Static Single Point Positioning Using The Extended Kalman Filter

Global Positioning System (GPS) technology is widely used today in the areas of geodesy and topography as well as in aeronautics mainly for military purposes. Due to the military usage of GPS, full access and use of this technology is being denied to the civilian user who must then work with a less accurate version. In this paper we focus on the estimation of the receiver coordinates ( X, Y, Z ) and its clock bias ( δtr ) of a fixed point based on pseudorange measurements of a single GPS receiver. Utilizing the instantaneous coordinates of just 4 satellites and their clock offsets, by taking into account the atmospheric delays, we are able to derive a set of pseudorange equations. The estimation of the four unknowns ( X, Y, Z , δtr ) is achieved by introducing an extended Kalman filter that processes, off-line, all the data collected from the receiver. Higher performance of position accuracy is attained by appropriate tuning of the filter noise parameters and by including other forms of biases.

• I. Sarras
• G. Gerakios
• A. Diamantis
• A. I. Dounis
• G. P. Syrcos

• Extended Kalman filter
• GPS
• Pseudorange

[1] Leick, A., GPS Satellite Surveying , Second Edition, John Wiley&Sons,
INC., 1995.
[2] Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J., GPS Theory and
Practice, Third Revised Edition, Springer-Verlag, New York, NY, 1994.
[3] Gelb, Arthur, Ed., Applied Optimal Estimation, M.I.T. Press,
Cambridge, MA, 1974.
[4] Brown R.G., Hwang P., Introduction to Random Signals and Applied
Kalman Filtering, Second Edition, John Wiley&Sons, INC., 1992.
[5] Dana H. Peter, Global Positioning System Overview, (Online)
http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html
[6] OBE Consulting Engineers Rinex format data,
www.obec.com/data/TRSDATA/Rinex/index.htm
[7] Dermanis A., Space Geodesy and Geodynamimcs, Editions Ziti, 1999.
[8] Rossikopoulos D., Topographic networks and computations, 2nd edition,
Editions Ziti, 1992. (in Greek)
[9] Kalman R. E., "A new approach to linear filtering and prediction
problems," Transactions of the ASME---Journal of Basic Engineering,
pp. 35-45, March 1960.
[10] Julier, S. J., Uhlmann J. K. and Durrant-Whyte, H. F., "A new approach
for filtering nonlinear systems," Proc. American Control Conference,
Seattle, Washington, pp. 1628-1632, 1995.
[11] Chen G., Wang J. and Shieh L., "Interval kalman filtering," IEEE Trans.
Aerosp. Electron. Syst. 33, pp. 250-259, 1997.
[12] Guanrong C., Qingxian X. and Shieh L.S., "Fuzzy kalman filtering," Inf.
Sci. 109, pp. 197-209, 1998.
[13] Mao ,X., Wada, M. and Hashimoto, H., "Nonlinear GPS models for
position estimate using low-cost GPS receiver," IEEE Intel. Transp.
Syst. Proc., 12-15 Oct., pp.637-642, Vol. 1, 2003.
[14] Swanson, S. R., "A fuzzy navigational state estimator for GPS/INS
integration," Position Location and Navigation Symposium IEEE , 20-23
Apr., pp. 541-548, 1998.
[15] Villalon-Turrubiates, I.E., Ibarra-Manzano, O.G., Shmaliy, Y.S. and
Andrade-Lucio, J.A., "Three-dimensional optimal Kalman algorithm for
GPS-based positioning estimation of the stationary object," Proceedings
of First International Conference on Advanced Optoelectronics and
Lasers, 16-20 Sept., pp. 274 - 277, Vol.2, 2003.
[16] Ponomaryov, V.I., Pogrebnyak, O.B., de Rivera, L.N. and Garcia, J.C.S.,
"Increasing the accuracy of differential global positioning systemby
means of use the Kalman filtering technique," Proceedings of the 2000
IEEE International Symposium on Industrial Electronics, pp. 637 - 642,
Vol.2, 2000.