Sensor Localization Using Time of Arrival Measurements in a Multi-Media and Multi-Path Application of In-Situ Wireless Soil Sensing

Abstract

The problem of localization of nodes of a wireless sensor network placed in different physical media (anchor nodes above ground and sensor nodes underground) is addressed in this article. We use time of arrival of signals transmitted between neighboring sensor nodes and between satellite nodes and sensor nodes as the ranging measurement. The localization problem is formulated as a parameter estimation of the joint distribution of the time of arrival values. The probability distribution of the time of arrival of a signal is derived based on rigorous statistical analysis and its parameters are expressed in terms of the location coordinates of the sensor nodes. Maximum likelihood estimates of the nodes’ location coordinates as parameters of the joint distribution of the various time of arrival variables in the network are computed. Sensitivity analysis to study the variation in the estimates with respect to error in measured soil complex permittivity and magnetic permeability is presented to validate the model and methodology.