1. Signal, Instruments and Systems Project 5: Sensor accuracy in environmental sensor networks

2. Introduction We deal with the important question of calibration of sensor devices. Here we focuse on the Mica-Z temperature sensor. How can we obtain the best accuracy limiting the costs ? I. Experiments to collect data II. Methods of calibration : the interpolating polynomial III. Results IV. Difficulties met and observations

3. Experiments done Differents experiments : at ambiant temperature cooling (1) fast heating (2) cooling and then smooth heating (3) First results : reference data always under the measured one. the gap between the two raised at the extremes.

4. Results of experiments 1) cooling 2) fast heating 3) Cooling and slow heating

5. Calibration : Methodology Hypothesis : The difference between the reference temperature and the observed one depends on the temperature. We create a vector ε =Treference – Tobserved We use polyfit function to calculate an interpolating polynomial ε(Tobserved) to match ε. The calibrated temperature is equal to : Tcalibrated = Tobserved + ε(Tobserved)

6. Calibration : The interpolating polynomial For each set of data collected, we create several polynomials of different degrees. We compare them. The final choice of the experiment and the degree used are experimental.

7. Interpolating polynomial of degree 2

8. Interpolating polynomial of degree 4

9. Interpolating polynomial of degree 10

10. Interpolating polynomial : observations The higher the degree is, the more the interpolating polynomial fits the data. BUT with a high degree, the divergence is greater and faster when there is no data. We decide to keep the slow heating experiment data to calibrate our sensor (more data). The calibration will be valid over a greater range of temperature.

11. Results of the calibration : Slow heating case Remarks : Influence of the degree Mean error reduction: 83% (degree 2), 93% (degree 10) Best approximation at the plateau

12. Results of the calibration : Fast heating case Remarks : Calibration correct in both case Mean error reduction : 69% (degree 2), 68% (degree 10) Effect of the divergence at the extremes

13. Results of the calibration : Cooling case Remarks : Best calibration at degree 2 Mean error calibration : 66% (degree 2), 32% (degree 10) Different phenomena (heating vs cooling ?)

14. Difficulties and observations The difference of temperature between our sensor and the reference one seems to vary in each experiment for a given temperature. Example : at 292.5 Kelvin : ε 1 ═ -0.16 K; ε 2 ═ -1.71 K; ε 3 ═ -2.28 K Existence of a latency between the real temperature and the measure one ? Different adaptation time between cooling and heating ?

15. Difficulties and observations We don't obtain the same results in the behavior of the curve ! First experiments : the difference between the reference and observed sensors raises at extreme temperature New experiments : the difference between the reference and observed sensors is smaller at extreme temperature ! Local turbulence ?

16. Conclusion The slow heating curve seems to be valid to correct a rising temperature or for non variating temperature. To improve our calibration, the best is to have the most data as possible and at the largest scale Choice of the calibration’s degree: depend on what we want To extrapolate : small degree To be precise inside the range of obs. temp : high degree Another experiment ?

17. Thank you for your attention ! Any questions ?