Computational Sensor Networks

Abstract

We propose Computational Sensor Networks as a methodology to exploit models of physical phenomena in order to better understand the structure of the sensor network. To do so, it is necessary to relate changes in the sensed variables (e.g., temperature) to the aspect of interest in the sensor network (e.g., sensor node position, sensor bias, etc.), and to develop a computational method for its solution. As examples, we describe the use of the heat equation to solve (1) the sensor localization problem, and (2) the sensor bias problem. Simulation and physical experiments are described.

Sensor node localization methods based on local observations of distributed natural phenomena

“…Furthermore, within this framework, the often remaining uncertainties in the sensor node locations can be considered during the reconstruction process of the distributed phenomenon [2]. The use of such a mathematical model for node localizations was proposed in [8]. However, there was no consideration of uncertainties naturally occuring in the measurements and in the used model.…”

“…1) Spatial and Temporal Discretization: The simplest method for the spatial and temporal discretization of distributed phenomena is the finite-difference method [7], [8]. In order to solve the partial differential equation (1), the derivatives need to be approximated with finite differences according to…”

“…In order to cope with this problem, the system description has to be converted from a distributed-parameter form into a lumped-parameter form. In general, the conversion of the system description (1) can be achieved by methods for solving partial differential equations, such as modal analysis [4], the finite-difference method [7], [8], the finite-element method [2], and finite-spectral method [13]. Basically, these methods consist of two steps, namely spatial decomposition and temporal decomposition.…”

“…There are several methods to exploit the linear substructure in the combined linear/nonlinear system equation (7) and measurement equation (8). The marginalized particle filter [14] integrates over the linear subspace in order to reduce the dimensionality of the state-space.…”

“…Thanks to the conditionally linear dynamic system model (7) and measurement model (8), the ChapmanKolmogorov equation for the prediction step and the Bayes formula for the measurement step can be solved analytically. The proof is omitted here; rather the resulting predicted density is stated.…”