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

At this time, geophysicists typically process GPS data in a way to yield a single position measurement out of an entire day's worth of data. This scientific practice raises the question -- is the solar day (24 hours) or the sidereal day (roughly 23 hours 56 minutes) best for single-day GPS position solutions, or does the concept of a "day" even matter in the final solution? The GPS satellites are in orbits around Earth creating orbital periods of one-half a sidereal day; however, geophysicists typically process data based on the solar day. Does it introduce error to process geophysical GPS data sets based on the solar day instead of the sidereal day, where the same GPS satellites are visible for the same duration each day?

This project analyzes the importance of GPS constellation repeatability by quantifying the differences between GPS position estimates based on the solar day and the sidereal day. I conducted about 6 months of short-baseline, four-station network data processing using JPL's GIPSY software package, providing both absolute position estimates of each station and baseline lengths between selected stations. The first round of processing created position estimates based on the current standard (and the default data file sizes) of the solar day. The second round of processing required extensive combining and rewindowing of existing data sets, but yielded data files and position solutions based on the sidereal day. At a rate of 4 minutes per day, the GPS constellation geometry shows a significant difference (50%) between sidereal and solar days after six months.

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. If the different methods were propagated for 180 days, the difference in baseline estimations is small compared to the baseline length -- 2.9691 cm for a 1396.32 km baseline, and 0.22 cm for a 33.8 km baseline. When looking at position components, the east and baseline length components show some temporal variability, but the vertical and north components are zero mean for the entire study.

The Global Positioning System plays an important role in studies of the earth, and is increasingly becoming the premier tool for studying crustal deformation. The signals related to crustal deformation are extremely small and slow [Fowler, 1990], on the order of millimeters to centimeters per year; consequently, crustal studies typically do not require processing GPS data in a way to yield high-rate positon solutions [King et. al, 1995; Larson et. al, 1997; Prescott, 1989]. It has therefore become standard practice in the geophysical community to process an entire day's GPS data to yield a single position solution.

In order to approach this issue, a few concepts fundamental to geophysics and astrodynamics should be throughly established.

1. Plate Tectonics and Permanent Stations
   
   

   The surface of the Earth is broken up into a series of tectonic plates. These plates vary in size; the most significant plates are the size of continents or large ocean basins (about 7 total), but many smaller plates also exist.

   The plates move relative to each other at very slow (but geologically significant) rates. Therefore, using the Global Positioning System to quantify these plate movements requires long-duration measurements either through extensive field campaigns or data from permanent GPS stations.

   My research typically uses data from permanent GPS stations, specifically stations that are members of the International GPS Service. Part of a station's membership in this network relies upon making all the station's continuous data available in the Receiver Independent Exchange (RINEX) format. Normal RINEX files from permanent GPS stations contain 24 hours of data; I have provided an example here.

   Since analysis of tectonic motion and other geophysical applications does not require high-rate position estimations, most geophysicists (including myself) process data in the easiest way possible -- a single position estimate using the 24 hours of data provided in a standard RINEX file. Then, many days of data are analyzed together to detect any crustal motion - for example, see the study of global plate velocities conducted by Larson et. al [1997].

2. Solar and Sidereal Time
   
   

   As stated in Vallado [2001], the difference between solar and sidereal time is the difference between juding time by the sun versus the stars. In Vallado's own words:
   
   

   • "Solar time is loosely defined by successive transits of the Sun over a local meridian of longitude, although we need a fixed reference point on the Earth to define the beginning of each day." For GPS time, which is closely related to UTC, the 'reference point on the Earth' is the Greenwich meridian, the 0 degree longitude point.
   • "We define sidereal time as the time between successive transits of the stars over a particular meridian."
   
   

   A sidereal day is roughly equivalent to 23 hours 56 minutes of a solar day (24 hours).

3. GPS Satellite Orbits
   
   

   The orbital parameters of the GPS satellites were chosen to give the satellites orbital periods equivalent to half of a sidereal day [Hoffman-Wellenhof et. al, 1992]. Since the sidereal day is 4 minutes shorter than a solar day, the same GPS satellite will pass through the same portion of the sky (relative to a fixed observer) every 11 hours 58 minutes. Therefore, the GPS satellite constellation appearing over a particular permanent GPS station will repeat twice per solar day minus 4 minutes.