The topic is motivated by the following problem of [2, Page 53]: According to Newton’s law of cooling, an object of higher temperature than its environment cools at a rate that is proportional to the difference in temperature. A thermometer reading 21C, which has been inside a house for a long time, is taken outside. After one minute the thermometer reads 15C; after two minutes it reads 11C. Using Newton’s law of cooling and the thermometer readings, find the outside temperature.

The underlying idea is that knowledge of the measurement device’s dynamics (in the example, a first order linear time-invariant differential system) makes possible to predict the steady state value of the measured variable from a small number of observations (in the example, three). This leads to a speed-up of the measurement process.

The aim of the project is to generalise the solution of the motivating problem to higher order multi-variable measurement processes and noisy data. The expected output is a recursive algorithm suitable for

real-time digital signal processor implementation and a working prototype. The Lego Mindstorm setup, shown in the figure below, will be used as a testbed.

## References

- S. Eichstädt, C. Elster, T. Esward, and J. Hessling. Deconvolution filters for the analysis of dynamic measurement processes: a tutorial. Metrologia, 47:522–533, 2010.
- D. G. Luenberger. Introduction to Dynamical Systems: Theory, Models and Applications. John Wiley, 1979.
- I. Markovsky. Fast measurements of slow processes. Technical Report 22082, ECS, Univ. of Southampton, http://eprints.ecs.soton.ac.uk/22082/, 2011.
- W.-Q. Shu. Dynamic weighing under nonzero initial conditions. IEEE Trans. Instrumentation Measurement, 42(4):806–811, 1993.

2018