H∞ Filtering Approach for GSM Navigation Systems
Institute of Automatic Control Engineering, Feng Chia University
The GSM navigation system designs using H∞ filtering approach is conducted and the resulting performance is assessed. The H∞ filtering problem is shown to have many solutions for each proper value of the prescribed design parameter γ, which is different from the Kalman filter with only one solution. The Kalman filter, which employed in the GSM receiver as the navigational state estimator, provides optimal solution if the noise statistics for both the measurement and the system process are completely known. Practically, the noises are varying with time, which results in filtering performance degradation. In design, H∞ filter can be employed to ensure that the energy gain from the disturbances to the estimation error will not exceed an upper bound.
-  O. Kinsman, “Pattern Recognition by Hidden Markov Models for Supporting Handover Decisions in the GSM System,” Proc. 6th Nordic Seminar Dig. Mobile Radio Comm., Stockholm, Sweden, pp. 195-202, 1994.
-  O. Kennemann, “Continuous Location of Moving GSM Mobile Stations by Pattern Recognition Techniques,” Proc. 5th Int. Symp. Personal, Indoor, Mobile, Radio Comm., Den Haag, Holland, pp. 630-634, 1994.
-  H. L. Song, “Automatic Vehicle Location in Cellular Communication Systems,” IEEE Transactions on Vehicular Technology, Vol.43, No.2, pp. 902-908, 1994.
-  Z. Salcic and E. Chan, “Mobile Station Positioning Using GSM Cellular Phone and Artificial Neural Networks,” Wireless Personal Communications, Vol.14, No.3, pp. 235-254, 2000.
-  M. Green and D. Limebeer, Linear Robust Control, Prentice-Hall, 1995.
-  R. N. Banavar and J. L. Speyer, “A Linear Quadratic Game Theory Approach to Estimation and Smoothing,” Proc. IEEE ACC, pp. 2818-2822, 1991.
-  U. Shaked and Y. Theodor, “H∞ Optimal Estimation: A Tutorial,” Proc. 31st IEEE CDC, pp. 2278-2286, 1992.
-  I. Yaesh and U. Shaked, “A Transfer Function Approach to the Problem of Discrete-Time System: H∞-Optimal Linear Control and Filtering,” IEEE Trans. on Automatic Control, Vol.36, No.4, pp. 1264-1271, 1991.
-  X. Shen and L. Deng, “Game Theory Approach to Discrete H∞ Design,” IEEE Trans. on Signal Processing, Vol.45, No.2, pp. 1902-1905, 1997.
-  X. Shen and L. Deng, “A Dynamic System Approach to Speech Enhancement Using the H∞ Filtering Algorithm,” IEEE Trans. on Speech and Audio Processing, Vol.47, No.4, pp. 1902-1905, 1999.
-  X. He, Y. Q. Chen, and B. Vik, “Design of Minimax Filtering for an Integrated GPS/INS System,” Journal of Geodesy, Vol.73, No.1, pp. 407-411, 1999.
-  D. Simon and H. El-Sherief, “Hybrid Kalman/Minimax Filtering in Phase-Locked Loops,” Journal of Control Engineering Practice, Vol.42, No.2, pp. 615-623, 1996.