Relative information of multi-rate sensors

Fusion of the information provided by distributed sensors is important in the future pervasive computing systems. The objective of this paper is to quantify the relative amount of information delivered by individual sensors in a distributed sensor system. To formalize our approach, we consider the problem of fusing the statistical information obtained using low-rate sensor recordings viðnÞ in order to find the power spectrum of a high-rate random signal xðnÞ. It turns out that this problem is inherently illposed since, in general, low-rate observations are not sufficient for specifying a unique solution. We use the Maximum Entropy principle to resolve this issue. It is known that a complete statistical description of a Gaussian wide-sense stationary process xðnÞ is provided by its power spectrum. This leads us to a measure of informativity for multirate sensors based on the qualities of the maximum entropy solution. We study the main properties of the proposed measure and provide computational methods for its calculation. Finally, we illustrate the concepts and methods discussed in the paper using a detailed simulation example. 2004 Elsevier B.V. All rights reserved.