Accuracy of range-based localization schemes in random sensor networks: A lower bound analysis

Accuracy is a fundamental performance requirement in network localization. This paper studies the accuracy of range-based localization schemes for random sensor networks with respect to network connectivity and scale. We show that the variance of localization errors is proportional to the average geometric dilution of precision (AGDOP). The paper proves a novel lower bound of expectation of AGDOP (LB-E-AGDOP). Our analysis based on LB-E-AGDOP shows that localization accuracy is approximately inversely proportional to the average degree of network. A further analysis shows that when network connectivity merely guarantees localizability, increasing sensor nodes leads to bounded monotonic increase in AGDOP; when a network is densely connected, increasing sensor nodes leads to bounded monotonic decrease in AGDOP. Finally, these conclusions are validated by numerical simulations.