Single-Day GPS Position Estimates:
Solar or Sidereal Day?

Further analysis is warranted to cement the conclusions drawn below. A number of logical extensions to the work presented here could be explored further:

1. Conduct the same rewindowing and data analysis for an additional 180 days beyond the 180 days examined here. After 360 days, the GPS constellation will repeat for solar and sidereal days, but be shifted by a full day. Will the position estimates still average out? Will trends observed in east and baseline length components continue or change?
2. Use the same processes used in this study on a different network of stations. If the network size is increased, does this effect the distibution of sidereal-solar day differences? Does the orientation of the baselines (mostly north-south vs. mostly east-west) change any of the trends observed here? With even longer baselines (> 1500 km), do the sidereal-solar day differences continue to increase?
3. Reprocess the existing data after permanently removing outliers from the data files, and then bias-fixing. Bias-fixing, also known as carrier-phase ambiguity resolution, is essential for creating truly rigourous results. This study did not bias-fix because the process involves too much computation time (over 24 hours per data batch for 30-second epoch rates, as used in this study) for the scope of this project.
4. One severe shortcoming of the analysis done in this project is the use of statistics. Sadly, my statistics skills are quite lacking, so I found myself unable to adequately describe the errors and the data itself. Without additional data processing, the description of the work done here could be improved with a better use of data statistics.

Overall, sidereal and solar day processing methods revealed small differences between the two methods, but these differences are not significant given the uncertainty in the measurements. As stated in the Results section, if one were to propagate the solar-sidereal trends forward for 180 days then the difference in the baseline estimations would be very small compared to the total baseline length -- 2.9691 cm for the 1396.32 km MDO1-CAT1 baseline, and 0.22 cm for the 33.8 km CAT1-PVE3 baseline. Since these differences comprise a small fractional percentage of the total baseline length, using one method instead of another is likely not an important distinction. Likewise, the absolute station positions show little difference between solar and sidereal day processing. Averages of latitude, longitude, and height for both methods are identical when considering the inherent measurement errors.

If the differences are indeed significant (due to a shortcoming in my statistical analysis), then the north and vertical components are unaffected by a solar-sidereal day distinction but the east and therefore baseline components show changes based on the method used. The link between the east component and the solar-sidereal day distinction should be studied further, and would be made more robust with ambiguity resolution incorporated into the GIPSY processing.

The most interesting result of this study is the dissimilarity between long and short baselines when differencing the solar and sidereal data points. In particular, the east component appears to trend back to zero after 130 days when analyzing longer baselines [plot], whereas the east component difference increases slowly and linearly for shorter baselines [plot]. Processing a full 360 days or more of data, and incorporating a wider range of baselines into the study, would yield more definitive results.

The geophysical community has little to worry about with respect to the solar day versus sidereal day question. From the results shown here, the minor differences between solar and sidereal day processing appear to average out over the time scales (months and years) which normally concern geophysicists. However, when analyzing trends on the scale of a few months or weeks, the solar versus sidereal day question could become important. One cannot answer this question definitively without further study.