This article is part of the series Wireless Location Technologies and Applications.

Open Access Research Article

A Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

KW Cheung1*, HC So1, W-K Ma2 and YT Chan3

Author Affiliations

1 Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

2 Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan

3 Department of Electrical & Computer Engineering, Royal Military College of Canada, Kingston, ON, Canada, K7K 7B4

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EURASIP Journal on Advances in Signal Processing 2006, 2006:020858  doi:10.1155/ASP/2006/20858


The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2006/1/020858


Received:20 May 2005
Revisions received:25 November 2005
Accepted:8 December 2005
Published:20 April 2006

© 2006 Cheung et al.

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

References

  1. CC Docket no. 94-102, Revision of the Commissions Rules to Ensure Compatibility with Enhanced 911 Emergency Calling Systems, RM-8143 July, 1996

  2. C Drane, M Macnaughtan, C Scott, Positioning GSM telephones. IEEE Communications Magazine 36(4), 46–54, 59 (1998). Publisher Full Text OpenURL

  3. H Koshima, J Hoshen, Personal locator services emerge. IEEE Spectrum 37(2), 41–48 (2000). Publisher Full Text OpenURL

  4. Y Zhao, Mobile phone location determination and its impact on intelligent transportation systems. IEEE Transactions on Intelligent Transportation Systems 1(1), 55–64 (2000). Publisher Full Text OpenURL

  5. D Porcino, Performance of a OTDOA-IPDL positioning receiver for 3GPP-FDD mode. Proceedings of the IEE 2nd International Conference on 3G Mobile Communication Technologies (3G '01), March 2001, London, UK, 221–225

  6. JJ Caffery Jr.., Wireless Location in CDMA Cellular Radio Systems (Kluwer Academic, Boston, Mass, USA, 2000)

  7. JC Liberti, TS Rappaport, Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications (Prentice-Hall, Upper Saddle River, NJ, USA, 1999)

  8. M McGuire, KN Plataniotis, A comparison of radiolocation for mobile terminals by distance measurements. Proceedings of International Conference on Wireless Communications, 2000, 1356–1359

  9. JJ Caffery Jr.., GL Stuber, Subscriber location in CDMA cellular networks. IEEE Transactions on Vehicular Technology 47(2), 406–416 (1998). Publisher Full Text OpenURL

  10. MA Spirito, On the accuracy of cellular mobile station location estimation. IEEE Transactions on Vehicular Technology 50(3), 674–685 (2001). Publisher Full Text OpenURL

  11. WH Foy, Position-location solutions by Taylor-series estimation. IEEE Transactions on Aerospace and Electronic Systems 12(2), 187–194 (1976)

  12. DJ Torrieri, Statistical theory of passive location systems. IEEE Transactions on Aerospace and Electronic Systems 20, 183–197 (1984)

  13. JO Smith, JS Abel, Closed-form least-squares source location estimation from range-difference measurements. IEEE Transactions on Acoustics, Speech, and Signal Processing 35(12), 1661–1669 (1987). Publisher Full Text OpenURL

  14. YT Chan, KC Ho, A simple and efficient estimator for hyperbolic location. IEEE Transactions on Signal Processing 42(8), 1905–1915 (1994). Publisher Full Text OpenURL

  15. Y Huang, J Benesty, GW Elko, RM Mersereati, Real-time passive source localization: a practical linear-correction least-squares approach. IEEE Transactions on Speech and Audio Processing 9(8), 943–956 (2001). Publisher Full Text OpenURL

  16. A Pages-Zamora, J Vidal, DR Brooks, Closed-form solution for positioning based on angle of arrival measurements. Proceedings of the 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '02), September 2002, Lisbon, Portugal 4, 1522–1526

  17. L Cong, W Zhuang, Hybrid TDOA/AOA mobile user location for wideband CDMA cellular systems. IEEE Transactions on Wireless Communications 1(3), 439–447 (2002). Publisher Full Text OpenURL

  18. HC So, SP Hui, Constrained location algorithm using TDOA measurements. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E86-A(12), 3291–3293 (2003)

  19. KW Cheung, HC So, W-K Ma, YT Chan, Received signal strength based mobile positioning via constrained weighted least squares. Proceedings of the IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 5, 137–140

  20. KW Cheung, HC So, W-K Ma, YT Chan, Least squares algorithms for time-of-arrival-based mobile location. IEEE Transactions on Signal Processing 52(4), 1121–1130 (2004). Publisher Full Text OpenURL

  21. SM Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, NJ, USA, 1993)

  22. H-L Song, Automatic vehicle location in cellular communications systems. IEEE Transactions on Vehicular Technology 43(4), 902–908 (1994). Publisher Full Text OpenURL

  23. J Vidal, M Najar, R Jativa, High resolution time-of-arrival detection for wireless positioning systems. Proceedings of 56th IEEE Vehicular Technology Conference (VTC '02), September 2002, Vancouver, BC, Canada 4, 2283–2287

  24. J Riba, A Urruela, A robust multipath mitigation technique for time-of-arrival estimation. Proceedings of 56th IEEE Vehicular Technology Conference (VTC '02), September 2002, Vancouver, BC, Canada 4, 2263–2267

  25. S Al-Jazzar, JJ Caffery Jr.., H-R You, A scattering model based approach to NLOS mitigation in TOA location systems. Proceedings of 55th IEEE Vehicular Technology Conference (VTC '02), May 2002, Birmingham, Ala, USA 2, 861–865

  26. MP Wylie-Green, SS Wang, Robust range estimation in the presence of the non-line-of-sight error. Proceedings of 54th IEEE Vehicular Technology Conference (VTC '01), September 2001, Atlantic City, NJ, USA 1, 101–105

  27. N Patwari, AO Hero III., M Perkins, NS Correal, RJ O'Dea, Relative location estimation in wireless sensor networks. IEEE Transactions on Signal Processing 51(8), 2137–2148 (2003). Publisher Full Text OpenURL

  28. KW Cheung, HC So, A multidimensional scaling framework for mobile location using time-of-arrival measurements. IEEE Transactions on Signal Processing 53(2), 460–470 (2005)

  29. TK Moon, WC Stirling, Mathematical Methods and Algorithms for Signal Processing (Prentice-Hall, Upper Saddle River, NJ, USA, 2000)