Copyright © 2007 IFAC
The 5 th IFAC Intl. WS DECOM-TT 2007, May 17-20, Cesme, Turkey
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1. INTRODUCTION - MAIN HEADING,
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2. SECOND SECTION TITLE
Tables!
A compact GPS unit is a convenient positioning system that directly gives the absolute longitude, latitude and height coordinates of the object (Bi, Hu,
Zhu & Sun, 2003). However, the position information provided by the commercial GPS unit is subjected to disturbance that causes the error in measurements. There are many sources of possible errors that will degrade the accuracy of positions computed by a GPS receiver. Table 1 shows these error sources and their values (Redmill et al., 2001).
Table 1 Typical GPS error sources and their quantities (in meters).
Error Source
Orbit errors
Ionosphere effects
Troposphere effects
Multipath distortion
Receiver noise
Selective availability (SA)
2.5
5.0
0.5
1.0
0.6
30.0
Effect







Satellite clock errors
2.0
He, Wang, Phain & Yu (2002) consider the application GPS-based navigation systems on various fields. Specifically, GPS has a broad application area in vehicle localization and navigation systems. Since the SA (selective availability error) degradation has been switched off by U.S. Government in June 2000, standard GPS measurement accuracy increased around 30 meters. As a result, this improvement has enhanced civil applications of GPS, primarily for general navigation tasks, even with the aid of ordinary, everyday (low-cost) GPS receivers.
Ponomaryov, Pogrebnyak, Rivera & Garcia (2000) employed only DGPS to improve accuracy in GPS position and velocity, and then presented a modified
Kalman filter for DGPS, to enhance the estimation of the position and velocity. Their experimental results showed that with that application their positional errors were about 5 meters (Ponomaryov et al .,
2000).
Figures!
According to (Zogg, 2002), the same GPS satellite errors are valid for any receiver within a radius of
200 kilometers, since they all use the same satellites.
RF Antenna
(Transmit-
Receive) station
RS-232 Serial
Communication
Mobile GPS
RF Antenna
(Transmit-Receive)
Computer (Runs the DGPS algorithm, Kalman filter algorithm and the control algorithm)
Fig. II General working philosophy of the vehicle navigation.
The figure above (Figure II) shows the guidance of the vehicle schematically. Both coordinates; namely, longitude and latitude, should ensure the condition that they must be lower than 1 meter. Figure III and
IV show the realization of the guidance philosophy in longitudinal criterion.
Kalman Filter Results
27.2308
27.2308
27.2307
27.2307
27.2306
27.2306
27.2305
27.2305
27.2304
0 20 40 60 80 sample time
100 120 140
Fig. V Longitude coordinate of the desired location and the filter performance.
In Figure V, it is seen that at the end of the control algorithm (after 133 seconds) the longitudinal distance to the desired longitude is computed as
0.4019 meters.
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3. THIRD SECTION TITLE
Equations!
Equations are to be centred and, in principle, have to be enumerated, beginning with (1) until the last number needed: Within in the text, they are cited solely by the respective number or by Eq. (number), inequality (number) or formula (number).
The state-space model and the filtering equations are x k

1
 Φ k x k
 w k
( 1) z k

H k x k
 v k
(2) where x k

 x ( k ) y ( k ) v x
( k ) v y
( k )

T
(3)
Φ k


1

 0


0
 0
0
1
0
0
T
0
1
0
0

T


0
1



(4) w k


0 z k

0
 z w
1
( k ) x
( k ) w
2
( k )

T
(5) z y
( k )

T
(6)
H k



1
0
0
1
0
0
0
0

 , v k

 v
1
( k ) v
2
( k )

T
(7) where v x
( k ) and v y
( k ) are latitude and longitude velocities, respectively. The discrete Kalman filter equations for the system are:
… … …
4. CONCLUSION
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REFERENCES
Brown, R. G. (1983). Introduction to random signal analysis and Kalman filtering . John Wiley &
Sons, New York.
Grewal, M. S., and A. P. Andrews (2001). Kalman filtering: Theory and practice using MATLAB
(2nd ed.). John Wiley & Sons, New York.
Kutay, A. T., Y. Tulunay, E. Tulunay, and O.
Tekinalp (2001). Neural network based orbit prediction for a geostationary stalite (Plenary
Paper 2). In: Automatic Systems for Building the
Infrastructure in Developing Countries 2001-
Proceedings of the 2 nd IFAC DECOM WS (G. M.
Dimirovski (Ed.)), Ohrid, MK, pp. 3-14.
Pergamon Elsevier Ltd, Oxford, UK.
Kalman, R. (1960). A new approach to linear filtering and prediction problems. Journal of Basic
Engineering, Trans. of the ASME , Series D , 82
(1), 35-45.
Kobayashi, K., Cheok, K. C., Watanabe, K.,
Munekata, F. (1998). Accurate differential global positioning system via fuzzy logic Kalman filter sensor fusion technique. IEEE Transactions on
Industrial Electronics , 45 (3), 510-518.
Negenborn, R. (2003). Robot localization and
Kalman filters, on finding your position in a noisy world , M.Sc thesis. Retrieved May 14,
2006, from http://www.negenborn.net/kal_loc/.
Ponomaryov, V. I., O. B. Pogrebnyak, L. N. de
Rivera, and J. C. S. Garcia, (2000). Increasing the accuracy of differential global positioning system by means of use the Kalman filtering technique. In: Proceedings of the 2000 IEEE
International Symposium on Industrial
Electronics, Vol. 2, 637-642. The IEEE,
Piscataway, NJ.
Qi, H., Moore, J. B. (2002). Direct Kalman filtering approach for GPS/INS integration. IEEE
Aerospace and Electronic Systems Magazine , 38 ,
687-693.
Roumeliotis, S. I., and G. A. Bekey (2000).
Collective localization: A distributed Kalman filter approach to localization of groups of mobile robots. In: Proceedings of the 2000 IEEE
International Conference on Robotics &
Automation, San Francisco, CA, pp. 2958-2965.
The IEEE, Piscataway, NJ.
Simon, D. (2001). Kalman Filtering . Retrieved May
07, 2006, from http://academic. csuohio.edu
/simond
Simon, D., El-Sherief, H. (1995). Real-time navigation using the global positioning system.
IEEE Aerospace and Electronic Systems
Magazine , 10 (1), 31-37.
Zogg, J. M. (2002). GPS Basics, Introduction to the
System, Application Overview . Retrieved June
05, 2006, from http://www.u-blox.com