Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB001 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB006 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB007 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <s> Frequent sensor calibration is essential in sensor networks with low-cost sensors. We exploit the fact that temporally and spatially close measurements of different sensors measuring the same phenomenon are similar. Hence, when calibrating a sensor, we adjust its calibration parameters to minimize the differences between co-located measurements of previously calibrated sensors. In turn, freshly calibrated sensors can now be used to calibrate other sensors in the network, referred to as multi-hop calibration. We are the first to study multi-hop calibration with respect to a reference signal (micro-calibration) in detail. We show that ordinary least squares regression---commonly used to calibrate noisy sensors---suffers from significant error accumulation over multiple hops. In this paper, we propose a novel multi-hop calibration algorithm using geometric mean regression, which (i) highly reduces error propagation in the network, (ii) distinctly outperforms ordinary least squares in the multi-hop scenario, and (iii) requires considerably fewer ground truth measurements compared to existing network calibration algorithms. The proposed algorithm is especially valuable when calibrating large networks of heterogeneous sensors with different noise characteristics. We provide theoretical justifications for our claims. Then, we conduct a detailed analysis with artificial data to study calibration accuracy under various settings and to identify different error sources. Finally, we use our algorithm to accurately calibrate 13 million temperature, ground ozone (O3), and carbon monoxide (CO) measurements gathered by our mobile air pollution monitoring network. <s> BIB008 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB009 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB010 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Open Issues in Calibration Approaches <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> BIB011
Few research studies on multi-hop approaches exist BIB001 BIB008 BIB011 BIB004 . Multi-hop approaches have the problem of regression dilution. Recently, Maag et al. BIB011 have proposed how to minimize or eliminate the regression dilution effect in multi-hop approaches by using geometric mean regression. Relative to the accumulated error in multi-hop approaches, other calibration techniques robust against regression dilution and use of a ground-truth node or an already calibrated node as reference in the multi-hop approaches are other issues to be investigated. Most of the works that analyzed blind-calibration used temperature data sets BIB003 BIB006 BIB010 or synthetic data sets BIB009 BIB002 BIB007 BIB005 . We believe that although blind calibration is a promising calibration technique, it has to be tested with wider sets of sensors and in real scenarios or testbeds. Moreover, knowing the complexity of blind calibration used in low-computational sensor networks and in distributed approaches is another question to be answered. Most of the calibration approaches found in the literature are distributed-based. However, they are analyzed as centralizedbased systems. This is probably because of the small number of real testbeds deployed and the difficulty of implementing realscenario distributed approaches. We believe that distributed approaches, in general, are an open area that has to be developed and most of the approaches that are distributed have to be proven that they can work in a distributed manner, for example, by evaluating their complexity and feasibility in a real testbed.