Research report | An Investigation into the Possibility of Numerical Ephemeris Extension for GPS

Abstract

We investigate the possibility of a purely numerical extrapolation of parameters to extend the period of validity of any given set of GPS ephemeris parameters. The sought-for benefit is a faster time to first fix for a user who has been away from GPS satellite visibility for some days, and who thus holds outdated ephemeris data. Such a numerical extrapolation is not guaranteed a priori to result in more accurate satellite position forecasting, and indeed we show that for the extrapolation schemes chosen in this report, it does not result in more accurate forecasting. It therefore will not give any statistical improvement to the time taken for the above user to obtain a position fix.

Executive Summary

An entity that starts to acquire visibility of GPS satellites after a down time of some days might wish to establish its absolute position quickly. A user of GPS for this purpose needs accurate knowledge of the current positions of GPS satellites. These positions are predicted by the GPS receiver from its on-board ephemeris data. This data would normally be updated every two hours from satellite transmissions received if the GPS receiver were switched on and constantly visible to satellites. But a user who has been out of such visibility for some days holds old ephemeris data, and this data might no longer be an accurate parametrisation of the satellite orbits. Satellite positions predicted from such an ephemeris will tend to be inaccurate, resulting in a longer “time to first fix” for the receiver to lock on to a selection of satellites. This time might be unacceptably long.

In this report we investigate the extent to which such a user can predict satellite positions accurately from old ephemeris data, thus shortening the time to first fix. We examine the possibility of numerically extrapolating the outdated ephemeris data forward to the moment when the user sets his GPS receiver to begin searching for satellites, using that extrapolated data as a pseudo-current ephemeris. An improvement on this procedure based on physical modelling of satellite orbits is currently being investigated by commercial GPS receiver companies wanting to provide their civilian customers with shorter times to first fix in urban and indoor environments. We ask instead whether it's possible to update or “extend” an ephemeris purely by numerical extrapolation only. Our conclusion is that at least for the fairly generic extrapolation schemes chosen in this report, numerical extrapolation is not accurate enough to form a useful method of ephemeris extension.