Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Nonlinear Functions <s> Calibration is the process of mapping raw sensor readings into corrected values by identifying and correcting systematic bias. Calibration is important from both off-line and on-line perspectives. Major objectives of calibration procedure include accuracy, resiliency against random errors, ability to be applied in various scenarios, and to address a variety of error models. In addition, a compact mapping function is attractive in terms of both storage and robustness. We start by introducing the nonparametric statistical approach for conducting off-line calibration. After that, we present the non-parametric statistical percentile method for establishing the confidence interval for a particular mapping function. Furthermore, we propose the first model-based on-line procedure for calibration. The calibration problem is formulated as an instance of nonlinear function minimization and solved using the standard conjugate gradient approach. A number of trade-offs between the effectiveness of calibration and noise level, latency, size of network and the complexity of phenomena are analyzed in a quantitative way. As a demonstration example, we use a system consisting of photovoltaic optical sensors. <s> BIB001 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Nonlinear Functions <s> Calibrating nonlinear mobile sensors in-field is a challenging task due to the unavailability of controlled signal field and pre-calibrated sensor devices. In this paper, we propose a Density Guided blind Calibration (DGC) scheme for nonlinear mobile sensors by approximating the nonlinear calibration functions using piecewise linear functions. The DGC scheme exploits the fact that sensors moving in the same region collect similar fraction of true values in any given interval over time. The proposed scheme tackles the nonlinear calibration problem through an optimization formulation which is very easy to solve. The effectiveness of the proposed scheme is verified through simulations and an experiment with MICA2 light sensors. <s> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Nonlinear Functions <s> This paper proposes a system for activity recognition using multi-sensor fusion. In this system, four sensors are attached to the waist, chest, thigh, and side of the body. In the study we present two solutions for factors that affect the activity recognition accuracy: the calibration drift and the sensor orientation changing. The datasets used to evaluate this system were collected from 8 subjects who were asked to perform 8 scripted normal activities of daily living (ADL), three times each. The Naive Bayes classifier using multi-sensor fusion is adopted and achieves 70.88%-97.66% recognition accuracies for 1–4 sensors. <s> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Nonlinear Functions <s> Wireless sensor networks are typically composed of low-cost sensors that are deeply integrated in physical environments. As a result, the sensing performance of a wireless sensor network is inevitably undermined by biases in imperfect sensor hardware and the noises in data measurements. Although a variety of calibration methods have been proposed to address these issues, they often adopt the device-level approach that becomes intractable for moderate-to large-scale networks. In this article, we propose a two-tier system-level calibration approach for a class of sensor networks that employ data fusion to improve the sensing performance. In the first tier of our calibration approach, each sensor learns its local sensing model from noisy measurements using an online algorithm and only transmits a few model parameters. In the second tier, sensors' local sensing models are then calibrated to a common system sensing model. Our approach fairly distributes computation overhead among sensors and significantly reduces the communication overhead of calibration compared with the device-level approach. Based on this approach, we develop an optimal model calibration scheme that maximizes the target detection probability of a sensor network under bounded false alarm rate. Our approach is evaluated by both experiments on a testbed of TelosB motes and extensive simulations based on synthetic datasets as well as data traces collected in a real vehicle detection experiment. The results demonstrate that our system-level calibration approach can significantly boost the detection performance of sensor networks in scenarios with low signal-to-noise ratios. <s> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Nonlinear Functions <s> Abstract The performances of several field calibration methods for low-cost sensors, including linear/multi linear regression and supervised learning techniques are compared. A cluster of ozone, nitrogen dioxide, nitrogen monoxide, carbon monoxide and carbon dioxide sensors was operated. The sensors were either of metal oxide or electrochemical type or based on miniaturized infra-red cell. For each method, a two-week calibration was carried out at a semi-rural site against reference measurements. Subsequently, the accuracy of the predicted values was evaluated for about five months using a few indicators and techniques: orthogonal regression, target diagram, measurement uncertainty and drifts over time of sensor predictions. The study assessed if the sensors were could reach the Data Quality Objective (DQOs) of the European Air Quality Directive for indicative methods (between 25 and 30% of uncertainty for O 3 and NO 2 ). In this study it appears that O 3 may be calibrated using simple regression techniques while for NO 2 a better agreement between sensors and reference measurements was reached using supervised learning techniques. The hourly O 3 DQO was met while it was unlikely that NO 2 hourly one could be met. This was likely caused by the low NO 2 levels correlated with high O 3 levels that are typical of semi-rural site where the measurements of this study took place. <s> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Nonlinear Functions <s> Abstract In this work the performances of several field calibration methods for low-cost sensors, including linear/multi linear regression and supervised learning techniques, are compared. A cluster of either metal oxide or electrochemical sensors for nitrogen monoxide and carbon monoxide together with miniaturized infra-red carbon dioxide sensors was operated. Calibration was carried out during the two first weeks of evaluation against reference measurements. The accuracy of each regression method was evaluated on a five months field experiment at a semi-rural site using different indicators and techniques: orthogonal regression, target diagram, measurement uncertainty and drifts over time of sensor predictions. In addition to the analyses for ozone and nitrogen oxide already published in Part A [1], this work assessed if carbon monoxide sensors can reach the Data Quality Objective (DQOs) of 25% of uncertainty set in the European Air Quality Directive for indicative methods. As for ozone and nitrogen oxide, it was found for NO, CO and CO 2 that the best agreement between sensors and reference measurements was observed for supervised learning techniques compared to linear and multilinear regression. <s> BIB006
Acoustic, seismic, and electromagnetic signals BIB001 BIB004 BIB002 BIB003 attenuate with the distance, d, from the source of the signal. Let us assume that sensor n is d n meters from the source that transmits a signal with energy S . The attenuated signal, y n , at the position of sensor n is BIB004  where f (β n , d n ) is a decreasing function of d n , and β n is a set of parameters of the signal decay function f (·) at sensor n. Some of the signal decay functions used are illustrated next. Power law decay: The propagation of mechanical waves, such as acoustic and seismic signals, follows a power law decay BIB004 : where β n = {k n , r n }; k n is the decay parameter, and r n is the reference distance determined by sensor shape. Exponential decay: The intensity of light attenuates with the travel distance and follows an exponential decay BIB004 : where β n = {λ n }; λ n is a decaying parameter, and it is referred to as the Lambert absorption coefficient. Other phenomena are known to yield a linear response. However, when the samples are taken, due to imperfections of the sensor technology or other causes including the existence of drift or of a maximum dynamic range, the sensor response is nonlinear. For illustration of this fact, refer to Figure 1a , which shows the samples obtained from a metal-oxide ozone MIC2714 sensor of a WSN deployed in the H2020 CAPTOR project during summer 2017. The output of the uncalibrated sensor is in kiloohm. The ozone sensor is connected to a voltage divider circuit. The voltage divider has a load resistor and a variable resistor. The variable resistor varies according to the ozone concentration, which is what it is obtained at each measurement. The y-axis of Figure 1a shows the resistor values recorded at each sample time. The sampling rate is one sample per hour. The data set comprises approximately 900 samples, Table 1 : Data models for arrays of gas sensors BIB005 BIB006 .