Large infrastructure networks (e.g. for transportation and power distribution) require constant monitoring for failures, congestion, and other adversarial events. However, assigning a sensor to every link in the network is often infeasible due to placement and maintenance costs. Instead, sensors can be placed only on a few key links, and machine learning algorithms can be leveraged for the inference of missing measurements (e.g. traffic counts, power flows) across the network. This paper investigates the sensor placement problem for networks. We first formalize the problem under a flow conservation assumption and show that it is NP-hard to place a fixed set of sensors optimally. Next, we propose an efficient and adaptive greedy heuristic for sensor placement that scales to large networks. Our experiments, using datasets from real-world application domains, show that the proposed approach enables more accurate inference than existing alternatives from the literature. We demonstrate that considering even imperfect or incomplete ground-truth estimates can vastly improve the prediction error, especially when a small number of sensors is available.
PySensors is a Python package for selecting and placing a sparse set of sensors for classification and reconstruction tasks. Specifically, PySensors implements algorithms for data-driven sparse sensor placement optimization for reconstruction (SSPOR) and sparse sensor placement optimization for classification (SSPOC). In this work we provide a brief description of the mathematical algorithms and theory for sparse sensor optimization, along with an overview and demonstration of the features implemented in PySensors (with code examples). We also include practical advice for user and a list of po…
A sensor is a small electronic device which has the ability to sense, compute and communicate either with other sensors or directly with a base station (sink). In a wireless sensor network (WSN), the sensors monitor a region and transmit the collected data packets through routes to the sinks. In this study, we propose a mixed--integer linear programming (MILP) model to maximize the number of time periods that a WSN carries out the desired tasks with limited energy and budget. Our sink and sensor placement, scheduling, routing with connected coverage ($SPSRC$) model is the first in the literatu…
This paper explores a new sequential selection framework for the optimal sensor placement (OSP) in Electrocardiography imaging networks (ECGI). The proposed methodology incorporates the use a recent experimental design method for the sequential selection of landmarkings on biological objects, namely, Gaussian process landmarking (GPLMK) for better exploration of the candidate sensors. The two experimental design methods work as a source of the training and the validation locations which is fitted using a spatiotemporal Gaussian process (STGP). The STGP is fitted using the training set to predi…
Source localization plays a key role in many applications including radar, wireless and underwater communications. Among various localization methods, the most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), and Received Signal Strength (RSS) based. Since the Cramér-Rao lower bounds (CRLB) of these methods depend on the sensor geometry explicitly, sensor placement becomes a crucial issue in source localization applications. In this paper, we consider finding the optimal sensor placements for the TOA, TDOA and RSS based localization scenarios. We first unify the three…
This paper proposes a novel algorithm to determine the optimal placement of redundant inertial sensors such as accelerometers and gyroscopes (gyros) for increasing the sensing accuracy. In this paper, we have proposed a novel iterative algorithm to find the optimal sensor configuration. The proposed algorithm utilizes the majorization-minimization (MM) algorithm and the duality principle to find the optimal configuration. Unlike the state-of-the-art which are mainly geometrical in nature and restricted to certain noise statistics, the proposed algorithm gives the exact positions of the sensors…
Sensor placement for linear inverse problems is the selection of locations to assign sensors so that the entire physical signal can be well recovered from partial observations. In this paper, we propose a fast sampling algorithm to place sensors. Specifically, assuming that the field signal $\mathbf{f}$ is represented by a linear model $\mathbf{f}=\pmbϕ\mathbf{g}$, it can be estimated from partial noisy samples via an unbiased least-squares (LS) method, whose expected mean square error (MSE) depends on chosen samples. First, we formulate an approximate MSE problem, and then prove it is equival…
Location is one of the basic information required for underwater optical wireless sensor networks (UOWSNs) for different purposes such as relating the sensing measurements with precise sensor positions, enabling efficient geographic routing techniques, and sustaining link connectivity between the nodes. Even though various two-dimensional UOWSNs localization methods have been proposed in the past, the directive nature of optical wireless communications and three-dimensional (3D) deployment of sensors require to develop 3D underwater localization methods. Additionally, the localization accuracy…
Source localization techniques incorporating hybrid measurements improve the reliability and accuracy of the location estimate. Given a set of hybrid sensors that can collect combined time of arrival (TOA), received signal strength (RSS) and angle of arrival (AOA) measurements, the localization accuracy can be enhanced further by optimally designing the placements of the hybrid sensors. In this paper, we present an optimal sensor placement methodology, which is based on the principle of majorization-minimization (MM), for hybrid localization technique. We first derive the Cramer-Rao lower boun…
We propose a novel method for solving optimal sensor placement problem for high-dimensional system using an annealing machine. The sensor points are calculated as a maximum clique problem of the graph, the edge weight of which is determined by the proper orthogonal decomposition (POD) mode obtained from data based on the fact that a high-dimensional system usually has a low-dimensional representation. Since the maximum clique problem is equivalent to the independent set problem of the complement graph, the independent set problem is solved using Fujitsu Digital Annealer. As a demonstration of …
Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference. Equivalently, the expected information entropy of the posterior of the model parameters is minimized over all possible sensor configurations for a given sensor budget. In the context of structural dynamical systems, this minimization is computationally expensive because of the large number of possible sensor configurations. Here, a very efficient convex rel…
The paper studies optimal sensor selection for source estimation in energy harvesting Internet of Things (IoT) networks. Specifically, the focus is on the selection of the sensor locations which minimizes the estimation error at a fusion center, and to optimally allocate power and bandwidth for each selected sensor subject to a prescribed spectral and energy budget. To do so, measurement accuracy, communication link quality, and the amount of energy harvested are all taken into account. The sensor selection is studied under both analog and digital transmission schemes from the selected sensors…
Optimal sensor placement (SP) usually minimizes an impact measure, such as the amount of contaminated water or the number of inhabitants affected before detection. The common choice is to minimize the minimum detection time (MDT) averaged over a set of contamination events, with contaminant injected at a different location. Given a SP, propagation is simulated through a hydraulic software model of the network to obtain spatio-temporal concentrations and the average MDT. Searching for an optimal SP is NP-hard: even for mid-size networks, efficient search methods are required, among which evolut…
Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devisesufficiently accurate models to observe, control or predict the state of real systems in biology, economics or other fields. A largely overlooked fact is that these systems are typically open and receive unknown inputs from their environment. A further fundamental obstacle are structural model errors caused by insufficient or inaccurate knowledge about the quantitative interactions in the real system. Here, we show that unknown inputs to open systems and model errors can be treated under t…
