Sensor Selection Problem Research Articles

Sensing Time Optimisation and Sensor Selection in Multi‐channel Multi‐antenna Wireless Cognitive Sensor Networks

Energy efficiency of cooperative spectrum sensing is a critical issue in wireless cognitive sensor networks (CSNs). However, sensor nodes consume high energy to support cognitive radio (CR) functionalities such as channel sensing. In this study, the energy-efficient cooperative spectrum sensing in multi-channel multi-antenna CSNs is investigated. First, a multi-channel CSN is considered to obtain sensing sensors and sensing time for each band in a CR system. The criteria is to minimise energy consumption of cooperative spectrum sensing under the global probabilities of detection and false alarm constraints. The authors employ a convex optimisation method to obtain optimal sensing time and sensing nodes for each band. Next, their analysis is extended into multi-antenna sensors, which is a promising solution instead of using more sensors. In multi-antenna cooperative spectrum sensing, diversity helps sensors behave virtually the same as multi-sensors systems. Then, the problem of sensor selection and also setting the sensing time for each band is solved based on the convex optimisation framework. Simulation results highlight that in their proposed algorithms a significant energy is saved compared with the baseline methods with equal sensing time in all bands.

Adaptive Sensor Selection for Nonlinear Tracking via Sparsity-Promoting Approaches

In this paper, we propose a few sparsity-promoting approaches for sensor selection in wireless sensor networks (WSNs) to reach the optimal tradeoff between the tracking performance and the sensing-communication cost. The proposed framework is valid for general nonlinear target tracking without explicit linearization and not restricted to any specific estimator. We formulate the sensor selection problem as the design of a sparse selection vector. The cardinality of the selection vector is added as a sparsity-promoting penalty term to the cost function where the conditional posterior Cramer–Rao lower bound is used as the criterion for sensor selection. To cope with large-scale WSNs, by combining iterative reweighted $\ell _1$ -norm minimization with the accelerated proximal gradient method and the alternating direction method of multipliers (ADMM), we develop two efficient sensor selection algorithms, respectively. We further develop a low-complexity distributed version of the ADMM where each sensor makes a local sensor selection decision. We test the proposed algorithms by simulations based on an extended Kalman filter using analog data and a particle filter using quantized data, respectively, which provide valuable insights and demonstrate the proposed algorithms’ performance.

Sensor selection for fault diagnosis in uncertain systems

ABSTRACTFinding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.

Sensor Network Configuration Learning for Maximizing Application Performance.

Numerous applications rely on data obtained from a wireless sensor network where application performance is of utmost importance. However, energy usage is also important, and oftentimes, a subset of sensors can be selected to maximize application performance. We cast the problem of sensor selection as a local search optimization problem and solve it using a variant of stochastic hill climbing extended with novel heuristics. This paper introduces sensor network configuration learning, a feedback-based heuristic algorithm that dynamically reconfigures the sensor network to maximize the performance of the target application. The proposed algorithm is described in detail, along with experiments conducted and a scalability study. A quick method for launching the algorithm from a better starting point than random is also detailed. The performance of the algorithm is compared to that of two other well-known algorithms and randomness. Our simulation results obtained from running sensor network configuration learning on a number of scenarios show the effectiveness and scalability of our approach.

The Cramér-Rao Bounds and Sensor Selection for Nonlinear Systems with Uncertain Observations.

This paper considers the problems of the posterior Cramér–Rao bound and sensor selection for multi-sensor nonlinear systems with uncertain observations. In order to effectively overcome the difficulties caused by uncertainty, we investigate two methods to derive the posterior Cramér–Rao bound. The first method is based on the recursive formula of the Cramér–Rao bound and the Gaussian mixture model. Nevertheless, it needs to compute a complex integral based on the joint probability density function of the sensor measurements and the target state. The computation burden of this method is relatively high, especially in large sensor networks. Inspired by the idea of the expectation maximization algorithm, the second method is to introduce some 0–1 latent variables to deal with the Gaussian mixture model. Since the regular condition of the posterior Cramér–Rao bound is unsatisfied for the discrete uncertain system, we use some continuous variables to approximate the discrete latent variables. Then, a new Cramér–Rao bound can be achieved by a limiting process of the Cramér–Rao bound of the continuous system. It avoids the complex integral, which can reduce the computation burden. Based on the new posterior Cramér–Rao bound, the optimal solution of the sensor selection problem can be derived analytically. Thus, it can be used to deal with the sensor selection of a large-scale sensor networks. Two typical numerical examples verify the effectiveness of the proposed methods.

Designing sampling schemes for multi-dimensional data

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramér–Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme.

Microphone Subset Selection for MVDR Beamformer Based Noise Reduction

In large-scale wireless acoustic sensor networks (WASNs), many of the sensors will only have a marginal contribution to a certain estimation task. Involving all sensors increases the energy budget unnecessarily and decreases the lifetime of the WASN. Using microphone subset selection, also termed as sensor selection, the most informative sensors can be chosen from a set of candidate sensors to achieve a prescribed inference performance. In this paper, we consider microphone subset selection for minimum variance distortionless response (MVDR) beamformer based noise reduction. The best subset of sensors is determined by minimizing the transmission cost while constraining the output noise power (or signal-to-noise ratio). Assuming the statistical information on correlation matrices of the sensor measurements is available, the sensor selection problem for this model-driven scheme is first solved by utilizing convex optimization techniques. In addition, to avoid estimating the statistics related to all the candidate sensors beforehand, we also propose a data-driven approach to select the best subset using a greedy strategy. The performance of the greedy algorithm converges to that of the model-driven method, while it displays advantages in dynamic scenarios as well as on computational complexity. Compared to a sparse MVDR or radius-based beamformer, experiments show that the proposed methods can guarantee the desired performance with significantly less transmission costs.

Early detection of dynamic harmful cascades in large-scale networks

Quickly detecting harmful cascades in networks can allow us to analyze the causes and prevent further spreading of destructive influence. Since it is often impossible to observe the state of all nodes in a network, a common method is to detect harmful cascades from sparsely placed sensors. However, the harmful cascades are usually dynamic (e.g., the cascade initiators and diffusion trajectories can change over the time), which can severely destroy the robustness of selected sensors. Meanwhile the large scale of current networks greatly increases the time complexity of sensor selection. Motivated by the observation, in this paper we investigate the scalable sensor selection problem for early detection of dynamic harmful cascades in networks. Specifically, we first put forward a dynamic susceptible-infected model to describe harmful cascades, and formally define a detection time minimization (DTM) problem which focuses on effective sensors placement for early detection of dynamic cascades. We prove that it is #P-hard to calculate the objective function exactly and propose two Monte-Carlo methods to estimate it efficiently. We prove the NP-hardness of DTM problem and design a corresponding greedy algorithm. Based on that, we propose an efficient upper bound based greedy (UBG) algorithm with the theoretical performance guarantee reserved. To further meet different types of large-scale networks, we propose two accelerations of UBG: Quickest-Path-UBG for sparse networks and Local-Reduction-UBG for dense networks to improve the time complexity. The experimental results on synthetic and real-world social networks demonstrate the practicality of our approaches.

Researching Signals from Workpiece Backside during Electron Beam Welding in Full Penetration Mode

In this research work, we consider the problem of sensor selection for the system controlling full penetration mode in electron beam welding. For this, we have investigated four signals from the backside of the workpiece: electron current in root plasma, ion current in root plasma, through-thickness electron current and penetrating bremsstrahlung X-ray. After having done the research we have estimated the advisability of two signals: one for cases if requirements for control precision are high and the other for other cases.

Static Optimal Sensor Selection via Linear Integer Programming: The Orthogonal Case

We consider the static optimal sensor selection problem, where we optimally select $d$ sensors among $s$ possible sensors with $d . Under the assumption that the $s$ sensors are mutually orthogonal to each other, we cast the optimal sensor selection problem as a linear integer program (LIP) that corresponds to minimization of the trace of the linear least-squares estimation error covariance. We show that even though general LIPs are NP-hard , our problem can be solved in polynomial time as a linear program; hence, it is not necessary to go for suboptimal solutions. This is due to the associated integral convex polyhedron constraint set followed by its total unimodularity property. We provide simulation results to demonstrate polynomial-time solvability of the corresponding problem with the orthogonality condition as well as additional sensor selection constraints.

A new sensor selection scheme for Bayesian learning based sparse signal recovery in WSNs

In this paper, we address the issue of sparse signal recovery in wireless sensor networks (WSNs) based on Bayesian learning. We first formulate a compressed sensing (CS)-based signal recovery problem for the detection of sparse event in WSNs. Then, from the perspective of energy saving and communication overhead reduction of the WSNs, we develop an optimal sensor selection algorithm by employing a lower-bound of the mean square error (MSE) for the MMSE estimator. To tackle the nonconvex difficulty of the optimum sensor selection problem, a convex relaxation is introduced to achieve a suboptimal solution. Both uncorrelated and correlated noises are considered and a low-complexity realization of the sensor selection algorithm is also suggested. Based on the selected subset of sensors, the sparse Bayesian learning (SBL) is utilized to reconstruct the sparse signal. Simulation results illustrate that our proposed approaches lead to a superior performance over the reference methods in comparison.

Many-Objective Sensor Selection in IoT Systems

The Internet of Things connects physical objects through sensor devices with multiple functionalities. At the planning stage of deploying an IoT system, we are concerned about sensor selection in the IoT system, which allocates predefined IoT services to multiple sensor devices so as to optimize one or more objectives associated with these allocations, under energy and distance constraints. The sensor selection problem that optimizes a utility function in other applications has been shown to be NP-hard, and the number of IoT services concerned is enormous in practice. Hence, it is suitable to apply evolutionary algorithms (EAs) for solving the large-scale problem with multiple objectives. Recently, the paradigm of multiple-objective EAs (which often address only two or three objectives) has advanced to many-objective EAs (which are intended to address four or more objectives that may be in conflict with each other in many cases). Therefore, this article considers many objectives of the sensor selection problem in the IoT system, including optimization of communication energy consumption, energy balancing on all devices, energy harvesting, green concerns, and QoS. The problem is resolved by a tailored many-objective EA based on decomposition to increase computational efficiency and solution quality. By simulation, the proposed EA is shown to be promising through scatter charts and parallel coordinates.

On sensor selection in linked information networks

Sensor networks are often redundant by design in order to achieve reliability in information processing. In many cases, the relationships between the different sensors are known a-priori, and can be represented as virtual linkages among the different sensors. These virtual linkages correspond to an information network of sensors, which provides useful external input to the problem of sensor selection. In this paper, we propose the unique approach of using external linkage information in order to improve the efficiency of very large scale sensor selection. We design efficient theoretical models, including a greedy approximation algorithm and an integer programming formulation for sensor selection. Our greedy selection algorithm provides an approximation bound of 1−1/e, where e is the base of the natural logarithm. We show that our approach is much more effective than baseline sampling strategies. We present experimental results that illustrate the effectiveness and efficiency of our approach.

Sensor selection for Kalman filtering of linear dynamical systems: Complexity, limitations and greedy algorithms

We consider the problem of selecting an optimal set of sensors to estimate the states of linear dynamical systems. Specifically, the goal is to choose (at design-time) a subset of sensors (satisfying certain budget constraints) from a given set in order to minimize the trace of the steady state a priori or a posteriori error covariance produced by a Kalman filter. We show that the a priori and a posteriori error covariance-based sensor selection problems are both NP-hard, even under the additional assumption that the system is stable. We then provide bounds on the worst-case performance of sensor selection algorithms based on the system dynamics, and show that greedy algorithms are optimal for a certain class of systems. However, as a negative result, we show that certain typical objective functions are not submodular or supermodular in general. While this makes it difficult to evaluate the performance of greedy algorithms for sensor selection (outside of certain special cases), we show via simulations that these greedy algorithms perform well in practice.

A Novel Sensor Selection and Power Allocation Algorithm for Multiple-Target Tracking in an LPI Radar Network.

Radar networks are proven to have numerous advantages over traditional monostatic and bistatic radar. With recent developments, radar networks have become an attractive platform due to their low probability of intercept (LPI) performance for target tracking. In this paper, a joint sensor selection and power allocation algorithm for multiple-target tracking in a radar network based on LPI is proposed. It is found that this algorithm can minimize the total transmitted power of a radar network on the basis of a predetermined mutual information (MI) threshold between the target impulse response and the reflected signal. The MI is required by the radar network system to estimate target parameters, and it can be calculated predictively with the estimation of target state. The optimization problem of sensor selection and power allocation, which contains two variables, is non-convex and it can be solved by separating power allocation problem from sensor selection problem. To be specific, the optimization problem of power allocation can be solved by using the bisection method for each sensor selection scheme. Also, the optimization problem of sensor selection can be solved by a lower complexity algorithm based on the allocated powers. According to the simulation results, it can be found that the proposed algorithm can effectively reduce the total transmitted power of a radar network, which can be conducive to improving LPI performance.

Sparse array synthesis for WBAN with minimised side lobe via convex optimisation

This study concerns sensor selection problem in wireless body area network (WBAN), which can reduce the burden of the human body and improve the energy efficiency. The authors highlight the sparse sensor array synthesis algorithm for different shapes of sensor arrays via convex optimisation to solve this problem. For simplicity, one regular spherical sensor array and five regular cuboid sensor arrays are considered to simulate the sensor distribution around the human body. As a comparison, the conventional method with one objective method is used to synthesise the sensor array first. Then the proposed algorithm which includes two objective variables: the l 1-norm of weight vector and the peak side-lobe level is used. Simulations demonstrate that the proposed sparse sensor array synthesis algorithm achieves array sparsity with lower side lobe and more concentrated main lobe when operated in spherical and cuboid sensor array. Hence, the sensor selection problem is achieved by the sparse sensor array synthesis.

Sensor Selection for Target Tracking in Wireless Sensor Networks With Uncertainty

In this paper, we propose a multiobjective optimization framework for the sensor selection problem in uncertain Wireless Sensor Networks (WSNs). The uncertainties of the WSNs result in a set of sensor observations with insufficient information about the target. We propose a novel mutual information upper bound (MIUB) based sensor selection scheme, which has low computational complexity, same as the Fisher information (FI) based sensor selection scheme, and gives estimation performance similar to the mutual information (MI) based sensor selection scheme. Without knowing the number of sensors to be selected a priori, the multiobjective optimization problem (MOP) gives a set of sensor selection strategies that reveal different trade-offs between two conflicting objectives: minimization of the number of selected sensors and minimization of the gap between the performance metric (MIUB and FI) when all the sensors transmit measurements and when only the selected sensors transmit their measurements based on the sensor selection strategy. Illustrative numerical results that provide valuable insights are presented.

Sensor Selection for Estimation with Correlated Measurement Noise

In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime, and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

Sensor Selection for Cooperative Spectrum Sensing in Multiantenna Sensor Networks Based on Convex Optimization and Genetic Algorithm

This letter addresses the sensor selection problem for spectrum sensing in cognitive radio networks. Hereby, an energy-efficient cooperative spectrum sensing is proposed, which is based on sensing node selections in multiantenna structures. In this letter, the sensor selection problem is solved utilizing two methods: convex optimization and genetic algorithm. Simulation results indicate that the convex optimization with cooperative multiple antennas sensing improves the performance of a network in comparison with genetic algorithm while suffers from complexity and implementation costs.

Energy efficient cooperative spectrum sensing in wireless multi-antenna sensor network

This paper will address sensor selection problem for spectrum sensing in a cognitive radio network. The sensor's limited energy is an important issue which has attracted more attention in recent years. An energy efficient cooperative spectrum sensing will hereby be proposed when multi-antenna sensors are used. Two decision-making techniques are utilized for the combination of antennas' signals in each sensor: hard and soft decision-making. OR rule is used for hard decision-making technique while selection combining, equal gain combining and maximum ratio combining (MRC) are used for the soft one. In each combination scheme, the sensor selection is a problem by means of which both the energy consumption is minimized and the detection performance gets satisfied. The problem is solved based on the standard convex optimization method. Simulation results show the achievement of a significant energy saving compared to the networks using single-antenna sensors specifically in low signal to noise ratio state. Among all methods, MRC combining enjoys the least energy consumption, as well; it satisfies the desired detection performance.