Optimal resilient sensor placement problem for secure state estimation

In an increasing number of scientific and commercial mission scenarios at sea, it is required to simultaneously localize a group of underwater targets. The latter may include moored systems, autonomous vehicles, and even human divers. For reasons that have to do with the unavailability of Global Positioning System underwater, cost reduction, and simplicity of operation, there is currently a surge of interest in the development of range-based multiple target localization systems that rely on the computation of the distances between the targets and a number of sensor nodes deployed at the ocean surface, equipped with acoustic range measuring devices. In the case of a single target, there is a wealth of literature on the problem of optimal acoustic sensor placement to maximize the information available for target localization using trilateration methods. In the case of multiple targets, however, the literature is scarce. Motivated by these considerations, we address the problem of optimal sensor placement for multiple underwater target positioning. In this setup, we are naturally led to a multiple objective optimization problem, the solution of which allows for the analysis of the trade-offs involved in the localization of the targets simultaneously. To this end, we resort to tools from estimation theory and multi-objective optimization. For each target, the function to be minimized (by proper choice of the sensor configuration) is related to the determinant of the corresponding Fisher information matrix, which yields information on the minimum possible covariance of the error with which the position of the target can be estimated using any non-biased estimator. To deal with the fact that more than one target is involved, we exploit the concept of multiple objective Pareto-optimal solutions to characterize the best possible accuracy with which each of the targets can be positioned, given constraints on the desired positioning accuracy of the other targets. Simulation examples illustrate how, for a three-sensor network and two targets, it is possible to define an optimal sensor configuration that yields large positioning accuracy for both targets simultaneously, using convex optimization tools. When more than two targets are involved, however, more than three sensors are required to exploit an adequate trade-off of the accuracy with which each target can be positioned by resorting to non-convex and Pareto-optimization tools. We show how in this case the optimal sensor configurations depend on the Pareto weights assigned to each of the targets, as well as on the number of sensors, the number of targets, and the uncertainty with which the positions of the targets are known a priori.

The author defines the problem of optimal sensor placement in two-dimensional space to address the issue of choosing a configuration of multiple sensors to minimize the uncertainty in the consensus estimate obtained by combining the sensor measurements. The algebraic structure of sensor errors with respect to sensor placement is studied, and a necessary condition for the optimal placement is derived. The solution to the problem is obtained by comparing sensor configurations that satisfy the necessary condition. The method does not assume specific sensor modality and is applicable to sensors of any type that are capable of providing position information.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This report summarizes the achievements and final results of this program. The objective of this program is to develop a general model-based sensor network design methodology and tools to address key issues in the design of an optimal sensor network configuration: the type, location and number of sensors used in a network, for online condition monitoring. In particular, the focus in this work is to develop software tools for optimal sensor placement (OSP) and use these tools to design optimal sensor network configuration for online condition monitoring of gasifier refractory wear and radiant syngas cooler (RSC) fouling. The methodology developed will be applicable to sensing system design for online condition monitoring for broad range of applications. The overall approach consists of (i) defining condition monitoring requirement in terms of OSP and mapping these requirements in mathematical terms for OSP algorithm, (ii) analyzing trade-off of alternate OSP algorithms, down selecting the most relevant ones and developing them for IGCC applications (iii) enhancing the gasifier and RSC models as required by OSP algorithms, (iv) applying the developed OSP algorithm to design the optimal sensor network required for the condition monitoring of an IGCC gasifier refractory and RSC fouling. Two key requirements for OSP for condition monitoring are desired precision for the monitoring variables (e.g. refractory wear) and reliability of the proposed sensor network in the presence of expected sensor failures. The OSP problem is naturally posed within a Kalman filtering approach as an integer programming problem where the key requirements of precision and reliability are imposed as constraints. The optimization is performed over the overall network cost. Based on extensive literature survey two formulations were identified as being relevant to OSP for condition monitoring; one based on LMI formulation and the other being standard INLP formulation. Various algorithms to solve these two formulations were developed and validated. For a given OSP problem the computation efficiency largely depends on the “size” of the problem. Initially a simplified 1-D gasifier model assuming axial and azimuthal symmetry was used to test out various OSP algorithms. Finally these algorithms were used to design the optimal sensor network for condition monitoring of IGCC gasifier refractory wear and RSC fouling. The sensors type and locations obtained as solution to the OSP problem were validated using model based sensing approach. The OSP algorithm has been developed in a modular form and has been packaged as a software tool for OSP design where a designer can explore various OSP design algorithm is a user friendly way. The OSP software tool is implemented in Matlab/Simulink© in-house. The tool also uses few optimization routines that are freely available on World Wide Web. In addition a modular Extended Kalman Filter (EKF) block has also been developed in Matlab/Simulink© which can be utilized for model based sensing of important process variables that are not directly measured through combining the online sensors with model based estimation once the hardware sensor and their locations has been finalized. The OSP algorithm details and the results of applying these algorithms to obtain optimal sensor location for condition monitoring of gasifier refractory wear and RSC fouling profile are summarized in this final report.

Aerosols affect the Earth&amp;#8217;s energy budget by both scattering and absorbing solar radiation. Measuring parameters that separately quantify the two components, such as the aerosol absorption optical depth (AAOD), is key to better understanding the aerosol direct climate effect. As most satellite instruments can only retrieve the total aerosol extinction signal, the most reliable source of global AAOD observations is the ground-based AERONET sensor network. AERONET comprises hundreds of stations worldwide; however, their spatial distribution is uneven and coverage remains sparse in many relevant regions. To effectively reduce our uncertainty related to absorbing aerosols and efficiently expand the network, new stations should be placed in locations that maximise measurement informativeness. In this study, we address the problem of optimal sensor placement using convolutional neural processes (ConvNPs). ConvNPs are meta-learning models that use convolutional neural networks to learn maps from heterogeneous input datasets to a context-dependent Gaussian predictive model. We train ConvNPs using reanalysis data to learn to model daily global AAOD from sparse point observations given at station locations and additional gridded auxiliary data. The model&amp;#8217;s probabilistic predictions are then harnessed in an active learning framework to sequentially propose new observation locations that optimally reduce model uncertainty and improve the network's informativeness. Our subsequent analysis considers further practical factors that might trade off with informativeness in the selection of new station locations, such as cloudiness and remoteness. The resulting proposed placements identify locations that would optimally enhance ground-based AAOD observation and can inform and focus future network expansion efforts.

A methodology is presented in this paper for the identification of an effective way to install a given number of sensors on a structure to extract as much information as possible for structural model identification utilizing measured dynamic data. The information entropy is employed as a measure to quantify the uncertainties of the set of identified model parameters. The problem of optimal sensor placement is then formulated as a discrete optimization problem, in which the information entropy measure is minimized, with the sensor configurations as the minimization variables. The methodology is illustrated numerically and experimentally using shear building models. The performance of the optimal sensor placement technique is verified using the identification results based on the measured acceleration responses of a 4‐storey shear building model under laboratory conditions.

This paper addresses the problem of Optimal Sensor Placement in Road Transportation Networks. The performance of the sensors is measured in terms of estimation error covariance of the Best Linear Unbiased Estimator of cumulative flows in the network over a long period. Sensors are to be placed in such a way that the sum of the error covariance and of a cost penalizing the number of sensors is minimized. The problem, inherently combinatorial, is relaxed using the concept of Virtual Variance. The resulting problem can be cast as a convex problem, whose computational load is much lower than the original combinatorial problem. Several variations are discussed, and the algorithm is applied to a regular grid network, for which an explicit comparison with the true optimum is offered, and, using data from the Grenoble Traffic Lab sensor network, to the real-world scenario of Rocade Sud in Grenoble, France.

SOURCE LOCALIZATION WITH MINIMAL NUMBER OF NETWORKED SENSORS

Kriging-enhanced ensemble variational data assimilation for scalar-source identification in turbulent environments

This paper considers the optimal sensor placement problem for angle-of-arrival (AOA) target localization in the 2D plane with a Gaussian prior. Optimal sensor locations are analytically determined for a single AOA sensor using the D- and A-optimality criteria and an approximation of the Bayesian Fisher information matrix (BFIM). Optimal sensor placement is shown to align with the minor axis of the prior covariance error ellipse for both optimality criteria. The approximate BFIM is argued to be valid for a sufficiently small prior covariance compared with the target range. Optimal sensor placement results obtained for Bayesian target localization are extended to manoeuvring target tracking. For sensor trajectory optimization subject to turn-rate constraints, numerical search methods based on the D- and A-optimality criteria as well as a new closed-form projection algorithm that aims to achieve alignment with the minor axis of the prior error ellipse are proposed. It is observed that the two optimality criteria generate significantly different optimal sensor trajectories despite having the same optimal sensor placement for the localization of a stationary target. Analysis results and the performance of the sensor trajectory optimization methods are demonstrated with simulation examples. It is observed that the new closed-form projection algorithm achieves superior tracking performance compared with the two numerical search methods.

Heuristic linear algebraic rank-variance formulation and solution approach for efficient sensor placement

Inspired by recent advances in multistatic radar systems, the problem of sensor placement is investigated. Our study is motivated by the fact that it is not always clear what the placement of the radars giving the best performance for the targets of interest might be. To account for the issue, we derive the multistatic Cramer-Rao lower bounds (CRLBs) for range and velocity estimation as the fitness function. Then we use genetic algorithms (GAs) to perform the optimized sensor placement as one of global optimization. The simulation example indicates that our proposed approach is a flexible and effective tool and is capable of suggesting optimal sensor placement strategies to meet required radar performance goals.

This paper concentrates on the optimal sensor placement problem in ambient vibration based structural health monitoring. More specifically, the paper examines the covariance of estimated parameters during system identification using auto‐regressive and moving average vector (ARMAv) model. By utilizing the discrete‐time steady state Kalman filter, this paper realizes the structure's finite element (FE) model under broad‐band white noise excitations using an ARMAv model. Based on the asymptotic distribution of the parameter estimates of the ARMAv model, both a theoretical closed form and a numerical estimate form of the covariance of the estimates are obtained. Introducing the information entropy (differential entropy) measure, as well as various matrix norms, this paper attempts to find a reasonable measure to the uncertainties embedded in the ARMAv model estimates. Thus, it is possible to select the optimal sensor placement that would lead to the smallest uncertainties during the ARMAv identification proc...

Source localization is an important application of wireless sensor networks (WSNs). Many types of sensors can be used for source localization, e.g. range-only sensors, bearing-only sensors and time-of-arrival (TOA) sensors, etc. It is well known that the relative sensor-source geometry can significantly affect the performance of any particular localization algorithm. Existing works in the literature mainly deal with the geometry analysis for a single type of sensors. However, in real applications, different types of sensors may be utilized for source localization simultaneously. Hence, in this paper, we consider the optimal sensor placement problem in heterogeneous sensor networks, where two types of sensors are deployed for source localization. Relative optimal sensor-source configurations with the minimum number of sensors for source localization, are identified under the D-optimality criterion with potential extensions to a general case. Explicit characterizations of optimal sensor-source geometries are given for hybrid range-only and bearing-only sensors as well as hybrid bearing-only and TOA sensors, respectively.

Accurate localization is a critical task in underwater navigation. Typical localization methods use a set of acoustic sensors and beacons to estimate relative position, whose geometric configuration has a significant impact on the localization accuracy. Although there is much effort in the literature to define optimal 2D or 3D sensor placement, the optimal sensor placement in irregular and constrained 3D surfaces, such as autonomous underwater vehicles (AUVs) or other structures, is not exploited for improving localization. Additionally, most applications using AUVs employ commercial acoustic modems or compact arrays, therefore the optimization of the placement of spatially independent sensors is not a considered issue. This article tackles acoustic sensor placement optimization in irregular and constrained 3D surfaces, for inverted ultra-short baseline (USBL) approaches, to improve localization accuracy. The implemented multi-objective memetic algorithm combines an evaluation of the geometric sensor's configuration, using the Cramer-Rao Lower Bound (CRLB), with the incidence angle of the received signal. A case study is presented over a simulated homing and docking scenario to demonstrate the proposed optimization algorithm.

Optimal sensor placement is an important problem to look at. This problem becomes all the more relevant nowadays due to advancements in infrastructure monitoring robotic technologies including underground sensing. While there are multiple ways to solve optimal sensor placement problems, one of the most generic methods available is Bayesian Optimization and its variants. In this paper, we present a simple benchmark-like formulation for exploiting Gaussian Process uncertainty for sensor placement to measure a scalar field.