Wireless sensor networks have emerged as a technology that enables the monitoring and control of processes in manufacturing plants or smart cities. In the case of air quality monitoring in smart cities, for example, particularly polluted places could be identified in real-time and citizens protected from the effects of air pollution. These networks consist of many distributed sensor nodes that collect data and transmit them to a central place where they can be processed.
Such measurement systems, however, place new demands on calibration, e.g., in terms of scale and frequency. More precisely, these countless sensors are often of inferior quality and therefore need calibration more often. Manually calibrating each node or collecting all nodes and bringing them to a laboratory (for calibration) would be too tedious, if not impossible, and would also result in downtime and missing data. Still, calibrations are necessary because they make measurements comparable in space and time. If sensors drift, their measured values do not correspond to the truth. As a result, decisions based on such data will be unreasonable.
How to keep sensor networks calibrated has therefore been the subject of research, giving rise to so-called blind calibration algorithms (among other types of automated calibration techniques), which aim at improving the data quality of measurements of the sensors and delay (or even omit) expensive manual calibrations. Simply put, they use an initial calibration as a reference; the key idea is to exploit correlations between sensor signals, allowing to compute new calibration coefficients using techniques from linear algebra and mathematical optimization. This article explains the theory behind such algorithms and demonstrates their potential and limitations with a practical example.
The starting point is a sensor network consisting of n nodes, each sensing a certain process. At time t, the individual measurements are collected as in a vector y = [y₁, …, yₙ]. If the individual sensors “see the same thing”, their…