Distributed Multi-Scale Calibration of Low-Cost Ozone Sensors in Wireless Sensor Networks

Abstract

New advances in sensor technologies and communications in wireless sensor networks have favored the introduction of low-cost sensors for monitoring air quality applications. In this article, we present the results of the European project H2020 CAPTOR, where three testbeds with sensors were deployed to capture tropospheric ozone concentrations. One of the biggest challenges was the calibration of the sensors, as the manufacturer provides them without calibrating. Throughout the paper, we show how short-term calibration using multiple linear regression produces good calibrated data, but instead produces biases in the calculated long-term concentrations. To mitigate the bias, we propose a linear correction based on Kriging estimation of the mean and standard deviation of the long-term ozone concentrations, thus correcting the bias presented by the sensors.

Keywords: air pollution sensors; calibration; error estimation; low-cost sensors; wireless sensor networks.

Figure 1

(a) Captor box, (b) Palau Reial reference station with captor nodes in calibration process, (c) captor nodes in Volunteer houses.

Figure 2

(a) RMSE for the set of sensors, (b) RMSE versus correlation coefficient (R${}^2$).

Figure 3

RMSE classified for testbed and place: (a) Spanish Testbed, (b) Italian Testbed.

Figure 4

RMSE classified by testbed and node: (a) Spanish Testbed, (b) Italian Testbed.

Figure 5

Map with the Captor nodes: the reference stations (in red), Captor nodes (in blue), Captor label number below or behind the Captor mark.

Figure 6

Case 1: Training set size increases in forward direction. Test set size fixed.

Figure 7

Case 2: Training set size increases in backward direction. Test set size fixed.

Figure 8

Case 3: Training set size fixed. Test set size fixed but moves in forward direction.

Figure 9

(a) Case 1: Training data increases in forward direction, (b) Case 2: Training data increases in backward direction.

Figure 10

(a) Case 3: Captors Test RMSE in per day basis with training set of 3 weeks, (b) Case 3: Average ozone ($\mathsf{\mu }$g/m${}^3$) in per day basis in the reference station.

Figure 11

Case 3: Ozone concentration ($\mathsf{\mu }$g/m${}^3$) for (a) Captor node C17013 (Manlleu), (b) Captor node C17016 (Vic).

Figure 12

Mean normalized bias and normalized centred CRMSE: (a) sensor s${}_4$ Captor 17013 (Manlleu), (b) sensor s${}_4$ Captor 17017 (Tona).

Figure 13

(a) Test RMSE versus average temperature in a per day basis, (b) Test RMSE versus average Relative Humidity in a per day basis. In green the single-scale case and in orange the multi-scale case.

Figure 14

(a) Average temperature versus average relative humidity in a per day basis, (b) Test RMSE versus average ozone concentrations in a per day basis.

Figure 15

Case 3: Test RMSE in per day basis with training set of 3 weeks, single-scale versus multi-scale with exact correction, (a) Captor 17016 (Vic), (b) Captor 17017 (Tona).

Figure 16

Case 3: Mean normalized bias and normalized CRMSE, single-scale (green), multi-scale with exact correction (black) and multi-scale with Kriging estimates (orange), (a) Captor 17016 (Vic), (b) Captor 17017 (Tona).

Figure 17

Case 3: Training set of 3 weeks: Mean ozone concentration for single-scale versus multi-scale with exact correction and Kriging estimation (daily), (a) in Captor 17016 (Vic), (b) in Captor 17017 (Tona).

Figure 18

Case 3: Training set of 3 weeks: Standard deviation (STD) ozone concentration for single-scale versus multi-scale with exact correction and Kriging estimation (daily), (a) in Captor 17016 (Vic), (b) in Captor 17017 (Tona).

Figure 19

Case 3: Test RMSE with training set of 3 weeks, single-scale versus multi-scale with exact correction and Kriging estimation, (a) daily in s${}_4$ of Captor 17016 (Vic), (b) daily in s${}_4$ of Captor 17017 (Tona).