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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 956895, 15 pages
Research Article

Localization Accuracy of Range-Only Sensors with Additive and Multiplicative Noise

State Key Laboratory of Industrial Control Technology, Institute of Industrial Control Zhejiang University, Hangzhou, China

Received 11 December 2013; Accepted 24 January 2014; Published 25 March 2014

Academic Editor: Zhengguang Wu

Copyright © 2014 Xiufang Shi et al. 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.


The localization accuracy of range-only sensors with both additive and multiplicative noises is investigated. The main contributions consist of three parts. First, the Cramer-Rao Lower Bound (CRLB) of range-only localization system is derived, based on which the area of the uncertain ellipse about estimation is proposed as the metric to evaluate the localization accuracy. In addition, the analytical relationships between target-sensor distance and localization accuracy and between noise and localization accuracy are derived. Second, the metric is utilized to evaluate the localization accuracy for three important regular patterns of sensor deployment, that is, triangle, square, and hexagon. Two aspects of localization accuracy have been examined and discussed, respectively, for three patterns by numerical methods, including (a) the geometric distribution of localization accuracy and (b) the average localization accuracy. Both theoretical and numerical results show that the multiplicative noise will influence significantly the localization accuracy. Third, on a lab-scale ultrasonic range-only sensor system the existence of additive and multiplicative noises is verified. It is also shown that the experimental localization accuracy is close to the previously analyzed theoretical accuracy.