Error Propagation in Sensor Network Localization with Regular Topologies

Location information for sensors in wireless sensor networks (WSNs) is essential to many tasks. In the presence of noise, locations must be estimated and thus the errors are unavoidable. Moreover, the errors can propagate (i.e. increase) as sensors progressively more distant from anchors are localized. Understanding the rules governing error propagation is quite helpful to deploying WSNs and improving performances of localization systems. In this paper, we investigate error propagation measured by the Cramer-Rao Lower Bound (CRLB) in a type of regular 1-Dimensional WSNs whose Fisher Information Matrices are symmetric band Toeplitz matrices. Approximate analytic formulas for the CRLBs in the regular and almost regular WSNs are derived, and properties of error propagation are also obtained. In addition, we derive a magic number relating to the number of range measurements, which indicates a turning point as to system localization accuracies.