Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Accuracy of the 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> BIB001 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Accuracy of the 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> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Accuracy of the 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> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Accuracy of the Model <s> The definition of appropriate performance criteria is one of the key issues for the benchmarking of air quality models in regulatory applications. As part of the FAIRMODE benchmarking activities (Thunis et al., 2010), suitable criteria for air quality modelling in the frame of the EU air quality directive (AQD) 2008 are proposed and tested. The suggested approach builds on the target indicator (Jolliff et al., 2009) as support to the relative directive error, the current official statistical parameter as defined in the AQD (EEA, 2011), for quantitatively estimating model performances in air quality modelling applications. This study describes the advantages of using the target compared to the actual limitations of RDE and addresses the main links between the target and some ‘traditional’ statistical indicators (MFB, R, FAC2, σ ). It also describes the application of this methodology to NO 2 , O 3 and PM 10 concentrations on three different model-observations datasets. Among these datasets two focus on the... <s> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Accuracy of the Model <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> BIB005
Given the twofold goal of a calibration process -to recover the true values of a phenomenon and to detect sensory faults -a good estimation of the calibration parameters and the accuracy of the process determine the effectiveness of the model. The way to quantify the accuracy or QoI of a fitting model is BIB003 https://crawdad.org/ 9 https://archive.ics.uci.edu/ml/ by minimizing an error function  that measures the misfit between the output Y and the response function f(β,x) for any given value of β and the data set X. If the size of the data set Y is K, then a choice of an error function is the square of the errors between the predictions f (β, x k ) for each data point x k and the target value y k : where RSS stands for residual sum of squares. Then, the goal is to minimize the error function The calibration parameters, β * , are the solution of the minimization problem. The error is positive except whenever the function f (β * , x k ) passes exactly through each target point y k , in which case the error is zero. The following QoI metrics can be defined. (i) The mean squared error (MSE) measures the average of the squares of the errors. It is the second moment (about the origin) of the error and thus incorporates the variance of the calibration curve. (ii) The root mean squared error (RMS E) allows comparing different sizes of data sets, because it is measured on the same scale as the target value y k . (iii) The coefficient of determination (R 2 ) measures the proportion of variability in Y that can be explained using X, and it is bounded between 0 and 1. A value of R 2 close to 1  Multiple linear regression Mean error Real Photosynthetically active radiation (PAR) BIB005 Maximum likelihood Relative bias error Synthetic Air pollution indicates that a large proportion of the variability in the response has been explained by the regression. (iv) The normalized mean bias error (N MBE) represents effectively a total percent error. The use of percent differences rather than absolute differences normalizes the size of errors in the calibrated measurements. (v) The mean absolute error (MAE) is a quantity used to measure how close the calibrated measurements are to the ground-truth data. Other times, the calibration parameters are represented by a probability distribution. An example is a response function that follows a normal distribution of mean y k = f (β, x k ) and variance σ 2 . Now, the objective is to obtain a distribution with meanβ and varianceσ 2 β . In this case, other QoI metrics can also be obtained. (vi) The Cramèr-Rao bound (CRB), or information inequality, expresses a lower bound on the variance of a parameter's estimators. There are metrics that allow measuring the accuracy or precision of the estimation and depend on the algorithm or application defined by the authors. One example is the KullbackLeibler (KL) divergence, which measures how one probability distribution diverges from a second expected probability distribution BIB001  . Other examples are the average value of the relative bias error (RBE), the average value of the relative deviation error (RDE) BIB005 , and the Bayes risk in event detection applications BIB002 . Tables 2, 3, and 4 show how different sensor applications use different QoI metrics to assess the performance of the sensor network. The most used metrics are MS E, RMS E, and R 2 . Other authors use the target diagram BIB004 that provides information in one plot about the mean bias (MB), the standard deviation, the RMSE, the centered root mean square error (CRMSE), and the correlation coefficient, R. However, the QoI metrics in general are linked to the calibration model selected and to the application. For example, R 2 and RMS E, MAE, and MS E are good metrics to assess whether the assumptions of the model are correct and estimate whether the error is large.