Sensor Node Localization Methods based on Local Observations of Distributed Natural Phenomena

Abstract — This paper addresses the model-based localization of sensor networks based on local observations of a distributed phenomenon. For the localization process, we propose the rigorous exploitation of strong mathematical models of distributed phenomena. By unobtrusively exploiting background phenomena, the individual sensor nodes can be localized by only observing its local surrounding without the necessity of heavy infrastructure. In this paper, we introduce two novel approaches: (a) the polynomial system localization method (PSL-method) and (b) the simultaneous reconstruction and localization method (SRL-method). The first approach (PSLmethod) is based on restating the mathematical model of the distributed phenomenon in terms of a polynomial system. These equations depend on both the state of the phenomenon and the node locations. Solving the system of polynomials for each individual sensor node directly leads to the desired locations. The second approach (SRL-method) basically regards the localization problem as a simultaneous state and parameter estimation problem with the node locations as parameters. By this means, the distributed phenomenon is reconstructed and the individual nodes are localized in a simultaneous fashion. In addition, within this framework the uncertainties in the mathematical model and the measurements are considered. The performance of the two different localization approaches is demonstrated by means of simulation results. I