Point averaging of the position components, before and after S/A is turned off


Data Collection
We developed a software to collect and save the raw data received from GPS receiver. Then we set the receiver in a known position and saved the long-term raw data collected from Binary Message No.103. Once we execute this program, the system asks for a binary filename in order to saving the data. Then it starts to collect and save the received data in the binary file. Data collecting has been in two different periods, before and after 1st May 2000 (June to December 1999, and July to September 2001).

Table 2: Error reduction by point averaging. (S/A on)
Time of Averaging X Component Y Component Z Component
Standard Deviation Amplitude Standard Deviation Amplitude Standard Deviation Amplitude
Raw data 43.2 345 45.5 360 48 393
5 min 26.5 75.6 30.2 82.2 27.6 92.8
10 min 19.3 50.5 26 77.8 20.4 68
45 min 15.8 49.6 9.6 25.3 5.4 17.2
1 hour 12.2 32.9 5.9 18.2 4.6 12.7
5 hour 4.9 14.2 5.4 17.9 4 11.5



Later, we sketched the variation in position components (X, Y, and Z in WGS 84 system) due to time, by a software developed for this purpose. Figure 2 and 3 show these variations, before and after S/A is turned off respectively. As the graphs show, the errors have clearly been reduced after turning S/A off. Measurements for 6 months data collecting in two periods, show that maximum of error amplitude in presence of S/A is more Than 300 meters while without S/A this quantity reduces to tens of meters.

Finally, wards, we averaged position components for various periods of time (5, 10, 45, 60 minutes & 5 hours) using a recursivealgorithm based on the following equations:

Xn+1 = ((n-1)/n) Xn + (1/n) Xn+1 (1)
Yn+1 = ((n-1)/n) Yn + (1/n) Yn+1 (2)
Zn+1 = ((n-1)/n) Zn + (1/n) Zn+1 (3)

Where X, Y and Z are measured position components, and n is the number of measurements.

The results of averaging for data collected while S/A was on are shown in table 3. Those for the period in which S/A was off are given in table 4.



Table 3: Error reduction by point averaging. (S/A off)
Time of Averaging X Component Y Component Z Component
Standard Deviation Amplitude Standard Deviation Amplitude Standard Deviation Amplitude
Raw data 8.3 39 7.9 34.5 9.2 43.6
5 min 7.1 31.5 6.7 28.8 7.5 33
10 min 5.2 24 4.5 22.7 5.3 25.6
45 min 3.2 13.1 3 12.5 2.9 11.1
1 hour 2.2 7.7 2.3 8.2 2.3 9.1
5 hour 2.1 7.4 2.2 7.6 2.3 7.9


Conclusion
In this research, we studied and saved position parameters received from a Low Cost GPS engine both in presence and absence of intentional errors (S/A). This measurement was performed for a known position. The results show that the measured position components are more accurate in the absence of S/A than its presence. Averaging the raw position components improved the accuracy of our measurement, which was increased, with the duration of averaging. So, that position measurement error before turning off the S/A, was decreased from more than 300 to less than 18 meters after averaging. Similarly, the error was reduced to less than 8 meters after turning off the S/A, while it was about 40 meter before averaging.

References
  • Hofmann-Wellenhof, H. Lichtenegger, J. Collins, Global Positioning Systerm Theory and Practice, Third revised edition, ISBN 3-211-82591-6, Springer-Verlag Wien New York April 1994.
  • Timothy Barnes, Selective Availability via the Levinson Predictor, ION GPS-95, September 1995, P.P. 533-542.
  • GPS Error Sources, Axiom Navigation Incorporated, www.axiomnav.com/differential-gps, 2001.
  • Point Averaging, University of North Carolina, www.cpc.unc.edu/services/spatial/postproc.htm, 27 January, 2000.
  • Ian Strachan, 2000, GPS System Accuracy After 1 May 2000, Some UK Test Without DGPS and SA off, 4 May 2000, http://joe.mehaffey.com/saoffaccuracy.htm
  • Microtracker LP Designer’s Guide, Rockwell International Corporation, GPS-22, January 1, 1995.
  • Microtracker LP Operations Manual, Rockwell International Corporation, GPS-16, January 10, 1994.

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