NOTE--before a bug fix on 9 Oct 2006, this program gave repeat times that are too short by 1 sec exactly.
This program, given a set of concatenated .sp3 files, and a time and place (on the command line), writes out the repeat time for each GPS satellite: that is, the time until the satellite is at the same place in the sky (elevation and azimuth): that is, the same aspect. This information is useful in correcting high-rate GPS data; see, for example, Choi et al, Geophysical Research Letters, 2004, paper L22608 (available here as paper 41). Here is a preprint describing some results using artrep. The program gives the difference in place (in milliradians on the sky), as well as the elevation, azimuth, and some additional information. The computation is done using polynomial interpolation from the 15-minute ECEF positions in the .sp3 file; see this site for code and discussion.
The program (Fortran 77) is available here. For a routine that uses the broadcast ephemeris, and is not station-specific, see Kristine Larson's program.
Thanks to Kristine Larson for comments and testing.