Abstract—Distance estimation is fundamental for many functionalities of wireless sensor networks and has been studied intensively in recent years. A critical challenge in distance estimation is handling anisotropic problems in sensor networks. Compared with isotropic networks, anisotropic networks are more intractable in that their properties vary according to the directions of measurement. Anisotropic properties result from various factors, such as geographic shapes, irregular radio patterns, node densities, and impacts from obstacles. In this paper, we study the problem of measuring irregularity of sensor networks and evaluating its impact on distance estimation. In particular, we establish a new metric to measure irregularity along a path in sensor networks, and identify turning nodes where a considered path is inflected. Furthermore, we develop an approach to construct a virtual ruler for distance estimation between any pair of sensor nodes. The construction of a virtual ruler i...