Theoretical and Practical Limits in Position Estimation Based on Received Signal Strength Measurements

In this study, theoretical limits in position estimation in Wireless Sensor Network (WSN) using a trilateration method are derived in the form of probability density functions (PDFs) and compared with practical limits obtained via received signal strength (RSS) measurements in an anechoic chamber. In particular, the PDF of the radius of error of an unknown node's position has been derived as having a Nakagami-m distribution. The theoretical PDFs is validated via Kolmogorov-Smirnov hypothesis tests at 95% confidence level against the empirical results of position estimation in a 4 m x 4 m area using the RSS measured in an ideal environment of an anechoic chamber. High-resolution equipment is used in the RSS measurements to ensure the inaccuracies due to limited-capability WSN equipment can be quantified. A lower bound of positioning accuracy to be expected in real environments via the received signal strength method has been established to be in the range of 11 cm from the true position with 95% confidence level. Better results cannot be expected in the real environments with bigger variations than the variations observed in the anechoic chamber unless a more sophisticated algorithm, equipment with better resolution and/or more precise measurement methods are employed.