Beyond Triangle Inequality: Sifting Noisy and Outlier Distance Measurements for Localization

Knowing accurate positions of nodes in wireless ad hoc and sensor networks is essential for a wide range of pervasive and mobile applications. However, errors are inevitable in distance measurements and we observe that a small number of outliers can degrade localization accuracy drastically. To deal with noisy and outlier ranging results, triangle inequality, is often employed in existing approaches. Our study shows that triangle inequality has many limitations, which make it far from accurate and reliable. In this study, we formally define the outlier detection problem for network localization and build a theoretical foundation to identify outliers based on graph embeddability and rigidity theory. Our analysis shows that the redundancy of distance measurements plays an important role. We then design a bilateration generic cycles-based outlier detection algorithm, and examine its effectiveness and efficiency through a network prototype implementation of MicaZ motes as well as extensive simulations. The results show that our design significantly improves the localization accuracy by wisely rejecting outliers.