Open Access

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

EURASIP Journal on Advances in Signal Processing20062006:020858

DOI: 10.1155/ASP/2006/20858

Received: 20 May 2005

Accepted: 8 December 2005

Published: 20 April 2006


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.


Authors’ Affiliations

Department of Electronic Engineering, City University of Hong Kong
Department of Electrical Engineering, National Tsing Hua University
Department of Electrical & Computer Engineering, Royal Military College of Canada


  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. Drane C, Macnaughtan M, Scott C: Positioning GSM telephones. IEEE Communications Magazine 1998, 36(4):46-54, 59. 10.1109/35.667413View ArticleGoogle Scholar
  3. Koshima H, Hoshen J: Personal locator services emerge. IEEE Spectrum 2000, 37(2):41-48. 10.1109/6.819928View ArticleGoogle Scholar
  4. Zhao Y: Mobile phone location determination and its impact on intelligent transportation systems. IEEE Transactions on Intelligent Transportation Systems 2000, 1(1):55-64. 10.1109/6979.869021View ArticleGoogle Scholar
  5. Porcino D: 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.View ArticleGoogle Scholar
  6. Caffery JJ Jr.: Wireless Location in CDMA Cellular Radio Systems. Kluwer Academic, Boston, Mass, USA; 2000.Google Scholar
  7. Liberti JC, Rappaport TS: Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications. Prentice-Hall, Upper Saddle River, NJ, USA; 1999.Google Scholar
  8. McGuire M, Plataniotis KN: A comparison of radiolocation for mobile terminals by distance measurements. Proceedings of International Conference on Wireless Communications, 2000 1356-1359.Google Scholar
  9. Caffery JJ Jr., Stuber GL: Subscriber location in CDMA cellular networks. IEEE Transactions on Vehicular Technology 1998, 47(2):406-416. 10.1109/25.669079View ArticleGoogle Scholar
  10. Spirito MA: On the accuracy of cellular mobile station location estimation. IEEE Transactions on Vehicular Technology 2001, 50(3):674-685. 10.1109/25.933304View ArticleGoogle Scholar
  11. Foy WH: Position-location solutions by Taylor-series estimation. IEEE Transactions on Aerospace and Electronic Systems 1976, 12(2):187-194.View ArticleGoogle Scholar
  12. Torrieri DJ: Statistical theory of passive location systems. IEEE Transactions on Aerospace and Electronic Systems 1984, 20: 183-197.View ArticleGoogle Scholar
  13. Smith JO, Abel JS: Closed-form least-squares source location estimation from range-difference measurements. IEEE Transactions on Acoustics, Speech, and Signal Processing 1987, 35(12):1661-1669. 10.1109/TASSP.1987.1165089View ArticleGoogle Scholar
  14. Chan YT, Ho KC: A simple and efficient estimator for hyperbolic location. IEEE Transactions on Signal Processing 1994, 42(8):1905-1915. 10.1109/78.301830MathSciNetView ArticleGoogle Scholar
  15. Huang Y, Benesty J, Elko GW, Mersereati RM: Real-time passive source localization: a practical linear-correction least-squares approach. IEEE Transactions on Speech and Audio Processing 2001, 9(8):943-956. 10.1109/89.966097View ArticleGoogle Scholar
  16. Pages-Zamora A, Vidal J, Brooks DR: 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.View ArticleGoogle Scholar
  17. Cong L, Zhuang W: Hybrid TDOA/AOA mobile user location for wideband CDMA cellular systems. IEEE Transactions on Wireless Communications 2002, 1(3):439-447. 10.1109/TWC.2002.800542View ArticleGoogle Scholar
  18. So HC, Hui SP: Constrained location algorithm using TDOA measurements. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2003, E86-A(12):3291-3293.Google Scholar
  19. Cheung KW, So HC, Ma W-K, Chan YT: 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.Google Scholar
  20. Cheung KW, So HC, Ma W-K, Chan YT: Least squares algorithms for time-of-arrival-based mobile location. IEEE Transactions on Signal Processing 2004, 52(4):1121-1130. 10.1109/TSP.2004.823465MathSciNetView ArticleGoogle Scholar
  21. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.MATHGoogle Scholar
  22. Song H-L: Automatic vehicle location in cellular communications systems. IEEE Transactions on Vehicular Technology 1994, 43(4):902-908. 10.1109/25.330153View ArticleGoogle Scholar
  23. Vidal J, Najar M, Jativa R: 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.View ArticleGoogle Scholar
  24. Riba J, Urruela A: 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.View ArticleGoogle Scholar
  25. Al-Jazzar S, Caffery JJ Jr., You H-R: 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.Google Scholar
  26. Wylie-Green MP, Wang SS: 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.Google Scholar
  27. Patwari N, Hero AO III, Perkins M, Correal NS, O'Dea RJ: Relative location estimation in wireless sensor networks. IEEE Transactions on Signal Processing 2003, 51(8):2137-2148. 10.1109/TSP.2003.814469View ArticleGoogle Scholar
  28. Cheung KW, So HC: A multidimensional scaling framework for mobile location using time-of-arrival measurements. IEEE Transactions on Signal Processing 2005, 53(2):460-470.MathSciNetView ArticleGoogle Scholar
  29. Moon TK, Stirling WC: Mathematical Methods and Algorithms for Signal Processing. Prentice-Hall, Upper Saddle River, NJ, USA; 2000.Google Scholar


© Cheung et al. 2006