Circular Uncertainty method for range-only localization with imprecise sensor positions

This study provides an effective new method to solve the range-only localization in the presence of sensor position errors. In practice, the sensors can stay only within a limited region whereas the target can be far from there. To increase the estimation capability, some peripheral measurements with moving sensors can be obtained, which results in the issue of imprecise sensor positions. In these situations, sensor positions also become unknown parameters which need to be jointly estimated together with the target location. Because of the large number of unknown parameters, reaching the global minimum becomes a significant challenge. Our study is dedicated to build a robust localization scheme for these scenarios. We propose a new search strategy, namely Circular Uncertainty which allows the localization system to safely find the global minimum of maximum likelihood cost function in case of imprecise sensor positions. Circular Uncertainty not only makes it possible to reach maximum likelihood estimation, but also significantly simplifies this task. Our solution is based on the observation that when the initial estimation is disturbed with new measurements, the disturbed estimation moves along the Circular Uncertainty which can be viewed as a circular valley along the cost surface. The new method is compared to nonlinear least squares as well as the squared range weighted least-squares algorithm which was previously designed in the literature specifically for localization with imprecise sensor positions. Since the proposed solution obtains maximum likelihood estimation, it attains Cramer Rao lower bound, where other competing methods partly fail.