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

The question posed above is an astrodynamics question because it deals with satellite constellation design. With that in mind, this project will investigate how satellite constellation geometry and repeatability can, if at all, effect position measurements taken using the satellites in the GPS constellation.

The orbital characteristics of the GPS satellites were chosen so the groundtracks of each GPS satellite would repeat in a given amount of time. So far, most of the positioning community has operated on the assumption that the satellite repeatability does not matter, provided that certain quality conditions are met first. Those conditions, primarily (1) enough satellites (4 or more) for a completely determined position solution, and (2) good satellite geometry (satellites spread throughout the sky), do not depend directly on satellite groundtrack repeatability, but can be influenced by the satellite positions.

This project utilizes the GPS Inferred Positioning System - Orbit Analysis and Simulation Software package (GIPSY-OASIS, here referred to simply as GIPSY) developed at the Jet Propulsion Laboratory [Lichten and Border, 1987; Gregorius, 1995]. GIPSY is a powerful tool for GPS post-processing, enabling the user to specify a number of reference frames, data models, clock information, tropospheric and ionospheric models, and other models for physical characteristics of the Earth. As a precision tool, GIPSY accounts for all major perturbing effects to the GPS satellites and any physical parameters that can change the time and path of the GPS signal between satellite and receiver. GIPSY also provides the ability to estimate orbits of the GPS satellites; however, this project uses precise orbital information provided by JPL or the IGS instead of estimating orbital parameters.

Instead of processing the data for a single station, I chose to process four stations simultanteously in a network solution. The primary advantage of a network solution is that one can estimate a baseline length between two stations which are part of the same 'network'. A baseline length measurement can be considered a second 'position' measurement, in that the baseline length is independent of the absolute coordinates of the two stations. Basic information on the four stations used and approximate baseline lengths is given in the table below.

In order to yield an accurate GPS network solution, it was necessary to choose stations for use as a fixed point in the network and as a reference receiver clock. Station MDO1 was used as the fixed point in this solution. 'Fixing' a station in GIPSY means only that the station's position is able to move +/- 1 cm in the X, Y, and Z directions. This enables GIPSY to estimate fewer parameters and essentially "nail down" one corner of the network. MDO1 was chosen as the fixed station because it has the slowest and most consistent tectonic motion of the four stations, as shown by the JPL time series for MDO1, and because the location of MDO1 is well-known in the ITRF97 reference frame. Station TMGO was used as the reference clock as it is not a Trimble receiver (notorious for drifting and requiring resetting), shows decent time stability, and has data available for 178 of the 180 days analyzed in this project.

Two separate rounds of GIPSY processing were required to analyze the difference between position solutions based on the sidereal day and the solar day. Both rounds spanned January 3 to July 2, 2001, totalling 180 days of position solutions, and both rounds ignored GPS signals below 15 degrees elevation, thereby minimizing the effects of multipath. At a rate of 4 minutes per day, the GPS constellation geometry will show a significant difference between sidereal and solar days after roughly one month, and after 180 days of 4-minute shifts, processing of sidereal and solar days will have only 12 hours of data in common. If any differences in position estimates exist due to the change in satellites used for position determination, six months of contrasting solution methods should be sufficient to demonstrate them.

1. Solar day processing - As mentioned previously, GPS data files in the RINEX format typically contain 24 hours of data, spanning 00:00 to 24:00 UTC. Therefore, GPS processing based on the solar day required only processing existing data files, yielding one position estimate and/or baseline length per data file.



2. Sidereal day processing - To be completely accurate, the sidereal day is 0.997269566329084 times a solar day, or one sidereal day is equivalent to 23 hours 56 minutes 4.090524 seconds of solar time. This study ignores the 4.09 second difference between a true sidereal day and a 23 hour 56 minute approximate sidereal day because the GPS data files used are sampled at a 30 second rate. Therefore, ignoring the additional seconds should not introduce a significant error to the calculations presented here.
   
   In order to process data based on a sidereal day, it was necessary to combine then re-window existing RINEX files. The rewindowing progression began by truncating January 3 to span 00:00 to 23:56 UTC; all days after that point were 4 minutes earlier. To create a data set for a sidereal day, the following method was employed:
   
   
   1. Combine two data files containing two complete solar days. For example, if I combined data files for January 14 and 15, the composite data file would span 00:00 UTC 01jan14 to 24:00 UTC 01jan15.
   2. Truncate the data file:
      • subtract 4 minutes * #days from January 3rd off of the end of the data file
      • subtract the appropriate amount of time off the beginning of the composite file to yield 23 hours 56 minutes (1436 minutes) total file length.
      Continuing the January 14/15 example from above, the sidereal day file would end at 23:08 UTC 01jan15 (13 days from January 3 to January 15 * 4 minutes = 52 minutes), begin at 23:12 UTC 01jan14, and span 23 hours 56 mintues of time.
   
   Therefore, the composite files used for sidereal day processing were both shifted in time by 4 minutes per day since the starting day, and shortened to 23 hours 56 minutes in total length. Combining and trucating the files was accomplished by a UNIX shell script invoking the teqc GPS data management software from UNAVCO. As was the case with solar day processing, these files were used to produce one position estimate and/or baseline length per data file.

The results of the above processing were quantified using a number of data quality and position accuracy estimates:

1. Baseline length - the straight-line distance between two stations. This length is independent of the ECEF station positions calculated with GIPSY processing. This study chose to only analyze two baselines of different length -- a short baseline (33.80 km) between CAT1 and PVE3, and a long baseline (1396.32 km) between CAT1 and MDO1. Does sidereal or solar day processing change the apparent distance between the two stations? Does sidereal or solar day processing affect some position components (east/north/up) differently?
   
   
2. Absolute station positions - Earth-centered Earth-fixed (ECEF) positions of the permanent GPS stations. The components of station positions are compared between solar and sidereal day processing to check for discrepancies. Differences can easily be introduced when GIPSY throws out certain satellites for certain days, for example. Will these differences average out?
   
   
3. Data statistics - basic statistics to describe data distribution. For both baseline lengths and absolute station positions, measurements such as weighted means, root-mean-square (RMS), and scatter around the best-fit line are employed.