Resolution Limit of Positioning Error for Range-Free Localization Schemes

The metric of resolution limit of localization error plays an important role in the range-free localization schemes design, which can manifest the best error-recognition ability that the range-free schemes could achieve. The existing derived resolution limits are found to be smaller than the real resolution limit. Therefore, this article aims to obtain the real resolution limit of range-free localization error. To achieve the goal, two algorithms are proposed in ideal channel and shadow-fading channel, respectively. Specifically, in ideal channel, maximum movable distance is defined and its important features are introduced, then the concept of critical point and its related proposition are given accordingly. Subsequently, an algorithm is proposed to derive the real resolution limit in ideal channel. For the case of shadow-fading channel, based on stochastic channel model, first, at each time instant, the random variables are turned into definite values, then, the instant resolution limit is computed, and finally, the expectation of resolution limit can be calculated. Simulation results demonstrate the correctness of our derived resolution limit. The results also show that the resolution limits or lower bounds derived by the existing methods are much smaller than the real resolution limit.