Localization in the unknown environments and the principle of anchor placement

Received signal strength (RSS)-based localization has been widely used in location-aware applications due to its low cost and low complexity. The accuracy of RSS-based localization depends on the values of parameters used in the path-loss model, which is specific to the operating environment. Given the dependence, however, most work assumes the path-loss parameters are fixed and known, an assumption that costs positioning accuracy. In this paper, we estimate the target position and the path-loss parameters jointly for an arbitrary distribution of noise. We formulate the estimation problem as an optimization that has a prominent geometric structure. To achieve any level of positioning accuracy, as measured by the outage on the distance error, we prove that the anchors must be placed in certain ways and that the sample size of RSSs must be large enough. The method to place anchors and a guaranteed sample size are given in the paper. The proposed framework has practical utility to localization in unknown environments when the target node must be simple and yet able to supply accurate positioning.