Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> Calibration Approaches and Attributes <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> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <s> While wireless sensor networks offer new capabilities, there are a number of issues that hinder their deployment in practice. We argue that robotics can solve or greatly reduce the impact of many of these issues. Our hypothesis has been tested in the context of an autonomous system to care for houseplants that we have deployed in our office environment. This paper describes what we believe is needed to make sensor networks practical, the role robots can play in accomplishing this, and the results we have obtained in developing our application. <s> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> Calibration Approaches and Attributes <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> BIB007 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <s> The performance of time-interleaved analog-to-digital converters is often significantly degraded by timing mismatch errors. We develop methods for performing blind calibration of such converters, i.e., for estimating the unknown time-skew parameters and for performing signal reconstruction from these estimates. The methods are low in complexity and allow for accurate calibration in systems with large numbers of converters, provided that the skews are sufficiently small in magnitude. We also present modifications to calibrate gain mismatch as well as adaptive sequential methods of implementation. Performance and complexity analysis is provided to support the viability of the methods. <s> BIB008 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB009 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <s> Recently, large scale sensor networks are used in various service applications. In case of measuring the distribution of room temperature, the regular calibration of the sensors is necessary for obtaining reliable information. However it is not an easy task in the case of a large scale sensor network. The calibration in such a system is time consuming and costly. To solve this problem, we propose a new method which is based on the two concepts of regression analysis and cross validation. The new method is explained and the performance of the proposed method is verified by an experiment and a simulation. <s> BIB010 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB011 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB012 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB013 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB014 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB015 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB016 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> BIB017 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <s> Abstract Sensors play an important role in guiding building systems to achieve desired operation and efficiency. However, sensors are subject to continuous degradation and failures over time. Although a periodical calibration is needed, it is exceptionally difficult and/or impractical to many sensors with a conventional manual approach. Uncalibrated problematic sensors could significantly compromise the systems' performance and lead to unintended loss of energy efficiency in buildings. We propose a methodology, termed virtual in-situ calibration, to solve this critical issue. It is developed by mathematically extracting the characteristics of essential aspects involved in a calibration, including the environment assessment, benchmark establishment, and uncertainty quantification. A case study of a supply air temperature sensor in rooftop units illustrates the implementation process; the erratic uncertainty is reduced from ± 19.2 °C to ± 0.7 °C after the virtual in-situ calibration. The calibration method can be implemented online to significantly improve the reliability of sensor networks in buildings. <s> BIB018 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Approaches and Attributes <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> Calibration Approaches and Attributes <s> The design of high-precision sensing devises becomes ever more difficult and expensive. At the same time, the need for precise calibration of these devices (ranging from tiny sensors to space telescopes) manifests itself as a major roadblock in many scientific and technological endeavors. To achieve optimal performance of advanced high-performance sensors one must carefully calibrate them, which is often difficult or even impossible to do in practice. In this work we bring together three seemingly unrelated concepts, namely self-calibration, compressive sensing, and biconvex optimization. The idea behind self-calibration is to equip a hardware device with a smart algorithm that can compensate automatically for the lack of calibration. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations where both and the diagonal matrix (which models the calibration error) are unknown. By 'lifting' this biconvex inverse problem we arrive at a convex optimization problem. By exploiting sparsity in the signal model, we derive explicit theoretical guarantees under which both and can be recovered exactly, robustly, and numerically efficiently via linear programming. Applications in array calibration and wireless communications are discussed and numerical simulations are presented, confirming and complementing our theoretical analysis. <s> BIB020
Calibration in sensor networks has been applied to many fields including environmental and air quality monitoring BIB015 BIB016 BIB017 , weather monitoring BIB004 BIB006 BIB018 BIB012 BIB010 BIB014  , localization BIB001 BIB002  BIB009 , synchronization BIB019 BIB005 , target discovery BIB013 BIB007 , robotic, electronic, and radio sensing BIB003 BIB008 BIB020 , and water flow monitoring BIB011 . These calibration attempts have taken different forms, or approaches, and have employed a number of calibration models (section 3). A calibration approach is the description of the set of attributes that will characterize the calibration of the sensor. For example, some authors assume that the node has ground-truth data available, while others assume that no such data are available. Some calibration models are applied at a centralized server, while others are distributed. In general, there is a set of attributes that capture a specific calibration approach and that have been used and defined in the literature. We next describe the attributes of the general characteristics that a calibration approach has. In order to calibrate a wireless sensor network in uncontrolled environments, the following questions have to be answered: • How is the measurement area? Calibration can be micro (i.e., performed at given points) or macro (i.e., performed in given areas). • What is the number of sensors involved? Calibration can be single (i.e., using only one sensor) or sensor fusion, also called multi-sensor data fusion. Sensor fusion includes the case of an array of sensors (i.e., using multiple sensors). • What is the knowledge of the physical phenomenon? Calibration can be non-blind (i.e., with full information), semiblind (i.e., with partial information), or blind (i.e., with no information). • What is the position of the uncalibrated nodes with respect to the ground-truth node? Calibration can be performed by nodes that are collocated, multi-hop (i.e., iterative), or model-based. • How many times and when is the calibration performed? Calibration can be carried out during pre-deployment (i.e., before the deployment of nodes), post-deployment (i.e., after the deployment of nodes), opportunistically (i.e., whenever possible), or periodically (i.e., at given intervals of time). • How is the information processed with respect to the normal operation? Calibration can be off-line (i.e., network not operative, normally related to calibrating with a set of data samples) or on-line (i.e., network operative, normally related to calibrating at each sample arrival). • Where is the calibration performed? The process can be centralized (i.e., localized at a central station) or distributed (i.e., among nodes). Answering these questions is fundamental and facilitates the understanding of different sensor calibration approaches and of the calibration models that have been employed. These calibration attributes are described in the following subsections; Figure 2 shows a map of the calibration attributes.