Localization with snap-inducing shaped residuals (SISR): coping with errors in measurement

We consider the problem of localizing wireless nodes in an outdoor, open-space environment, using ad-hoc radio ranging measurements, e.g., 802.11. We cast these 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, unreliable hardware or antenna connectors, or imperfection in measurement models. Such potentially large, non-Gaussian errors in the measurement data ultimately produce inaccurate localization solutions. We propose a new error-tolerant localization method, called snap-inducing shaped residuals (SISR), to identify automatically "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 robust statistics, SISR's exploitation of the snap-in effect in localization appears to be novel. We provide analysis on the principle of SISR, illustrate errors in real-world measurements, and demonstrate a working SISR implementation in field experiments on a testbed of 37 wireless nodes, as well as show the superior performance of SISR in simulation with a larger number of nodes.