Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> Choosing a Model <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> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <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> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> Sensornet systems research is being conducted with various applications and deployment scenarios in mind. In many of these scenarios, the presumption is that the sensornet will be deployed and managed by users who do not have a background in computer science. In this paper we describe the "tiny application sensor kit" (TASK), a system we have designed for use by end-users with minimal sensornet sophistication. We describe the requirements that guided our design, the architecture of the system and results from initial deployments. Based on our experience to date we present preliminary design principles and research challenges that arise in delivering sensornet research to end users. <s> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB006 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> This paper proposes a method for calibrating networked sensors from local duplicated measurements in couples of sensors among them. In the Bayesian framework, we show the system and procedure for the optimum collaborative calibration/synchronization is composed by: 1) sensor-wise maintenance of the offset values and a corresponding column of inverse of the estimation error covariance matrix (confidence matrix), 2) incremental updates of the confidence matrix elements for the coupled sensors with the confidence of the duplicated measurement, and 3-1) centralized computation for inverting the confidence matrix into the estimation error covariance matrix and sensor-wise computation for obtaining updated estimates of the offset values, or 3-2) global iterative computation of the updated estimates among all the sensors. <s> BIB007 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> Rapidly deployable sensor networks are portable, reusable, and can take advantage of a human user in the field attending to the deployment. Unfortunately, even small disruptions or problems in collected data must be addressed quickly, as the overall quantity of data gathered is small relative to longterm deployments. In this paper we describe a procedure for calibration and a system for online fault remediation. Care in the calibration process for ion selective electrodes used for water quality assists interpretation of the data. Scientists will have more confidence in the data obtained from a rapid deployment if in-field users can detect and compensate for problems as they occur. We have designed and implemented a tool for use in the field to detect potential faults and provide actions to remedy or validate the faulty data. In January of 2006 we deployed 48 sensors over a period of 12 days in Bangladesh in order to aid in validating a hypothesis on the mass presence of arsenic in the groundwater. Our system is based on the the approximately 25,000 measurements we collected. <s> BIB008 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB009 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> We propose CaliBree, a self-calibration system for mobile wireless sensor networks. Sensors calibration is a fundamental problem in a sensor network. If sensor devices are not properly calibrated, their sensor readings are likely of little use to the application. Distributed calibration is challenging in a mobile sensor network, where sensor devices are carried by people or vehicles, mainly for three reasons: i)the sensing contact time, i.e., the amount of time nodes are within the sensing range of each other, can be very limited, requiring a quick and efficient calibration technique; ii)for scalability and ease of use, the calibration algorithm should not require manual intervention; iii)the computational burden must be low since some sensor platforms have limited capabilities. In this paper we propose CaliBree, a distributed, scalable, and lightweight calibration protocol that applies a discrete average consensus algorithm technique to calibrate sensor nodes. CaliBree is shown to be effective through experimental evaluation using embedded wireless sensor devices, achieving high calibration accuracy. <s> BIB010 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB011 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> The purpose for wireless sensor networks is to deploy low cost sensors with sufficient computing and communication capabilities to support networked sensing applications. Even when the sensors are properly calibrated at the time of their deployment, they develop drift in their readings leading to biased sensor measurements. Noting that a physical phenomenon in a certain area follows some spatio-temporal correlation, we assume that the sensors readings in that area are correlated. We also assume that the instantiations of drifts are uncorrelated. Based on these assumptions, and inspired by the resemblance of registration problem in radar target tracking with the bias error problem in wireless sensor networks, we follow a Bayesian framework to solve the Drift/Bias problem in wireless sensor networks. We present two methods for solving the drift problem in a densely deployed sensor network, one for smooth drifts and the other for unsmooth drifts. We also show that both methods successfully detect and correct sensor errors and extend the effective life time of the sensor network. <s> BIB012 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> In this paper we study the problem of estimating the channel parameters for a generic wireless sensor network (WSN) in a completely distributed manner, using consensus algorithms. Specifically, we first propose a distributed strategy to minimize the effects of unknown constant offsets in the reading of the radio strength signal indicator due to uncalibrated sensors. Then we show how the computation of the optimal wireless channels parameters, which are the solution of a global least-square optimization problem, can be obtained with a consensus-based algorithm. The proposed algorithms are general algorithms for sensor calibration and distributed least-square parameter identification, and do not require any knowledge either on the global topology of the network nor the total number of nodes. Finally, we apply these algorithms to experimental data collected from an indoor WSN. Copyright © 2009 John Wiley & Sons, Ltd. <s> BIB013 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> In this paper a novel consensus-based distributed algorithm for blind macro-calibration in sensor networks is proposed. It is proved, on the basis of an originally developed methodology for treating higher order consensus schemes, that the algorithm achieves asymptotic agreement for sensor gains and offsets in the mean square sense and with probability one. In the case of a given reference, all sensors are asymptotically calibrated. Simulation results illustrate properties of the algorithm. <s> BIB014 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <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> BIB015 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> We introduce a control algorithm for automated calibration of sensor networks and fault compensation that reduces overall system error. Our approach uses a novel combination of models (for the spatial phenomena and sensor faults) and data-driven methods, and it works under novel conditions of dynamic sensor noise and bias in which the phenomenon of interest is both time- and space-variant. Our algorithm combines noise compensation using the EM (expectation-maximization) algorithm and a gossip-based protocol for sharing calibration information. We demonstrate its effectiveness in simulations that model real-world sensor fault scenarios. <s> BIB016 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> Internet-of-Things (IoT) is a concept referring to interconnected people and objects and smart city is one of the many applications of IoT. Wireless Sensor Network (WSN) is a specific technology that helps to create “Smart Cities”. It aims at creating a distributed network of intelligent sensor nodes which can measure various parameters for efficient management of the city. The data thus collected through a range of sensors is processed and is delivered wirelessly in real-time to the citizens or the appropriate authorities. Since the application framework for smart city application is huge, it would require a large number of different types of sensors for its implementation and the project could be viable only if we use low resolution, low precision but inexpensive sensors. The sensors in sensor network can suffer from random or systematic errors. Most common problem with inexpensive sensors used in WSNs for smart city applications is of drift and bias. They can be calibrated at the time of deployment, but they develop drift, which is the slow change in the reading of sensor from actual value as time progresses. In this paper we have proposed a framework to automatically detect and correct the drift of the sensor nodes to keep the WSN usable. Kriging based interpolation of the sensor readings of neighboring sensors is used to predict actual value at the sensor node and the measured drift is then kalman filtered to get correct drift estimates. We have demonstrated the results of this algorithm on real sensor data obtained from Intel Research Berkeley Laboratory deployment and shown that our system is able to detect and correct smooth drift and bias generated in the sensors. We have also shown that our system is robust with respect to the number of sensor nodes drifting and significantly outperforms the traditional averaging based interpolation methods. <s> BIB017 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB018 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <s> A novel distributed algorithm for blind macro-calibration of large sensor networks is introduced. The algorithm is in the form of a system of gradient-type recursions for estimating parameters of local sensor calibration functions. The method does not require any fusion center. The convergence analysis is based on diagonal dominance of the dynamical systems with block matrices. It is proved that the asymptotic consensus is achieved for all the equivalent sensor gains and offsets (in the mean square sense and with probability one) in lossy sensor networks with possible communication outages and additive communication noise. An illustrative simulation example is provided. <s> BIB019 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <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> BIB020 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB021 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB022 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB023 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB024 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB025 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a Model <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> BIB026 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Choosing a 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> BIB027
The choice of calibration model depends on the type of phenomena that the nodes measure, the resources of the wireless sensor deployment, the type of sensors, and the computation, storage, and communication capabilities of the sensor node. Moreover, the mathematical machinery that has been used in calibration in the past few years is more sophisticated when the sensor resources increase. More complex calibration approaches are being formulated with the increased number of wireless sensor network deployments with real applications. We have to mention that one of the most challenging tasks will be to directly calibrate on a low-cost node. Most low-cost wireless sensor nodes have too low capabilities to be able to be calibrated on-line. Light-computational models for low-capability nodes are one of the most difficult challenges that will have to be solved. For increasing wireless sensor capability nodes, higher computational techniques can be implemented, facilitating on-line calibration or recalibration mechanisms. For example, SVR and ANN require high computational resources that most wireless nodes do not include. In contrast, gradient descent models typically applied in optimization can be easily implemented in the node to perform on-line calibration in linear or multiple linear regression. For instance, temperature sensors (Table 2) typically follow linear response functions and have been analyzed using linear regression BIB003 BIB005 for calibrating the sensors, Bayesian inference for modeling drift BIB012 , and maximum likelihood BIB016 , Gaussian processes BIB016 , or kriging BIB017 for state-space modeling applications. Light point sensors have mainly been calibrated using splines BIB004 BIB011 or support-vector regression BIB022 due to the presence of nonlinearities, and they have been analyzed with distributed consensus BIB010 to show how light sensing is affected by sensor orientation. In the case of localization applications (Table 3) , the most used calibration technique is maximum a posteriori BIB001  BIB006 although distributed consensus BIB013 is also used when spatial redundancy is present. Target detection BIB018 BIB009 uses maximum likelihood to estimate detection probabilities. For synchronization applications, Stankovic et al. BIB019 BIB014 defined the distributed algorithms that converge fast to estimate the offset and gain of the calibration function. Ando et al. BIB007 used an iterative Bayesian algorithm for estimating the offset time of each sensor after the k-th event. To finalize the set of examples, to monitor air pollution (Table 4), we mainly need arrays of sensors, because pollutants depend on several factors (Table 1 ). In general, air pollution sensors are analyzed using multiple linear regression (MLR) BIB008 BIB015 BIB020 BIB023 BIB024 BIB026  , although when nonlinearities due to the chemical composition of the sensor appear, techniques such as artificial neural networks (ANN), support-vector regression (SVR) or random forest are used BIB021 BIB025 BIB024 BIB027 . Table 3 : Localization, synchronization, and target location applications. References Calibration model Evaluation metric Data set Application BIB002 Least squares Mean error Real (acoustic) Localization BIB018 Nonlinear (maximum likelihood) Detection probability Synthetic/real Target detection BIB001 Bayesian (maximum a posteriori) Cramèr-Rao bound Real (acoustic) Localization  BIB006 Bayesian (maximum a posteriori) K-L divergence Synthetic Localization BIB009 Nonlinear (maximum likelihood) Bayes risk Synthetic Target detection BIB013 Distributed consensus Mean, avg. residual Real (RSSI) Localization BIB014 BIB019 Distributed macro-calibration Mean squared error Synthetic Synchronization BIB007 Bayesian (iterative) Error variance Synthetic Synchronization