Differential GPS
Elizabeth Hollingsworth
The goal of this project is to determine the effectiveness of differential GPS in
removing large error excursions. In order to analyze the effects of GPS, a class-generated
differential GPS system was created.
On Monday, March 27th, FRS 144 divided into 3 data-collecting groups: Elizabeth,
Rob, and Andrew; Julius, Peter H, and Jonathan; and Dominic, Brian, and Peter LC.
Each group was assigned an area: Cannon Green, the parking garage, and the baseball
field, respectively. Each group, using NMEA formatted data, collected data for an
hour—from 2:30 pm until 3:30pm—using a program similar to GPS Dialog. The data
was then compiled into a large, aggregative table by Professor Groth.
Each student was assigned three sets of data to analyze out of the 26 total sets in
which the receivers were locked on the same satellite. I was assigned to analyze CA-FD,
CR-CR, and FP-FP—Cannon Green Andrew-Field Dominic, Cannon Green Rob-Cannon
Green Rob, and Field Peter LC-Field Peter LC, respectively. Only data in which the
receivers were locked on the same satellites were used. Throughout the data collection
period, CA-FD were locked on the same satellites 14 times, CR-CR was locked 2073
times, and FP-FP was locked 1851 times.
When the satellites were locked on the same satellite, the differences of their
North-South meter deviations and East-West meter deviations were found to determine
the error present. For each data set, the average latitudes and longitudes were found and
subtracted from the actual latitude and longitude at each reading. Then, the differences
were converted to meters as follows: North-South meters= 6371000*Radians(latitude
differences)/60; East-West meters= 6371000*Cos(Radians(40))*Radians(longitude
differences)/60. The aforementioned North-South and East-West meter error differences
were differenced for the CA-FD data set. Standard deviations for the North-South and
East-West differences were found as well. The data can be summarized below:
Data Type
CA_Long avg
CA_Lat avg
FD_Long avg
FD_Lat avg
Std dev NS diff CA-FD (m)
Std dev EW diff CA-FD (m)
CR_Long avg
CR_Lat avg
Std dev NS diff CR-CR (m)
Std dev EW diff CR-CR (m)
FP_Long avg
FP_Lat avg
Std dev NS diff FP-FP (m)
Std dev EW diff FP-FP (m)
Value
7439.543836
4020.888664
7438.907314
4020.8347
1.275547514
1.89421298
7439.542798
4020.885872
2.088861301
1.146111147
7439.906326
4020.833838
1.73355704
.74870556
Note: A longitude of 7439.543836 represents 74 degrees and 39.543836. Same format
for latitude.
For each data set, the North-South meters of difference were plotted against the EastWest meters of difference.
The data shows considerably more North-South error for the CR-CR and FP-FP
data sets, and more East-West error for the CA-FD data set. The scatter plots appear
random and unsystematic with relatively small errors. The low standard deviations
demonstrate the ability for differential GPS to remove relatively large errors. No
standard deviations of the position differences (from the average) exceeded 2,
demonstrating the error-reducing ability of differential GPS. Some error was present, but
it appeared minimal as evidenced by the small units of measurement on the scatter plots.
Differential GPS uses a stationary receiver and a rove receiver that are close
together to determine the amount of error present. Differential GPS can correct for select
availability error and some atmosphere errors, although it cannot correct for multipath
errors. In this experiment, multiple receiver locations were used, so a comparison of the
data allows for an analysis of the amount of error present. Because the locations of all
the receivers were known, the amount of error can be minimized through comparison.
Although the procedure used does not exactly represent the differential GPS
system, this analysis illustrates the ability of differential GPS to minimize the number of
very large errant errors.