Accuracy of Range-Based Cooperative Localization in Wireless Sensor Networks: A Lower Bound Analysis

TL;DR

This paper develops a theoretical lower bound on localization accuracy in range-based wireless sensor networks, relating it to network connectivity parameters, and validates the findings through simulations.

Contribution

It introduces a novel lower bound on localization accuracy based on geometric DOP and provides a closed-form formula linking accuracy to network degrees and sensor count.

Findings

Localization accuracy is inversely proportional to average node degree.

Higher ratio of anchor to sensor degree improves accuracy.

Theoretical bounds closely match simulation results.

Abstract

Accurate location information is essential for many wireless sensor network (WSN) applications. A location-aware WSN generally includes two types of nodes: sensors whose locations to be determined and anchors whose locations are known a priori. For range-based localization, sensors' locations are deduced from anchor-to-sensor and sensor-to-sensor range measurements. Localization accuracy depends on the network parameters such as network connectivity and size. This paper provides a generalized theory that quantitatively characterizes such relation between network parameters and localization accuracy. We use the average degree as a connectivity metric and use geometric dilution of precision (DOP), equivalent to the Cramer-Rao bound, to quantify localization accuracy. We prove a novel lower bound on expectation of average geometric DOP (LB-E-AGDOP) and derives a closed-form formula that relates LB-E-AGDOP to only three parameters: average anchor degree, average sensor degree, and number of sensor nodes. The formula shows that localization accuracy is approximately inversely proportional to the average degree, and a higher ratio of average anchor degree to average sensor degree yields better localization accuracy. Furthermore, the paper demonstrates a strong connection between LB-E-AGDOP and the best achievable accuracy. Finally, we validate the theory via numerical simulations with three different random graph models.