Localization with Snap-Inducing Shaped Residuals (SISR) - Coping with Errors in Measurement

Abstract

We consider the problem of localizing wireless nodes in an outdoor, open-space environment, using ad-hoc radio ranging measurements, e.g., 802.11. As in other range-based methods, we cast ranging measurements as a set of distance constraints, thus forming an over-determined system of equations suitable for non-linear least squares optimization. However, ranging measurements are often subject to errors, induced by multipath signals and variations in path loss, or even faulty hardware or antenna connectors. Including such potentially large and non-Gaussian errors in the measurement data ultimately produces inaccurate localization solutions. We propose a new method, called snap-inducing shaped residuals (SISR), to automatically identify “bad nodes” and “bad links” arising from these errors, so that they receive less weight in the localization process. In particular, SISR snaps “good nodes” to their accurate locations and gives less emphasis to other nodes. While the mathematical techniques used by SISR are similar to those in robust statistics, SISR’s exploitation of the snap-in effect in localization appears to be novel. We provide analysis on the principle of SISR, and demonstrate a working SISR implementation in field experiments on a testbed of 20 wireless nodes, as well as the superior performance of SISR in simulation with a larger number of nodes.