Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> We describe an ad-hoc localization system for sensor networks and explain why traditional calibration methods are inadequate for this system. Building upon previous work, we frame calibration as a parameter estimation problem; we parameterize each device and choose the values of those parameters that optimize the overall system performance. This method reduces our average error from 74.6% without calibration to 10.1%. We propose ways to expand this technique to a method of autocalibration for localization as well as to other sensor network applications. <s> BIB001 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> Numerous factors contribute to errors in sensor measurements. In order to be useful, any sensor device must be calibrated to adjust its accuracy against the expected measurement scale. In large-scale sensor networks, calibration will be an exceptionally difficult task since sensor nodes are often not easily accessible and manual device-by-device calibration is intractable. In this paper, we present a two-phase post-deployment calibration technique for large-scale, dense sensor deployments. In its first phase, the algorithm derives relative calibration relationships between pairs of co-located sensors, while in the second phase, it maximizes the consistency of the pair-wise calibration functions among groups of sensor nodes. The key idea in the first phase is to use temporal correlation of signals received at neighboring sensors when the signals are highly correlated (i.e. sensors are observing the same phenomenon) to derive the function relating their bias in amplitude. We formulate the second phase as an optimization problem and present an algorithm suitable for localized implementation. We evaluate the performance of the first phase of the algorithm using empirical and simulated data. <s> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear 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> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> Air quality monitoring is extremely important as air pollution has a direct impact on human health. Low-cost gas sensors are used to effectively perceive the environment by mounting them on top of mobile vehicles, for example, using a public transport network. Thus, these sensors are part of a mobile network and perform from time to time measurements in each others vicinity. In this paper, we study three calibration algorithms that exploit co-located sensor measurements to enhance sensor calibration and consequently the quality of the pollution measurements on-the-fly. Forward calibration, based on a traditional approach widely used in the literature, is used as performance benchmark for two novel algorithms: backward and instant calibration. We validate all three algorithms with real ozone pollution measurements carried out in an urban setting by comparing gas sensor output to high-quality measurements from analytical instruments. We find that both backward and instant calibration reduce the average measurement error by a factor of two compared to forward calibration. Furthermore, we unveil the arising difficulties if sensor calibration is not based on reliable reference measurements but on sensor readings of low-cost gas sensors which is inevitable in a mobile scenario with only a few reliable sensors. We propose a solution and evaluate its effect on the measurement accuracy in experiments and simulation. <s> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> This paper gives a state-of-art of wireless sensor network (WSN) technologies and solutions applied to precision agriculture. The paper first considers applications and existing experiences that show how WSN technologies have been introduced in to agricultural applications. Then, a survey in hardware and software solutions is related with special emphasis on technological aspects. Finally, the paper shows how five networking and technological solutions may impact the next generation of sensors. These are: (1) scalar wireless sensor networks; (2) wireless multimedia sensor networks; (3) mobility of nodes; (4) tag-based systems; and (5) smart-phone applications. <s> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear 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> BIB006 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> High temperature gas sensors have been highly demanded for combustion process optimization and toxic emissions control, which usually suffer from poor selectivity. In order to solve this selectivity issue and identify unknown reducing gas species (CO, CH4, and CH8) and concentrations, a high temperature resistive sensor array data set was built in this study based on 5 reported sensors. As each sensor showed specific responses towards different types of reducing gas with certain concentrations, based on which calibration curves were fitted, providing benchmark sensor array response database, then Bayesian inference framework was utilized to process the sensor array data and build a sample selection program to simultaneously identify gas species and concentration, by formulating proper likelihood between input measured sensor array response pattern of an unknown gas and each sampled sensor array response pattern in benchmark database. This algorithm shows good robustness which can accurately identify gas species and predict gas concentration with a small error of less than 10% based on limited amount of experiment data. These features indicate that Bayesian probabilistic approach is a simple and efficient way to process sensor array data, which can significantly reduce the required computational overhead and training data. <s> BIB007 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> Frequent sensor calibration is essential in sensor networks with low-cost sensors. We exploit the fact that temporally and spatially close measurements of different sensors measuring the same phenomenon are similar. Hence, when calibrating a sensor, we adjust its calibration parameters to minimize the differences between co-located measurements of previously calibrated sensors. In turn, freshly calibrated sensors can now be used to calibrate other sensors in the network, referred to as multi-hop calibration. We are the first to study multi-hop calibration with respect to a reference signal (micro-calibration) in detail. We show that ordinary least squares regression---commonly used to calibrate noisy sensors---suffers from significant error accumulation over multiple hops. In this paper, we propose a novel multi-hop calibration algorithm using geometric mean regression, which (i) highly reduces error propagation in the network, (ii) distinctly outperforms ordinary least squares in the multi-hop scenario, and (iii) requires considerably fewer ground truth measurements compared to existing network calibration algorithms. The proposed algorithm is especially valuable when calibrating large networks of heterogeneous sensors with different noise characteristics. We provide theoretical justifications for our claims. Then, we conduct a detailed analysis with artificial data to study calibration accuracy under various settings and to identify different error sources. Finally, we use our algorithm to accurately calibrate 13 million temperature, ground ozone (O3), and carbon monoxide (CO) measurements gathered by our mobile air pollution monitoring network. <s> BIB008 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <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> BIB009 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear 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> BIB010 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <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> Multiple Linear Functions <s> Urban air pollution monitoring with mobile, portable, low-cost sensors has attracted increasing research interest for their wide spatial coverage and affordable expenses to the general public. However, low-cost air quality sensors not only drift over time but also suffer from cross-sensitivities and dependency on meteorological effects. Therefore calibration of measurements from low-cost sensors is indispensable to guarantee data accuracy and consistency to be fit for quantitative studies on air pollution. In this work we propose sensor array network calibration (SCAN), a multi-hop calibration technique for dependent low-cost sensors. SCAN is applicable to sets of co-located, heterogeneous sensors, known as sensor arrays, to compensate for cross-sensitivities and dependencies on meteorological influences. SCAN minimizes error accumulation over multiple hops of sensor arrays, which is unattainable with existing multi-hop calibration techniques. We formulate SCAN as a novel constrained least-squares regression and provide a closed-form expression of its regression parameters. We theoretically prove that SCAN is free from regression dilution even in presence of measurement noise. In-depth simulations demonstrate that SCAN outperforms various calibration techniques. Evaluations on two real-world low-cost air pollution sensor datasets comprising 66 million samples collected over three years show that SCAN yields 16% to 60% lower error than state-of-the-art calibration techniques. <s> BIB012 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> This study focuses on the investigation and quantification of low-cost sensor performance in application fields such as the extension of traditional air quality monitoring networks or the replacement of diffusion tubes. For this, sensor units consisting of two boxes featuring NO 2 and O 3 low-cost sensors and wireless data transfer were engineered. The sensor units were initially operated at air quality monitoring sites for three months for performance analysis and initial calibration. Afterwards, they were relocated and operated within a sensor network consisting of six locations for more than one year. Our analyses show that the employed O 3 and NO 2 sensors can be accurate to 2–5 and 5–7 ppb, respectively, during the first three months of operation. This accuracy, however, could not be maintained during their operation within the sensor network related to changes in sensor behaviour. Hence, the low-cost sensors in our configuration do not reach the accuracy level of NO 2 diffusion tubes. Tests in the laboratory revealed that changes in relative humidity can impact the signal of the employed NO 2 sensors similarly as changes in ambient NO 2 concentration. All the employed low-cost sensors need to be individually calibrated. Best performance of NO 2 sensors is achieved when the calibration models include also time dependent parameters accounting for changes in sensor response over time. Accordingly, an effective procedure for continuous data control and correction is essential for obtaining meaningful data. It is demonstrated that linking the measurements from low-cost sensors to the high quality measurements from routine air quality monitoring stations is an effective procedure for both tasks provided that time periods can be identified when pollutant concentrations can be accurately predicted at sensor locations. <s> BIB013 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Multiple Linear Functions <s> The remarkable advances in sensing and communication technologies have introduced increasingly low-cost, smart and portable sensors that can be embedded everywhere and play an important role in environmental sensing applications such as air quality monitoring. These user-friendly wireless sensor platforms enable assessment of human exposure to air pollution through observations at high spatial resolution in near-realtime, thus providing new opportunities to simultaneously enhance existing monitoring systems, as well as engage citizens in active environmental monitoring. However, data quality from such platforms is a concern since sensing hardware of such devices is generally characterized by a reduced accuracy, precision, and reliability. Achieving good data quality and maintaining error free measurements during the whole system lifetime is challenging. Over time, sensors become subject to several sources of unknown and uncontrollable faulty data which comprise the accuracy of the measurements and yield observations far from the expected values. This paper investigates calibration of low-cost air quality sensors in a real sensor network deployment. The approach leverages on the availability of sensor arrays in a wireless node to estimate parameters that minimize the calibration error using fusion of data from multiple sensors. The obtained results were encouraging and show the effectiveness of the approach compared to a single sensor calibration. <s> BIB014
In multiple linear response functions, the response variable y depends linearly on a set of parameters, as follows: Gas sensors, such as CO, O 3 , and NO 2 sensors, are examples BIB004 BIB006 BIB010 BIB007 BIB008 BIB009 BIB011 BIB012 BIB014 BIB013 of sensors that follow BIB005 The input parameters are called predictors, features, independent variables, or variables in machine learning and statistical learning terminology. BIB001 The output is also called response or dependent variable in machine learning and statistical learning terminology. BIB002 Temperature sensors in other fields not considered WSN, such as a temperature sensor in a 3D printer, can have other function responses that are nonlinear. BIB003 Polynomials on x belong to linear models since these ones are linear in coefficient β j . multiple linear responses. Some gas sensors (see Table 1 ) are better fitted, with interactions of several features following a model such as BIB006 BIB010 : An example BIB013 is an O 3 electrochemical sensor whose response depends on O 3 and temperature (T):