Localization accuracy of range-only sensors with additive and multiplicative noise

In this paper, the localization accuracy of range-only sensors is investigated. Being different from most previous studies, we consider a more general measurement model with both additive and multiplicative noise other than with only additive noise. The main contributions lie in twofold. First, a CRLB(Cramer-Rao Lower Bound)-based metric is proposed 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, numerical analysis is executed to evaluate the localization accuracy for three important regular patterns of sensor deployment, i.e., triangle, square and hexagon. Two aspects have been examined and discussed, including (a) the geometric distribution of localization accuracy, (b) the average localization accuracy. Both theoretical and numerical results show that the multiplicative noise will influence significantly the localization accuracy. This study also provides important guidelines for optimal sensor deployment.