Anchor-free localization: Estimation of relative locations of sensors

Some applications of sensor networks do not require the knowledge of absolute locations of sensors; knowledge of relative locations of sensors is sufficient. We study the problem of estimating relative locations of sensors, which we refer to as relative localization, under the assumption that each sensor can measure the distances between neighbor sensors. We show that the relative localization can be performed by setting up a non-linear optimization problem and solving it by standard optimization techniques such as the steepest descent method. We theoretically and numerically investigate the characteristics of the proposed relative localization and obtain several findings. For example, the relative locations of sensors can be accurately estimated even if the distance measurements include large errors. Thus, primitive distance measurement techniques, including RSSI-based measurements, are applicable for the relative localization. We also find that the relative localization has a preferable scaling property; it performs better as the number of sensors increases.