EURASIP Journal on Applied Signal Processing
Volume 2006 (2006), Article ID 20858, 23 pages
doi:10.1155/ASP/2006/20858

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

K. W. Cheung,1 H. C. So,1 W.-K. Ma,2 and Y. T. Chan3

1Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
2Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan
3Department of Electrical & Computer Engineering, Royal Military College of Canada, Kingston, ON, K7K 7B4, Canada

Received 20 May 2005; Revised 25 November 2005; Accepted 8 December 2005

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.