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.<\/p>\r\n","references":"[1] Leick, A., GPS Satellite Surveying , Second Edition, John Wiley&Sons,\r\nINC., 1995.\r\n[2] Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J., GPS Theory and\r\nPractice, Third Revised Edition, Springer-Verlag, New York, NY, 1994.\r\n[3] Gelb, Arthur, Ed., Applied Optimal Estimation, M.I.T. Press,\r\nCambridge, MA, 1974.\r\n[4] Brown R.G., Hwang P., Introduction to Random Signals and Applied\r\nKalman Filtering, Second Edition, John Wiley&Sons, INC., 1992.\r\n[5] Dana H. Peter, Global Positioning System Overview, (Online)\r\nhttp:\/\/www.colorado.edu\/geography\/gcraft\/notes\/gps\/gps_f.html\r\n[6] OBE Consulting Engineers Rinex format data,\r\nwww.obec.com\/data\/TRSDATA\/Rinex\/index.htm\r\n[7] Dermanis A., Space Geodesy and Geodynamimcs, Editions Ziti, 1999.\r\n[8] Rossikopoulos D., Topographic networks and computations, 2nd edition,\r\nEditions Ziti, 1992. (in Greek)\r\n[9] Kalman R. E., \"A new approach to linear filtering and prediction\r\nproblems,\" Transactions of the ASME---Journal of Basic Engineering,\r\npp. 35-45, March 1960.\r\n[10] Julier, S. J., Uhlmann J. K. and Durrant-Whyte, H. F., \"A new approach\r\nfor filtering nonlinear systems,\" Proc. American Control Conference,\r\nSeattle, Washington, pp. 1628-1632, 1995.\r\n[11] Chen G., Wang J. and Shieh L., \"Interval kalman filtering,\" IEEE Trans.\r\nAerosp. Electron. Syst. 33, pp. 250-259, 1997.\r\n[12] Guanrong C., Qingxian X. and Shieh L.S., \"Fuzzy kalman filtering,\" Inf.\r\nSci. 109, pp. 197-209, 1998.\r\n[13] Mao ,X., Wada, M. and Hashimoto, H., \"Nonlinear GPS models for\r\nposition estimate using low-cost GPS receiver,\" IEEE Intel. Transp.\r\nSyst. Proc., 12-15 Oct., pp.637-642, Vol. 1, 2003.\r\n[14] Swanson, S. R., \"A fuzzy navigational state estimator for GPS\/INS\r\nintegration,\" Position Location and Navigation Symposium IEEE , 20-23\r\nApr., pp. 541-548, 1998.\r\n[15] Villalon-Turrubiates, I.E., Ibarra-Manzano, O.G., Shmaliy, Y.S. and\r\nAndrade-Lucio, J.A., \"Three-dimensional optimal Kalman algorithm for\r\nGPS-based positioning estimation of the stationary object,\" Proceedings\r\nof First International Conference on Advanced Optoelectronics and\r\nLasers, 16-20 Sept., pp. 274 - 277, Vol.2, 2003.\r\n[16] Ponomaryov, V.I., Pogrebnyak, O.B., de Rivera, L.N. and Garcia, J.C.S.,\r\n\"Increasing the accuracy of differential global positioning systemby\r\nmeans of use the Kalman filtering technique,\" Proceedings of the 2000\r\nIEEE International Symposium on Industrial Electronics, pp. 637 - 642,\r\nVol.2, 2000.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 37, 2010"}