本論文的主要目標是在無線通訊系統中發展新穎的定位法則。我們提出的方法是在沒有任何非視線傳播誤差(non-line-of-sight, NLOS)的資訊下，利用時間抵達(time of arrival, TOA)所形成的兩圓及角度抵達(angle of arrival, AOA)所形成的兩線之所有可能交點估測行動台的位置。泰勒展開式(Taylor series algorithm, TSA)及混合位置線法(hybrid lines of position algorithm, HLOP)都會有收斂的問題，行動台(mobile station, MS)和基地台(base station, BS)的相對位置會大幅影響其定位精度，由模擬結果顯示我們提出的方法在任何非視線傳播誤差模式下，在行動台位置的估測上均勝過泰勒展開式及混合位置線法，特別是在行動台及基地台的幾何分佈不好的時候。
同時考慮基地台的幾何分布情況及非視線傳播誤差的統計特性下，我們選擇權重幾何精度因子(weighted geometric dilution of precision, WGDOP)以改善定位之精度，當四個量測單元可供定位時，我們提出兩種型態的權重幾何精度因子之解析解(closed-form solutions)，如此可以大幅降低計算的複雜度。
利用倒傳遞類神經網路(back-propagation neural network, BPNN)進行幾何精度因子估測的架構將會擴充到利用彈性倒傳遞類神經網路(resilient back-propagation, Rprop)估測權重幾何精度因子及幾何精度因子，另外並提出兩種新的架構。我們藉由選擇最小的權重幾何精度因子所形成的子集合估測行動台位置，而這個子集合是由優先選擇提供服務的基地台並結合其他三個較佳的基地台所組成，因此，子集合的數量會大幅降低並且不會影響其定位精度。我們找出若干個權重幾何精度因子較小的子集合，並求出這些子集合所估測的行動台位置，再將這些位置輸入到另一個彈性倒傳遞類神經網路進行最後行動台位置的估測，結果顯示這樣可以消除不好的幾何分佈且位置精度可以大幅改善。

The objective of this thesis is to develop novel mobile location schemes for the cellular communication systems. We proposed methods utilize two time of arrival (TOA) circles and two angle of arrival (AOA) lines to find all the possible intersections to locate the mobile station (MS) without requiring a priori information about the non-line-of-sight (NLOS) error. The Taylor series algorithm (TSA) and the hybrid lines of position algorithm (HLOP) have convergence problems, and the relative positioning between the MS and the base stations (BSs) greatly affects the location accuracy. Simulation results show that the proposed methods perform better than TSA and HLOP regardless of the NLOS error distribution, particularly when the MS/BSs have an undesirable geometric layout.
Incorporating not only BSs geometry but also NLOS error statistics, we can choose the weighted geometric dilution of precision (WGDOP) to improve the accuracy of location. We proposed closed-form solutions of two formations WGDOP with less computation when for four measurements are available for location.
The architectures of back-propagation neural network (BPNN) for GDOP approximation which will be extended to WGDOP based on resilient back-propagation (Rprop) are presented and two types of the new architectures are proposed. We combined the serving BS and optimal three measurements with minimum WGDOP to estimate MS location. As such, the number of subsets is reduced greatly without compromising the location estimation accuracy. We applied the MS locations of the first several minimum WGDOP to next Rprop to determine the final MS location estimation. The results show that the poor geometry problem can be eliminated and the location accuracy can be significantly improved.

[1] FCC, “Revision of the commissions rules to insure compatibility with enhanced 911 emergency calling systems,” Technical Report RM-8143., FCC, July 1996.
[2] J. H. Reed, K. J. Krizman, B. D. Woerner, and T. S. Rappaport, “An overview of the challenges and progress in meeting the E-911 requirement for location service,” IEEE Communications Magazine, vol. 36, no. 4, pp. 30-37, April 1998.
[3] Y. Zhao, “Standardization of mobile phone positioning for 3G systems,” IEEE Communications Magazine, vol. 40, no. 7, pp. 108-116, July 2002.
[4] J. J. Caffery, Jr. and G. Stuber, “Overview of radiolocation in CDMA cellular systems,” IEEE Communications Magazine, vol. 36, no. 4, pp. 38-45, April 1998.
[5] R. Muhamed and T. S. Rappaport, “Comparison of conventional subspace-based DOA estimation algorithms with those employing property-restoral techniques: simulation and measurements,” in Proc. IEEE International Universal Personal Communications Conference, vol. 2, pp. 1004-1008, October 1996.
[6] K. J. Krizman, T. E. Biedka, and T. S. Rappaport, “Wireless position location: fundamentals, implementation strategies, and sources of error,” in Proc. IEEE Vehicular Technology Conference, vol. 2, pp. 919-923, May 1997.
[7] M. Silventoinen and T. Rantalainen, “Mobile station emergency locating in GSM,” in IEEE International Conference on Personal Wireless Communications, pp. 232-238, February 1996.
[8] S. S. Woo, H. R. You, and J. S. Koh, “The NLOS mitigation technique for position location using IS-95 CDMA networks,” IEEE Vehicular Technology Conference, vol. 6, pp. 2556-2560, September 2000.
[9] J. J. Caffery, Wireless location in CDMA cellular radio systems, Kluwer Academic, 2000.
[10] A. Ghosh and R. Love, “Mobile station location in a DS-CDMA system,” in IEEE 48th Vehicular Technology Conference, vol. 1, pp. 254-258, May 1998.
[11] C. Ma, “Integration of GPS and cellular networks to improve wireless location performance,” in The Institute of Navigation, Proceedings of GPS 2003, pp. 1585-1596, September 2003.
[12] S. Tekinay, E. Chao, and R. Richton, “Performance benchmarking for wireless location systems,“ IEEE mmunications Magazine, vol. 36, no. 4, pp. 72-76, April 1998.
[13] G. L. Turin, W. S. Jewell, and T. L. Johnston, “Simulation of urban vehicle-monitoring systems,” IEEE Transactions on Vehicular Technology, vol. VT-21, no. 1, pp. 9-16, February 1972.
[14] D. J. Torrieri, “Statistical theory of passive location systems,” IEEE Transactions on Aerospace and Electronic Systems, vol. AES-20, no. 2, pp. 183-198, March 1984.
[15] T. S. Rappaport, J H. Reed, and B. D. Woerner, “Position location using wireless communications on highways of the future,” IEEE Communications Magazine, vol. 34, pp. 33-41, October 1996
[16] S. Riter and J. McCoy, “Automatic vehicle location—An overview,” IEEE Transactions on Vehicular Technology, vol. VT-26, no. 1, pp. 7-11, February 1977.
[17] J. J. Caffery and G. L. Stuber, “Vehicle location and tracking for IVHS in CDMA microcells,” in IEEE Personal Indoor Mobile Radio Conference, vol. 4, pp. 1227-1231, September 1994.
[18] J. J. Caffery and G. L. Stuber, “Radio location in urban CDMA microcells,” in Proc. IEEE International Symposium Personal, Indoor, Mobile Radio Communications, vol. 2, pp. 858-862, September 1995.
[19] W. Chen, L. Chen, Z. Chen, and S. Tu, “WITS: A wireless sensor network for intelligent transportation system,” in Proc. of the First International Multi-Symposiums on Computer and Computational Science, vol. 2, pp. 635-641, June 2006.
[20] S. S. Wang and M. Green, “Mobile location method for non-line-of-sight situation,” in Proc. IEEE Vehicular Technology Conference, vol. 2, pp. 608-612, September 2000.
[21] J. Ahn, J. Heo, S. Lim, J. Seo, and W. Kim, “A study of healthcare system for patient location data based on LBS,” Proc. International Conference Consumer Electronics, pp. 1-2, January 2008.
[22] J. S. Maltz, T. S. C. Ng, D. J. Li, J. Wang, K. Wang, W. Bergeron, R. Martin, and T. F. Budinger, “The trauma patient tracking system: implementing a wireless monitoring infrastructure for emergency response,” Proc. IEEE International Conference Engineering in Medicine and Biology Society, pp.2441-2446, January 2006.
[23] I. H. Shin, J. H. Lee, and H. C. Kim, “Ubiquitous monitoring system for chronic obstructive pulmonary disease and heart disease patients,” Proc. IEEE International Conference Engineering in Medicine and Biology Society, pp. 3689-3692, August 2007.
[24] S. H. Chew, P. A. Chong, E. Gunawan, K. W. Goh, Y. Kim, and C. B. Soh, “A hybrid mobile-based patient location tracking system for personal healthcare applications,” Proc. IEEE International Conference Engineering in Medicine and Biology Society, pp. 5188-5191, September 2006.
[25] J. M. Zagami, S. A. Parl, J. J. Bussgang, and K. D. Melillo, “Providing universal location services using a wireless E911 location network,” IEEE Communications Magazine, vol. 36, no. 4, pp. 66-71, April 1998.
[26] M. N. Borenovic, M. I. Simic, A. M. Neskovic and M. M. Petrovic, “Enhanced Cell-ID + TA GSM positioning technique,” International Conference on in Computer as a Tool, vol. 2, pp. 1176-1179, November 2005.
[27] W. G. Figel, N. H. Shepherd, and W. F. Trammell, “Vehicle location by a signal attenuation method,” IEEE Transactions on Vehicular Technology, vol. VT-18, no. 3, pp. 105-109, November 1969.
[28] H.-L. Song, “Automatic vehicle location in cellular communications systems,” IEEE Transactions on Vehicular Technology, vol. 43, no. 4, pp. 902-908, November 1994.
[29] M. P. Lotter and P. van Rooyen, “Space division multiple access for cellular CDMA,” in IEEE International Conference on Spread Spectrum Techniques and Applications, vol. 3, pp. 959-964, September 1998.
[30] P.-C. Chen, “A non-line-of-sight error mitigation algorithm in location estimation,” in Proc. IEEE Wireless Communications and Networking Conference, vol. 1, pp. 316-320, September 1999.
[31] B. T. Fang, “Simple solution for hyperbolic and related position fixes,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26, no. 5, pp. 748-753, September 1990.
[32] J. O. Smith and J. S. Abel, “Closed-form least squares source location estimation from range difference measurements,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. ASSP-35, no. 12, pp. 1661-1669, December 1987.
[33] M. Hata and T. Nagatsu, “Mobile location using signal strength measurements in a cellular system,”IEEE Transactions on Vehicular Technology, vol. VT-29, no. 2, pp. 245-252, May 1980.
[34] M. Riedmiller and H. Braun, “A direct adaptive method for faster backpropagation learning: the RPROP algorithm,” Proc. IEEE International Conferenceon Neural Network, vol.1, pp. 586-591, March 1993.
[35] M. Hellebrandt, R. Mathar, and M. Schiebenbogen, “Estimating position and velocity of mobiles in a cellular radio network,” IEEE Transactions on Vehicular Technology, vol. 46, no. 1, pp. 65-71,February 1997.
[36] M. Hellebrandt and R. Mathar, “Location tracking of mobiles in cellular radio networks,” IEEE transactions on Vehicular Technology, vol. 48, no. 5, pp. 1558-1562, September 1999.
[37] S. Anderson, M. Millnert, M. Viberg, and B. Wahlberg, “An adaptive array for mobile communication systems,” IEEE Transactions on Vehicular Technology, vol. 40, no. 1, pp. 230-236, February 1991.
[38] J. Caffery Jr. and G. L. Stuber, “Subscriber location in CDMA cellular networks,” IEEE Transactions on Vehicular Technology, vol. 47, no. 2, pp. 406-416, May 1998.
[39] A. Pges-Zamora, J. Vidal, and D. H. Brooks, “Closed-form solution for positioning based on angle of arrival measurements,” in Proc. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 4, pp. 1522-1526, September 2002.
[40] C.-S. Chen, S.-S. Su, and Y.-F. Huang, “Hybrid TOA/AOA geometrical positioning schemes for mobile location,” IEICE Transactions on Communications, vol. E92-B, no 2, pp. 396-402, February 2009.
[41] C.-S. Chen, S.-L. Su, and C.-D. Lu, “Geometrical positioning approached for mobile location estimation,” IEEE International Conference on Information Management and Engineering, pp. 268-272, April 2010.
[42] S. S. Wang, M. Green, and M. Malkawa, “E-911 location standards and location commercial services,”in IEEE Emerging Technologies Symposium: Broadband, Wireless Internet Access, pp. 1-5, April 2000.
[43] J. J. Caffery, Jr., “A new approach to the geometry of TOA location,” in Proc. IEEE Vehicular Technology Conference, pp. 1943-1949, Sept. 2000.
[44] M. Zhang and J. Zhang, “A fast satellite selection algorithm: beyond four satellites,” IEEE Journal of Selected Topics in Signal Processing, vol. 3 pp. 740–747, October 2009.
[45] W. H. Foy, “Position-location solutions by Taylor series estimation,” IEEE Transactions on Aerospace and Electronic Systems, vol. AES-12, no. 2, pp. 187-194, March 1976.
[46] K. C. Ho and Y. T. Chan, “Solution and performance analysis of geolocation by TDOA,” IEEE Transactions on Aerospace and Electronic Systems, vol. 29, no. 4, pp. 1311-1322, October 1993.
[47] Y. T. Chan and K. C. Ho, “A simple and efficient estimator for hyperbolic location,” IEEE Transactions on Signal Processing, vol. 42, no. 8, pp. 1905-1915, August 1994.
[48] E. D. Kaplan and C. J. Hegarty, Understanding GPS: principles and applications, Artech House Press, Boston, 2006.
[49] Y. Zhao, “Mobile phone location determination and its impact on intelligent transportation systems,”IEEE Transactions on Intelligent Transportation Systems, vol. 1, no. 1, pp. 55-64, March 2000.
[50] M. A. Spirito, “Further results on GSM mobile station location,” Electronics Letters, vol. 35, no. 11, pp. 867-869, May 1999.
[51] L. Cong and W. Zhuang, “Hybrid TDOA/AOA mobile user location for wideband CDMA cellular systems,” IEEE Transactions on Wireless Communications, vol. 1, no. 3, pp. 439-447, July 2002.
[52] L. Cong and W. Zhuang, “Hybrid TDOA/AOA mobile user location in wideband CDMA systems,” in Proc. IEEE International Conference on Third Generation Wireless Communications, pp. 675-682, June 2000.
[53] N. J. Thomas, D. G. M. Cruickshank, and D. I. Laurenson, “Performance of a TDOA-AOA hybrid mobile location system,” in International Conference on 3G Mobile Communication Technologies, pp. 216-220, March 2001.
[54] S. Venkatraman and J. Caffery, Jr., “Hybrid TOA/AOA techniques for mobile location in non-line-of-sight environments,” in Proc. IEEE Wireless Communications and Networking Conference,vol. 1, pp. 274-278, March 2004.
[55] P. Deng and P. Z. Fan, “An AOA assisted TOA positioning system,” in International Conference on Communication Technology Proceedings, vol. 2, pp. 1501-1504, March 2000.
[56] M. A. Spirito, “Mobile station location with heterogeneous data,” in IEEE Vehicular Technology Conference, vol. 4, pp. 1583-1589, September 2000.
[57] S. Al-Jazzar, J. Caffery, and H.-R. You, “A scattering model based approach to NLOS mitigation in TOA location systems,” in Proc. IEEE Vehicular Technology Conference, vol. 2, pp. 861-865, May 2002.
[58] S. Venkatraman, J. Caffery, and H.-R. You, “Location using LOS range estimation in NLOS environments,” in Proc. IEEE Vehicular Technology Conference, vol. 2, pp. 856-860, May 2002.
[59] M. P. Wylie and S. Wang, “Robust range estimation in the presence of the non-line-of-sight error,” in Proc. IEEE Vehicular Technology Conference, vol. 1, pp. 101-105, May 2001.
[60] M. P. Wylie and J. Holtzman, “The non-line of sight problem in mobile location estimation,” in Proc. IEEE International Conference Universal Personal Communication, vol. 2, pp. 827-831, September 1996.
[61] L. Xiong, “A selective model to suppress NLOS signals in angle-of-arrival (AOA) location estimation,” in Proc. IEEE International Conference Personal, Indoor, Mobile Radio Communications, vol. 1, pp. 461-465, September 1998.
[62] L. Cong and W. Zhuang, “Non-line-of-sight error mitigation in TDOA mobile location,” in Proc. IEEE Globecom, vol. 1, pp. 680-684, November 2001.
[63] L. Cong and W. Zhuang, “Nonline-of-sight error mitigation in mobile location,” IEEE Transactions on Wireless Communications, vol. 4, no. 2, pp. 560-573, March 2005.
[64] J. Borras, P. Hatrack, and N. B. Mandayam, “Decision theoretic framework for NLOS identification,” in Proc. IEEE Vehicular Technology Conference, vol. 2, pp. 1583-1587, May 1998.
[65] S. Venkatraman, J. Caffery, and H.-R. You, “A novel TOA location algorithm using LOS range estimation for NLOS environments,” IEEE Transactions on Vehicular Technology, vol. 53, no. 5, pp.1515-1524, September 2004.
[66] C.-S. Chen, S.-L. Su, and C.-D. Lu, “Hybrid TOA/AOA schemes for mobile location in cellular communication systems,” International Conference of World Academy of Science, Engineering and Technology, pp. 165-169, Februry 2010.
[67] C.-S. Chen and S.-L. Su, “Geometrical positioning with hybrid TOA/AOA approaches for mobile location in non-line-of-sight environments,” International Technical Conference on Circuits/System, Computers and vommunications, July 2006.
[68] P. V. Rooyen, M. N. Lötter, and D. V. Wyk, Space-time processing for CDMA mobile communications. New York: Kluwer, 2000.
[69] K.-T. Feng, C.-L. Chen, and C.-H. Chen, “GALE: an enhanced geometry-assisted location estimation algorithm for NLOS environments,” IEEE Transaction on Mobile Computing, vol. 7, no. 2, pp. 199-213, February 2008.
[70] K. Kawamura and T. Tanaka, “Study on the improvement of measurement accuracy in GPS,”International Joint Conference SICE-ICASE, pp. 1372-1375, October 2006.
[71] E.-J. Zhong and T.–Z. Huang, “Geometric dilution of precision in navigation computation,” International Conference Machine Learning and Cybernetics, pp. 4116-4119, August 2006.
[72] C. Hongwei and S. Zhongkang, “A nonlinear optimized location algorithm for bistatic radar system,” International Conference Aerospace and Electronics, vol. 1, pp. 201-205, May 1995.
[73] R. Yarlagadda, I. Ali, N. Al-Dhahir, and J. Hershey, “GPS GDOP metric,” IEE Proc.-Radar, Sonar Navigation, vol. 147, no. 5, pp. 259-264, October 2000.
[74] N. Levanon, “Lowest GDOP in 2-D scenarios,” IEE Proc.-Radar, Sonar and Navigation, vol. 147, no. 3, pp. 149-155, June 2000.
[75] C. Park, I. Kim, J. G. Lee, and G.-I. Jee, “A satellite selection criterion incorporating the effect of elevation angle in GPS positioning,” Control Engineering Practice, vol. 4, no. 12, pp. 1741-1746, December 1996.
[76] M. S. Phatak, “Recursive method for optimum GPS satellite selection,” IEEE Transactions on Aerospace and Electronic Systems, vol. 37, no. 2, pp. 751-754, April 2001.
[77] C.-S. Chen and S.-L. Su, “Hybrid TOA/AOA technique approaches for mobile location in wireless systems,” International Symposium on Communications, November 2005.
[78] G. Sun, J. Chen, W. Guo, and K.J. Ray Liu, “Signal processing techniques in network-aided positioning,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp.12-23, July 2005.
[79] Y. Hsu, “Relations between dilutions of precision and volume of the tetrahedron formed by four satellites,” in Proc. IEEE Position Location and Navigation Symposium, pp. 669-676, April 1994.
[80] J. Zhu, “Calculation of geometric dilution of precision,” IEEE Transactions on Aerospace and Electronic Systems, vol. 28, no. 3, pp. 893-895, July 1992.
[81] D. Simon and H. El-Sherief, “Navigation satellite selection using neural networks,” Neurocomputing, vol. 7, pp. 247-258, May 1995.
[82] D. Simon and H. El-Sherief, “Fault-tolerant training for optimal interpolative nets,” IEEE Transactions Neural Networks, vol. 6, no. 6, pp. 1531-1535, Novvember 1995.
[83] D.-J. Jwo and K.-P. Chin, “Applying back-propagation neural networks to GDOP approximation,” the Journal of Navigation, vol. 55, pp. 97-108, January 2002.
[84] C.-S. Chen and S.-L. Su, “Dilution of position calculation for accuracy improvement in wireless location systems,” International Technical Conference on Circuits/System, Computers and Communications, July 2007.
[85] C.-S. Chen and S.-L. Su, “Resilient back-propagation neural network for approximation 2-D GDOP,”International Technical MultiConference of Engineers and Computer Scientists, pp. 900-904, March 2010.
[86] C.-S. Chen, S.-L. Su, H.-N. Shou and C.-Y. Lu, “Resilient back-propagation neural network for approximation weighted geometric dilution of precision,” International IEEE Conference on Computer Science and Information Technology, July 2010.
[87] G.M. Siouris, Aerospace avionics systems: a modern synthesis, Academic Press, San Diego, 1993.
[88] H. Sairo, D. Akopian, and J. Takala, “Weighted dilution of precision as quality measure in satellite positioning,” IEE Proc. Radar, Sonar and Navigation, vol. 150, no.6, pp. 430-436, December 2003.
[89] Y. Yong and M. Lingjuan, “GDOP results in all-in-view positioning and in four optimum satellites positioning with GPS PRN codes ranging,” Position, Location and Navigation Symposium, pp. 723-727,April 2004.
[90] M. Pachter, J. Amt, and J. Raquet, “Accurate positioning using a planar pseudolite array,” Position, Location and Navigation Symposium, pp.433-440, May 2008.
[91] X. Bo and B. Shao, “Satellite selection algorithm for combined GPS galileo navigation receiver,”International Conference Autonomous Robots and Agents, pp.149-154, February 2009.
[92] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature, pp. 533-536, October 1986.
[93] L. M. Patnaik and K. Rajan, “Target detection through image processing and resilient propagation algorithms,” Neurocomputing, pp. 123-135, April 2000.
[94] J. H. Yap, S. Ghaheri-Niri, and R. Tafazolli, “Accuracy and hearability of mobile positioning in GSM and CDMA networks,” Third International Conference on 3G Mobile Communication Technologies, pp. 350 -354, May 2002.
[95] C.-H. Chen, K.-T. Feng, C.-L. Chen, and P.-H. Tseng, “Wireless location estimation with the assistance of virtual base stations,” IEEE Transactions on Vehicular Technology, vol. 58, no. 1, pp. 93-106, January 2009.
[96] W. C. Y. Lee, “Power control in CDMA (cellular radio),” in Proc. IEEE Vehicular Technology Conference, pp. 77-80, May 1991.
[97] C.-L. Chen and K.-T. Feng, “An efficient geometry-constrained location estimation algorithm for NLOS environments,” in International Conference Wireless Networks, Communications and Mobile Computing, vol. 1, pp. 244-249, June 2005.
[98] I. A. Getting, “The global positioning system,” IEEE Spectrum, pp. 36-47, December 1993.
[99] R. Lupas and S. Verdú, “Near-far resistance of multiuser detectors in asynchronous channels,” IEEE Transactions on Communications, vol. 39, no. 4, pp. 496-508, Aprl 1990.
[100] E. Trevisani and A. Vitaletti, “Cell-ID location technique, limits and benefits: an experimental study,” Proc. IEEE Workshop on Mobile Computing Systems and Applications, pp. 51-60, December 2004.
[101] M. Kihara, “Study of a GPS satellite selection policy to improve positioning accuracy,” IEEE Position Location and Navigation Symposium, pp.267-273, Aprl 1994.