Computation of Topocentric Satellite Predictions Using CPF Prediction Files
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Werner Gurtner
Astronomical Institute
University of Berne

Randall L. Ricklefs
Center for Space Research
University of Texas

The Consolidated Prediction Format has been defined by the ILRS ad hoc Predictions Format Study Group. A detailed description can be found on http://ilrs.gsfc.nasa.gov/working_groups/predictions_format_study_group/clrpf/index.html.

In contrast to the previously used tuned Inter-Range Vectors (TIRV) the new definition makes use of the full potential of the orbital force models used by the prediction centers for the generation of predicted orbits. CPFs for satellites basically contain tabulated three-dimensional coordinates of the satellite positions in an earth-fixed geocentric coordinate frame (International Terrestrial Reference Frame).

The computation of topocentric satellite positions or elements for tracking (azimuth and elevation), range gate settings, echo detection, screening, and normal point generation (ranges and flight times) consists of

- the interpolation of the tabulated positions for a given epoch by taking into account the time of flight (position of the satellite at reflection time) and the motion of the station due to earth rotation during the time of flight

- the conversion of the topcentric satellite position into azimuth, elevation, and range or time of flight

The total range and flight time are the sum of the outgoing and the incoming branch of the light path.

Azimuth and elevation can be interpolated/computed for a given epoch either for the direction of the outgoing beam or for the direction for the receiving telescope, depending on the needs of the stations. The sample code (see below) outputs azimuth/elevation of the outgoing beam and the point-behind angle to be added to get the direction for the receiving telescope. (This angle is always smaller than 11 arcseconds for our satellites).

The time interval between the tabulated positions depends on the satellite. It was chosen to allow for a simple polynomial interpolation of degree 9 with an interpolation error well below one nanosecond.

The polynomial interpolation centers 10 positions around the interpolation epoch for maximum interpolation accuracy, i.e., the interpolation is performed between the 5th and 6th position of the selected 10 positions.

Sample code to read CPF files (subroutine EPHINITU), for the interpolation (subroutine HERMITE), and for the computation of the topocentric elements (subroutine CPF_INTER) are made available, as well as a sample main program for the full computation (program CPF_PGM). Especially the main program will have to be re-written by the stations according to their needs.

CPF prediction files are distributed at least daily (by mail and through the Data Centers by ftp access) containing about five days of predictions, starting at least 5 epochs before distribution time. Elements for current passes or passes in the near future can be computed based on just this current CPF file.

Short-term pass lists could be generated by running CPF_INTER over the whole range of a CPF file in small steps by controlling the elevation.

The generation of long-term pass lists by the stations could be based on one geocentric position and velocity extracted from the CPF tabulated positions (subroutine HERMITE outputs on request also the first derivatives of the interpolated values), which would be analogous to the use of an IRV position and velocity.

Data screening and normal point generation will also have to be based on CPF predictions.

Satellite maneuvers will not have to be dealt with separately anymore as the positions in a CPF file can go through a maneuver 

Special air drag files are not necessary anymore because air drag is directly modeled into the CPF positions.