Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Area <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> Calibration Area <s> In this paper a novel consensus-based distributed algorithm for blind macro-calibration in sensor networks is proposed. It is proved, on the basis of an originally developed methodology for treating higher order consensus schemes, that the algorithm achieves asymptotic agreement for sensor gains and offsets in the mean square sense and with probability one. In the case of a given reference, all sensors are asymptotically calibrated. Simulation results illustrate properties of the algorithm. <s> BIB002 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Area <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> BIB003 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Area <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> BIB004 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Area <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> BIB005 </s> Self-Calibration Methods for Uncontrolled Environments in Sensor Networks: A Reference Survey <s> Calibration Area <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> BIB006
Sensor nodes are usually deployed in a specific area. Depending on the area of interest, calibration can be performed at a given point, in which case it is known as micro, or devicelevel, calibration. If the objective is a whole area involving a set of sensors or all of them, the calibration is called macro, or system-level, calibration. Micro-calibration refers to the method that tunes each individual sensor to output accurate readings at a specific given point (location) of the area, as illustrated in Figure 3 . Microcalibration algorithms calibrate every sensor according to a reference node in order to have accurate sensor measurements of the phenomenon monitored. Examples of micro-calibration are the calibration of a sensor light at a given location BIB001 and the calibration of a NOx sensor BIB005 with respect to a ground-truth reference station. Macro-calibration assumes a system-wide calibration in the area of interest and focuses on optimizing the measurements of that area as a whole. The main goal of macro-calibration is not to adjust sensor calibration according to a reference signal. Instead, calibration algorithms try to maximize the similarity among the measurements of all sensor nodes in the area. Hence, most macro-calibration algorithms do not require access to reference measurements BIB006 BIB003 BIB004 . For example, Stankovic et al. BIB006 BIB002 proposed a distributed macro-calibration approach based on the generalized consensus problem, in which all the equivalent sensor gains and offsets in the monitoring area covered by the sensor network should converge asymptotically to equal values, reducing the overall network error. Another example is that of BIB003 , in which a detection mechanism was leveraged for surveillance applications. Sensors give their readings to a centralized node (a cluster-head), which computes the calibration coefficients for each sensor node that participates in the process, with the goal of maximizing the detection probability subject to an upper bound of the false alarm rate specified by the application. 