Reconstruction of a signal from time-averaged data

National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK

^* e-mail: alistair.forbes@npl.co.uk

Abstract

In measurement applications such as air quality monitoring, sensors record the average of a signal of over a fixed time period, for example, every hour or every day. Sensor networks may involve a number of different types of sensors with different temporal resolutions, for instance, expensive reference sensors recording accurate, hourly averages and inexpensive sensors recording noisy averages every ten minutes. In addition, readings for some time periods may be missing. In this paper, we discuss methods to combine sensor data representing heterogeneous time averages in order to i) reconstruct an estimate and associated uncertainty of signal at any given time, and ii) use data from reference sensors to calibrate low cost sensors in situ.