefficients need to be transmitted to the remote locations. Various techniques of ephemeris compression have long been studied with the goal of providing the high accuracy of a numerical integrator coupled with the ease
I Presented
as paper AAS 97-689 at the AAS/ AIAA Astrodynamics Conference, Sun Valley, Idaho, August 4-7, 1997. 2Aerospace Engineer, GRC International at Naval Research Laboratory, Code 8233, Washington, DC 20375-5355. 3Head, Mathematics and Orbit Dynamics Section, Naval Research Laboratory, Code 8233, Washington, DC 20375-5355. 343
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of evaluation associated with relatively simple calculations such as polynomial evaluations. For example, the motions of the planets and other bodies in the solar system have been regularly published using polynomial approximations [1, 2]. Deprit and Poplarchek investigated Barrodale' s method of using Chebyshev polynomials for ephemeris compression [3,4]. This method was applied as well by Coffey, Eckstein, and Kelm, who also used Chebyshev polynomials to represent the compression coefficients themselves [5]. Vedder worked with the use of Hermitian interpolation to compress ephemerides [6]. Rothmuller and Rosenlof developed a cubic splines technique for compressing artificial satellite data [7]. Others have investigated methods which perform compression of data after the extraction of the Keplerian character from the moti
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