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Fuzzy Point Averaging of the GPS Position Components


V. Experimental Results
At first, 36000 (10 hours) the original fix positions were collected on the building of Computer Control and Fuzzy Logic Research Lab in the Iran University of Science and Technology. Data collecting has been in two different periods, before and after 1st May 2000 (June to December 1999, and July to September 2001). Then, position components were averaged with various periods of time and also with various R.F. using a recursive algorithm based on the following equations [5]:


Where Xn+1, Yn+1 and Zn+1 are average of position components, n is the number of sampled frames at averaging and xn+1, yn+1 and zn+1 are positions of measured at the time n+1 . The results are shown as the following. Table 3 shows summary of experimental results of the three systems for 10800-fix positions with R.F. equal to 0.20, before S/A was turned off.

Table 3. Error reduction by fuzzy and simple point averaging for 10800-fix positions with R.F. equal to 0.20 (S/A on)

Where "Error" is defined as follow:


Where X , Y and Z are average of position components. Also, X ref., Yref. and Zref. are components of reference point or desired point. Table 4 shows summary of experimental results of the three systems for 2880-fix positions with R.F. equal to 0.15, after S/A was turned off.

Table 4. Error reduction by fuzzy and simple point averaging for 2880-fix positions with R.F. equal to 0.15 (S/A off)

As shown in table 3 and table 4, fuzzy point averaging decreases better than simple point averaging position components error.

VI. Conclusions
In this research, was 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 demonstrated that fuzzy point averaging of the raw position components improved the measurement accuracy better than simple point averaging. So that position measurement error before turning off the S/A, was decreased from more than 170 to less than 4 meters by fuzzy point averaging. Similarly, the position error was reduced to less than 1 meter with turning off the S/A, while it was about 17 meters before fuzzy point averaging.

References
  • B.Hofmann-Wellenhof, H.Lichtenegger and J.Collins, “Global Positioning System: Theory and Practice”, Third Revised Edition, Springer-Verlag Wien New York, 1994.
  • "MicroTracker LP Designer’s Guide", Rockwell International Corporation, GPS-22, January 1, 1995.
  • M.R.Mosavi, K.Mohammadi and A. Ghalehnoee, “Improve the position Accuracy on Low Cost GPS Receiver with Fuzzy Logic“, The Third Iranian Seminar on Fuzzy Sets and Its Applications, University of Sistan and Baluchestan, June 2002, pp.171-179.
  • M.R.Mosavi, K.Mohammadi and M.H.Refan, “Fuzzy Processing on GPS Data to Improve Positioning Accuracy, before and after S/A Is Turned off”, The Asian GPS Conference 2002, India, pp.117-120.
  • M.H.Refan and K.Mohammadi, “Point Averaging of the Position Components, before and after S/A IS Turned off ”, The Asian GPS Conference 2001, India, pp.53-58.
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