Accuracy of Range-Based Cooperative Positioning: A Lower Bound Analysis

Accurate location information is essential for mobile systems such as wireless sensor networks. A location-aware sensor network generally includes two types of nodes: Sensors whose locations to be determined and anchors whose locations are known a priori. For range-based cooperative positioning, sensors' locations are deduced from anchor-to-sensor and sensor-to-sensor range measurements. Positioning accuracy depends on the network parameters such as network connectivity and size. This paper provides a generalized theory that quantitatively characterizes such a relation between network parameters and positioning accuracy. We use the average degree as a connectivity metric and use geometric dilution of precision (DOP) to quantify positioning accuracy. Under the assumption that nodes are randomly deployed, 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 positioning accuracy is approximately inversely proportional to the average degree, and a higher ratio of average anchor degree to average sensor degree yields better positioning accuracy. Furthermore, the paper shows a strong connection between LB-E-AGDOP and the best achievable accuracy. Finally, we demonstrate the theory via numerical simulations with three different random graph models.