Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> We consider the problem of locating and orienting a network of ::: unattended sensors that has been deployed in a scene with unknown ::: sensor locations and orientation angles, when no 'anchor' nodes ::: are present. Many localization problems assume that some nodes ::: have known locations and propagate location information about ::: other nodes using triangulation procedures. In our formulation, ::: we do not require such anchor nodes, but instead assume prior ::: probability density function for the nominal locations of a subset ::: of the nodes. These nominal locations typically have high ::: uncertainty, on the order of tens of meters. The self-calibration ::: solution is obtained in two steps. Relative sensor locations are ::: estimated using noisy time-of-arrival and direction-of-arrival measurements of calibration source signals in the scene, ::: and absolute location calibration is obtained by incorporating ::: prior nominal location knowledge. We consider a Bayes approach to the calibration problem and compute accuracy bounds on the calibration procedure. A maximum a posteriori estimation algorithm is shown to ::: achieve the accuracy bound. Experiments using both synthetic ::: data and field measurements are presented. <s> BIB001 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <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> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> Automatic self-localization is a critical need for the effective use of ad hoc sensor networks in military or civilian applications. In general, self-localization involves the combination of absolute location information (e.g., from a global positioning system) with relative calibration information (e.g., distance measurements between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of intersensor communication. We demonstrate that the information used for sensor localization is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then present and demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multimodal uncertainty. Using simulations of small to moderately sized sensor networks, we show that NBP may be made robust to outlier measurement errors by a simple model augmentation, and that judicious message construction can result in better estimates. Furthermore, we provide an analysis of NBP's communications requirements, showing that typically only a few messages per sensor are required, and that even low bit-rate approximations of these messages can be used with little or no performance impact. <s> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> In this paper, we present algorithms for in-situ calibration of sensor networks for distributed detection in the parallel fusion architecture. The wireless sensors act as local detectors and transmit preliminary detection results to an access point or fusion center for decision combining. In order to implement an optimal fusion center, both the performance parameters of each local detector (i.e., its probability of false alarm and probability of miss) as well as the wireless channel conditions must be known. However, in real-world applications these statistics may be unknown or vary in time. In our approach, the fusion center receives a collection of labeled samples from the sensor nodes after deployment of the network and calibrates the impact of individual sensors on the final detection result. In the case that local sensor decisions are independent, we employ maximum likelihood parameter estimation techniques, whereas in the case of arbitrarily correlated sensor outputs, we use the method of kernel smoothing. The obtained fusion rules are both asymptotically optimal and show good performance for finite sample sizes. <s> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <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> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <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> BIB006 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <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> BIB007 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> Over the past few years, many low-cost pollution sensors have been integrated into measurement platforms for air quality monitoring. However, using these sensors is challenging: concentrations of toxic substances in ambient air often lie at sensors' sensitivity boundaries, environmental conditions affect the sensor measurements, and the sensors often suffer from poor selectivity, i.e. are cross-sensitive to multiple pollutants. Datasheet information on these effects is scarce or may not cover deployment conditions. Consequently the sensors need to undergo extensive pre-deployment testing to examine their feasibility for a given application and to find the optimal measurement setup that allows accurate data collection and calibration. In this work, we propose a novel method to conduct in-field testing of low-cost sensors. The algorithm proposed is based on multiple least-squares and leverages the physical variation of urban air pollution to quantify the amount of explained and unexplained sensor signal. We verify (i) whether a sensor is feasible for air quality monitoring in a given environment and underpin our analysis with positive and negative examples of sensors available on the market, (ii) model sensor cross-sensitivities to interfering gases and environmental effects and (iii) compute the optimal sensor array and its calibration parameters for stable and accurate sensor measurements over long time periods in a given environment. Finally, we provide an experimental evaluation of our approach using over 9 million measurements of various low-cost sensors collected in an urban area. Based on the results from our testing methodology we propose an optimized sensor array setup. Further, we show---compared to a state-of-the-art calibration technique---a significantly lower calibration error with better long-time stability of the calibration parameters. <s> BIB008 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> The diffusion of the Internet of Things paradigm, in the last few years, has led to the need of deploying and managing large-scale Wireless Sensor Networks (WSNs), composed by a multitude of geographically distributed sensors, like the ones needed for Smart City applications. The traditional way to manage WSNs is not suitable for this type of applications, because manually managing and monitoring every single sensor would be too expensive, time consuming and error prone. Moreover, unattended sensors may suffer of several issues that progressively make their measures unreliable and consequently useless. For this reason, several automatically techniques have been studied and implemented for the detection and correction of measurements from sensors which are affected by errors caused by aging and/or drift. These methods are grouped under the name of self-calibration techniques. This paper presents a distributed system, which combines an incremental machine learning technique with a non-linear Kalman Filter estimator, which allows to automatically re-calibrate sensors leveraging the correlation with measurements made by neighbor sensors. After the description of the used model and the system implementation details, the paper describes also the proof-of-concept prototype that has been built for testing the proposed solution. <s> BIB009 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <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> BIB010 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> Machine learning techniques will take an increasingly central role in the distributed sensing realm and specifically in smart cities scenarios. Pervasive air quality monitoring as one of the primary city service requires a significant effort in term of data processing for extracting the needed semantic value. In this paper, after briefly reviewing the emerging relevant literature, we compare several machine learning tools for the purpose of devising intelligent calibration components to be run on board or in cloud computing architectures for pollutant concentration estimation. Two cities field experiments provide the needed on field recorded datasets to validate the approaches. Results are discussed both in terms of performance and computational impact for the specific application. <s> BIB011 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Sensor model <s> Low-cost sensing strategies hold the promise of denser air quality monitoring networks, which could significantly improve our understanding of personal air pollution exposure. Additionally, low-cost air quality sensors could be deployed to areas where limited monitoring exists. However, low-cost sensors are frequently sensitive to environmental conditions and pollutant cross-sensitivities, which have historically been poorly addressed by laboratory calibrations, limiting their utility for monitoring. In this study, we investigated different calibration models for the Real-time Affordable Multi-Pollutant (RAMP) sensor package, which measures CO, NO 2 , O 3 , and CO 2 . We explored three methods: (1) laboratory univariate linear regression, (2) empirical multiple linear regression, and (3) machine-learning-based calibration models using random forests (RF). Calibration models were developed for 16–19 RAMP monitors (varied by pollutant) using training and testing windows spanning August 2016 through February 2017 in Pittsburgh, PA, US. The random forest models matched (CO) or significantly outperformed (NO 2 , CO 2 , O 3 ) the other calibration models, and their accuracy and precision were robust over time for testing windows of up to 16 weeks. Following calibration, average mean absolute error on the testing data set from the random forest models was 38 ppb for CO (14 % relative error), 10 ppm for CO 2 (2 % relative error), 3.5 ppb for NO 2 (29 % relative error), and 3.4 ppb for O 3 (15 % relative error), and Pearson r versus the reference monitors exceeded 0.8 for most units. Model performance is explored in detail, including a quantification of model variable importance, accuracy across different concentration ranges, and performance in a range of monitoring contexts including the National Ambient Air Quality Standards (NAAQS) and the US EPA Air Sensors Guidebook recommendations of minimum data quality for personal exposure measurement. A key strength of the RF approach is that it accounts for pollutant cross-sensitivities. This highlights the importance of developing multipollutant sensor packages (as opposed to single-pollutant monitors); we determined this is especially critical for NO 2 and CO 2 . The evaluation reveals that only the RF-calibrated sensors meet the US EPA Air Sensors Guidebook recommendations of minimum data quality for personal exposure measurement. We also demonstrate that the RF-model-calibrated sensors could detect differences in NO 2 concentrations between a near-road site and a suburban site less than 1.5 km away. From this study, we conclude that combining RF models with carefully controlled state-of-the-art multipollutant sensor packages as in the RAMP monitors appears to be a very promising approach to address the poor performance that has plagued low-cost air quality sensors. <s> BIB012
Manufacturer Gas Multiple linear model EdinburghSensors, ELT Sensors CO 2 Y = β 0 + β 1 x CO2 + β 2 x T + β 3 x RH collected over 5.5 weeks. The WSN was collocated with a reference ground-truth node (see Section 5.4). Figure 1b shows the scatterplot of the sensor node data and reference node data. The values are normalized to their mean and standard deviation. In general, it is well-known BIB007 BIB010 BIB008 that ozone sensors can be calibrated using a multiple linear regression using an array of sensors (see Section 5.2 and Table 1 ). Figure 1c shows the calibrated sensor using a frequentist multiple linear regression (MLR). Although the error is low, RMS E = 9.09 µgr/m 3 with an R 2 = 0.947, we can observe from the scatterplot (Figure 1b ) that a nonlinear model could improve the calibration error. The same sensor is calibrated using a nonlinear model called support-vector regression (SVR) having a RMS E = 6.21 µgr/m 3 with an R 2 = 0.976 in Figure 1d . This example shows that there is no golden rule for choosing a response function and that different models will calibrate the same sensor giving different QoI (quality of information), where QoI is measured in terms of the calibration error given by the model. Nonlinear responses can be analyzed using a variety of techniques such as (i) maximum likelihood (ML) BIB006 BIB004 or maximum a posteriori (MAP) BIB001  BIB003 in its Bayesian version, which finds the calibration parameters that better fit the data; (ii) splines BIB002 BIB005 , which approximate nonlinear response functions by a continuous piecewise linear function with m segments (i.e., step functions); (iii) support vector regression (SVR) BIB011 BIB009 , which classifies data by means of regression functions that depend on Lagrange multipliers and kernel functions; (iv) random forest BIB012 , which constructs an ensemble of decision trees using a training data set; the mean value from that ensemble of decision trees is then used to predict the value for new input data; (v) artificial neural networks (ANN) BIB007 BIB010 BIB011 , which consist of multiple layers formed by neural units. A single neuron has a number, I, of inputs, x i , and one output, y. There are a weight, w i , and a bias, w 0 , associated with each input. The neuron response is called activation rule and captures the nonlinearity of the sensors.