Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> Knowledge of Ground-Truth Data <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> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> This paper considers the problem of blindly calibrating sensor response using routine sensor network measurements. We show that as long as the sensors slightly oversample the signals of interest, then unknown sensor gains can be perfectly recovered. Remarkably, neither a controlled stimulus nor a dense deployment is required. We also characterize necessary and sufficient conditions for the identification of unknown sensor offsets. Our results exploit incoherence conditions between the basis for the signals and the canonical or natural basis for the sensor measurements. Practical algorithms for gain and offset identification are proposed based on the singular value decomposition and standard least squares techniques. We investigate the robustness of the proposed algorithms to model mismatch and noise on both simulated data and on data from current sensor network deployments. <s> BIB006 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB007 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB008 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB009 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> We consider the problem of joint sensor calibration and target signature estimation using distributed measurements over a large-scale sensor network. Specifically, we develop a new Distributed Signature Learning and Node Calibration algorithm (D-SLANC) which simultaneously estimates source signal's signature and estimates calibration parameters local to each sensor node. We model the sensor network as a connected graph and make use of the gossip-based distributed consensus to update the estimates at each iteration of the algorithm. The algorithm is robust to link and node failures. We prove convergence of the algorithm to the centralized data pooling solution. We compare performance with the Cramer-Rao bound, and study the scaling performance of both the CR bound and the D-SLANC algorithm. The algorithm has application to classification, target signature estimation, and blind calibration in large sensor networks. <s> BIB010 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB011 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> We present a long-term and cross-sectional study of a vibration-based water flow rate monitoring system in practical environments and scenarios. In our earlier research, we proved that a water flow monitoring system with vibration sensors is feasible by deploying and evaluating it in a small-scale laboratory setting. To validate the proposed system, the system was deployed in existing environments—two houses and a public restroom—and in two different laboratory test settings. With the collected data, we first demonstrate various aspects of the system's performance, including sensing stability, sensor node lifetime, the stability of autonomous sensor calibration, time to adaptation, and deployment complexity. We then discuss the practical challenges and lessons from the full-scale deployments. The evaluation results show that our water monitoring solution is a practical, quick-to-deploy system with a less than 5p average flow estimation error. <s> BIB012 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on blind calibration, using measures performed on a few unknown (but sparse) signals. A naive formulation of this blind calibration problem, using l 1 minimization, is reminiscent of blind source separation and dictionary learning, which are known to be highly non-convex and riddled with local minima. In the considered context, we show that in fact this formulation can be exactly expressed as a convex optimization problem, and can be solved using off-the-shelf algorithms. Numerical simulations demonstrate the effectiveness of the approach even for highly uncalibrated measures, when a sufficient number of (unknown, but sparse) calibrating signals is provided. We observe that the success/failure of the approach seems to obey sharp phase transitions. <s> BIB013 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 sub-problems with different conditions on the gains, specifially i) gains with different amplitude and the same phase, ii) gains with the same amplitude and different phase and iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided. <s> BIB014 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations. Therefore, correct calibration of the hardware is a central is- sue. In this paper we study the so-called blind calibration, i.e. when the training signals that are available to perform the calibration are sparse but unknown. We extend the approximate message passing (AMP) algorithm used in CS to the case of blind calibration. In the calibration-AMP, both the gains on the sensors and the elements of the signals are treated as unknowns. Our algorithm is also applica- ble to settings in which the sensors distort the measurements in other ways than multiplication by a gain, unlike previously suggested blind calibration algorithms based on convex relaxations. We study numerically the phase diagram of the blind calibration problem, and show that even in cases where convex relaxation is pos- sible, our algorithm requires a smaller number of measurements and/or signals in order to perform well. <s> BIB015 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB016 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> Knowledge of Ground-Truth Data <s> Technological advances in nanotechnology enabled the use of microelectromechanical systems (MEMS) in various application areas. With the integration of various sensor devices into MEMS, autonomously calibrating these sensors become a major research problem. When performing calibration on real-world embedded sensor network deployments, random errors due to internal and external factors alter the calibration parameters and eventually effect the calibration quality in a negative way. Therefore, during autonomous calibration, calibration paths which has low cost and low error values are preferable. To tackle the calibration problem on embedded wireless sensor networks, we present an energy efficient and minimum error calibration model, and also prove that due to random errors the problem turns into an NP-complete problem. To the best of our knowledge this is the first time a formal proof is presented on the complexity of an iterative calibration based problem when random errors are present in the measurements. We also conducted heuristic tests using genetic algorithm to solve the optimization version of the problem, on various graphs. The NP-completeness result also reveals that more research is needed to examine the complexity of calibration in a more general framework in real-world sensor network deployments. <s> BIB018 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> In sensor-based measurement systems, the sensor calibrations are crucial to obtain the correct measured values. In this paper, we propose a new blind calibration scheme for a massive mobile sensor network. The mutual calibration relationships between colocated sensors are utilized in a densely deployed sensor network. We model the calibration relationships in a linear algebraic model, and derive an equivalent Laplacian matrix. By just solving the Laplacian linear equation, we can determine how much each sensor has to be calibrated. The proposed calibration scheme is explained as a generalized extension of the simple mean model scheme to the mobile sensor network. Theoretical analysis and simulation results show that the proposed linear algebraic model improves the accuracy of the simple mean model by nearly σdrift2/σnoise2 times at maximum, in terms of mean square error, where usually σdrift ≫ σnoise. In addition, we show the feasibility of our scheme on human movements, by applying the scheme to the Levy-walk model in the simulation. The most important advantages of our scheme are that the calibration model is straightforward and that the solution is simply obtained with a matrix inversion. <s> BIB019 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> This paper considers the problem of blindly calibrating large sensor networks to account for unknown gain and offset in each sensor. Under the assumption that the true signals measured by the sensors lie in a known lower dimensional subspace, previous work has shown that blind calibration is possible. In practical scenarios, perfect signal subspace knowledge is difficult to obtain. In this paper, we show that a solution robust to misspecification of the signal subspace can be obtained using total least squares (TLS) estimation. This formulation provides significant performance benefits over the standard least squares approach, as we show. Next, we extend this TLS algorithm for incorporating exact knowledge of a few sensor gains, termed partially-blind total least squares. <s> BIB020 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB021 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB022 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> With widespread usages of smart phones, participatory sensing becomes mainstream, especially for applications requiring pervasive deployments with massive sensors. However, the sensors on smart phones are prone to the unknown measurement errors, requiring automatic calibration among uncooperative participants. Current methods need either collaboration or explicit calibration process. However, due to the uncooperative and uncontrollable nature of the participants, these methods fail to calibrate sensor nodes effectively. We investigate sensor calibration in monitoring pollution sources, without explicit calibration process in uncooperative environment. We leverage the opportunity in sensing diversity, where a participant will sense multiple pollution sources when roaming in the area. Further, inspired by expectation maximization (EM) method, we propose a two-level iterative algorithm to estimate the source presences, source parameters and sensor noise iteratively. The key insight is that, only based on the participatory observations, we can “calibrate sensors without explicit or cooperative calibrating process”. Theoretical analysis proves that, our method can converge to the optimal estimation of sensor noise, where the likelihood of observations is maximized. Also, extensive simulations show that, ours improves the estimation accuracy of sensor bias up to 20 percent and that of sensor noise deviation up to 30 percent, compared with three baseline methods. <s> BIB023 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB024 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <s> The lifetime of wireless sensor networks (WSNs) has been significantly extended, while in long-term large-scale WSN applications, the increasing sensor drift has become a key problem affecting the reliability of sensory data. In this paper, we propose a blind online drift calibration framework based on subspace projection and sparse recovery for sensor networks in general-purpose monitoring. Temporal sparse Bayesian learning is used in the proposed method to estimate the sensor drift from under-sampled observations. The proposed method needs neither dense deployment nor the presence of a prior data model. Both simulated and real-world data set are used to evaluate the proposed method. Experimental results demonstrate that the proposed method can detect and recover the sensor drift when the number of drifted sensors are less than 20%, and when 40% sensors are drifted, the recovery rate is 80%. <s> BIB025 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB026 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB027 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Knowledge of Ground-Truth Data <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> BIB028
Calibration can be blind, semi-blind, or non-blind depending on whether or not sensory data are processed in the presence of controlled stimuli, a reference model, or high-fidelity groundtruth values ( Figure 5) . In non-blind calibration, also known as reference-based, sensors are calibrated leveraging some reference information. These approaches are based on a priori knowledge of groundtruth data, from high-quality sensors, which can be useful for comparing the response with the expected values. Accordingly, the calibration parameters are adjusted using these known data inputs. A good example in which non-blind calibration techniques are easy to apply is temperature and gas sensors. In the case of gas sensors, in many countries there are organizations BIB021 that deploy high-accuracy reference stations to measure air pollution. These reference stations are not densely deployed due to their high costs (approximately 100 thousands euros) BIB002 , but they can be used to calibrate low-cost sensors located behind them (pair-wise or collocated calibration; see Section 5.4). Non-blind calibration was applied for sensor network calibration by BIB003 BIB011 BIB027 BIB024 BIB005 BIB012  . Moreover, some researchers use commercial instruments to provide ground-truth measurements that are later used to evaluate calibration models BIB022 BIB027 . These instruments are not calibration chambers in which the conditions can be manually adjusted; instead, they are accurate devices that allow comparing the low-cost readings against reference data. Blind calibration is the approach that calibrates sensor networks without relying on any controlled stimuli or high-fidelity ground-truth data BIB006 . Instead, blind calibration schemes leverage signal processing theory, a priori knowledge, such as physical models and constraints, of the sensed phenomenon, and exploit the advantages of dense sensor deployments, such as redundant measurements and temporal or spatial correlation among groups of sensors, to determine the fitting function and estimate the calibration parameters. Many blind calibration works have been proposed for sensor networks employing different techniques BIB010 BIB021 BIB006 BIB008 BIB019 BIB025 BIB020 BIB014 BIB013 BIB015 . Balzano et al. BIB006 used least squares to solve the linear blind calibration problem; later, Lipor and Balzano BIB020 also proposed blind calibration with model mismatch in which the subspace measured is not perfectly known, solving the problem using total least squares. Ramakrishnan et al. BIB010 estimated the signal signature and simultaneously calibrated the sensor nodes using gossipbased algorithms. Stankovic et al. BIB021 proposed a distributed BIB021 The European Environment Agency (EEA, http://www.eea.europa.eu/dataand-maps/data/airbase-the-european-air-quality-database-7) and the United States Environmental Protection Agency (EPA, https://www.epa.gov/outdoorair-quality-data) publish air pollution ground-truth data from reference stations of many countries in Europe and in the US, respectively. BIB002 Similar cost in US dollars. algorithm for blind macro-calibration of large sensor networks. Wang et al. BIB008 proposed a density guided blind calibration (DGC) scheme for nonlinear mobile sensors by approximating the nonlinear calibration functions using piecewise linear functions. DGC relies on the observation that different sensors that move in the same region record similar field statistics. Other authors BIB025 proposed a learning phase in which principal component analysis (PCA) is used on a subspace of drift-free samples, followed by a calibration phase in which compressed sensing is used to estimate the sensor drift. Compressed sensing (CS) exploits the fact that the signal is M-sparse, meaning that only M<K out of the K components are non-zero. The authors of BIB014 BIB013 BIB015 ] also applied compressed sensing to blind calibration frameworks with unknown gains. Semi-blind calibration is an intermediate case between blind and non-blind calibration. In semi-blind calibration, a sensor requires partial ground-truth information sent from a subset of nodes to calibrate itself BIB016 BIB028 BIB001 BIB026 BIB009 BIB017 BIB004 BIB023 or when interacting with a calibrated sensor BIB007 BIB018 , as illustrated in Figure 5 . For instance, in the semi-blind calibration proposed by BIB007 , uncalibrated nodes interact with calibrated nodes and run an average consensus algorithm using their measurements as partial ground-truth for calibration. Maag et al. BIB028 proposed a multi-hop calibration scheme in which sensors are calibrated using already calibrated sensors.