Automatic Calibration of Sensing Systems for Distributed Physical Fields

Abstract

This paper proposes a new automatic calibration method for the sensor networks which measure the distribution of physical fields, such as in-room thermal temperature fields. In case of measuring the distribution of room's temperature, the regular calibration of the sensors is necessary for obtaining reliable information. However, it is not an easy task in the case of a large scale sensor network, because the manual calibration in such a system is time consuming and costly. To solve the problem, this present study proposes the new method which is based on the two concepts of regression analysis and cross validation. The new method is explained and the efficient extensions are also proposed, and the performance of the proposed methods is verified by experiments and simulations.

Self-calibration methods for uncontrolled environments in sensor networks: A reference survey

“…Evaluation metric Data set Application [6] Linear regression Mean error Real (thermocouple) Temperature [7] Splines/optimization Confidence interval Real (photovoltaic) Point-lights [8] Distributed consensus Mean error real Light [11] Linear regression Mean error Real Light, temp., humidity [18] Linear regression Mean & median error Real (thermistor) Temp., humidity [35] Nonlinear/splines Mean squared error Real Light [36] Hidden Markov model Recognition accuracy Real Motion (accelerometer) [41] Support vector regression (SVR) Mean squared error Real Light [43] Bayesian Root mean squared error Synthetic Temperature [44] Maximum likelihood Absolute error Synthetic Temperature [45] Kriging Root mean squared error Real Temp., humidity, light [46,47,48] Gaussian process K-L divergence Real Temperature [49] Linear/nonlinear optimization Mean absolute error Real Vibration (water flow) [50] Distributed consensus Mean squared error Synthetic Temp., humidity, sound [51] PCA + compressive sensing Mean squared error Real Temperature Table 3: Localization, synchronization, and target location applications.…”

“…There are metrics that allow measuring the accuracy or precision of the estimation and depend on the algorithm or application defined by the authors. One example is the Kullback-Leibler (KL) divergence, which measures how one probability distribution diverges from a second expected probability distribution [40,48]. Other examples are the average value of the relative bias error (RBE), the average value of the relative deviation error (RDE) [56], and the Bayes risk in event detection applications [37].…”

“…[35] X X X X X X X X Light [36] X X X X X X X Motion (accelerometer) [41] X X X X X X X Light [43] X X X X X X X Temperature [44] X X X X X X X Temperature [45] X X X X X X X X Temp. Hum., Light [46,47,48] X X X X X X X Temperature [49] X X X X X X X Vibration (Water Flow) [50] X X X X X X X Temp., Hum., Sound [51] X X X X X X X Temperature Attributes used in localization, synchronization and target detection applications [5] X X X X X X X Localization [17] X X X X X X X X X Target Detection [37] X X X X X X X Target Detection [38] X X X X X X X Localization [39,40] X X X X X X X Localization [52] X X X X X X X Localization [53,10] X X X X X X X Synchronization [54] X X X X X X X Synchronization Attributes used in air pollution and water chemistry applications [12] X X X X X X X Water Chemistry [15] X X X X X X X X X O 3 [16,27] X X X X X X X O 3 ,CO,CO 2 ,NO,NO 2 [28] X X X X X X X CO,CH 4 ,C 3 H 8 ,CeO 2 ,NiO [29] X X X X X X X O 3 ,CO [30] X X X X X X X O 3 ,CO,NO 2 [31] X X X X X X X O 3 , NO, NO 2 [32] X X X X X X X X X O 3 , CO, NO 2 [33] X X X X X X X O 3 [55] X X X X X X X Photosynthetically Active Radiation (PAR) [56] X X X X X X X Air pollution CaliBree [8] is a model-based calibration network in which ground-truth calibrated nodes inform non-calibrated nodes, using a beacon protocol, that they will participate in the calibration process. These nodes, then, use a discrete consensus distributed algorithm to calibrate the uncalibrated node by computing the degree of disagreement between the reference nodes and t...…”

“…Evaluation metric Data set Application [6] Linear regression Mean error Real (thermocouple) Temperature [7] Splines/optimization Confidence interval Real (photovoltaic) Point-lights [8] Distributed consensus Mean error real Light [11] Linear regression Mean error Real Light, temp., humidity [18] Linear regression Mean & median error Real (thermistor) Temp., humidity [35] Nonlinear/splines Mean squared error Real Light [36] Hidden Markov model Recognition accuracy Real Motion (accelerometer) [41] Support vector regression (SVR) Mean squared error Real Light [43] Bayesian Root mean squared error Synthetic Temperature [44] Maximum likelihood Absolute error Synthetic Temperature [45] Kriging Root mean squared error Real Temp., humidity, light [46,47,48] Gaussian process K-L divergence Real Temperature [49] Linear/nonlinear optimization Mean absolute error Real Vibration (water flow) [50] Distributed consensus Mean squared error Synthetic Temp., humidity, sound [51] PCA + compressive sensing Mean squared error Real Temperature Least squares Mean error Real (acoustic) Localization [17] Nonlinear (maximum likelihood) Detection probability Synthetic/real Target detection [38] Bayesian (maximum a posteriori) Cramèr-Rao bound Real (acoustic) Localization [39,40] Bayesian (maximum a posteriori) K-L divergence Synthetic Localization [37] Nonlinear (maximum likelihood) Bayes risk Synthetic Target detection [52] Distributed consensus Mean, avg. residual Real (RSSI) Localization [53,10] Distributed macro-calibration Mean squared error Synthetic Synchronization [54] Bayesian (iterative) Error variance Synthetic Synchronization…”

“…Fujino et al [46,48] proposed to calibrate a network of N thermal sensors using Gaussian processes. All the sensors measure the same phenomenon, and then they are neighbors from the point of view of seeing similar correlated data, being the calibration form of type collocated or single-hop.…”