Quantification of redundancy in sensor networks and the relationship to measurement uncertainty

In this contribution the concept of redundancy is considered from a metrological perspective. Instead of counting the number of measurements and the degrees of freedom of the system, or considering the entropy of the system based on information theoretical grounds, a relatively practical and intuitive approach is chosen, in which the concept of redundancy is tightly linked to the measurement uncertainty. Metrological redundancy is defined by the change of the measurement uncertainty of the measurand, when removing sensors from the sensor network. An alternative is given by the specification of the largest number of sensors that can be removed from the network without that the uncertainty of the measurand transgresses a priorly selected value. Various metrics are defined to quantify the redundancy. The concepts and metrics are illustrated with the help of various examples. This concerns both simulated and real networks, and the sensors measure either the same quantity (homogeneous network) or different quantities (heterogeneous network).