Engin Masazade

A Multiobjective Optimization Approach to Obtain Decision Thresholds for Distributed Detection in Wireless Sensor Networks

For distributed detection in a wireless sensor network, sensors arrive at decisions about a specific event that are then sent to a central fusion center that makes global inference about the event. For such systems, the determination of the decision thresholds for local sensors is an essential task. In this paper, we study the distributed detection problem and evaluate the sensor thresholds by formulating and solving a multiobjective optimization problem, where the objectives are to minimize the probability of error and the total energy consumption of the network. The problem is investigated and solved for two types of fusion schemes: 1) parallel decision fusion and 2) serial decision fusion. The Pareto optimal solutions are obtained using two different multiobjective optimization techniques. The normal boundary intersection (NBI) method converts the multiobjective problem into a number of single objective-constrained subproblems, where each subproblem can be solved with appropriate optimization methods and nondominating sorting genetic algorithm-II (NSGA-II), which is a multiobjective evolutionary algorithm. In our simulations, NBI yielded better and evenly distributed Pareto optimal solutions in a shorter time as compared with NSGA-II. The simulation results show that, instead of only minimizing the probability of error, multiobjective optimization provides a number of design alternatives, which achieve significant energy savings at the cost of slightly increasing the best achievable decision error probability. The simulation results also show that the parallel fusion model achieves better error probability, but the serial fusion model is more efficient in terms of energy consumption.

Sparsity-Promoting Extended Kalman Filtering for Target Tracking in Wireless Sensor Networks

In this letter, we study the problem of target tracking based on energy readings of sensors. We minimize the estimation error by using an extended Kalman filter (EKF). The Kalman gain matrix is obtained as the solution to an optimization problem in which a sparsity-promoting penalty function is added to the objective. The added term penalizes the number of nonzero columns of the Kalman gain matrix, which corresponds to the number of active sensors. By using a sparse Kalman gain matrix only a few sensors send their measurements to the fusion center, thereby saving energy. Simulation results show that an EKF with a sparse Kalman gain matrix can achieve tracking performance that is very close to that of the classical EKF, where all sensors transmit to the fusion center.

Optimal Periodic Sensor Scheduling in Networks of Dynamical Systems

We consider the problem of finding optimal time-periodic sensor schedules for estimating the state of discrete-time dynamical systems. We assume that multiple sensors have been deployed and that the sensors are subject to resource constraints, which limits the number of times each can be activated over one period of the periodic schedule. We seek an algorithm that strikes a balance between estimation accuracy and total sensor activations over one period. We make a correspondence between active sensors and the nonzero columns of the estimator gain. We formulate an optimization problem in which we minimize the trace of the error covariance with respect to the estimator gain while simultaneously penalizing the number of nonzero columns of the estimator gain. This optimization problem is combinatorial in nature, and we employ the alternating direction method of multipliers (ADMM) to find its locally optimal solutions. Numerical results and comparisons with other sensor scheduling algorithms in the literature are provided to illustrate the effectiveness of our proposed method.

Dynamic Bit Allocation for Object Tracking in Wireless Sensor Networks

In this paper, we study the target tracking problem in wireless sensor networks (WSNs) using quantized sensor measurements where the total number of bits that can be transmitted from sensors to the fusion center is limited. At each time step of tracking, a total of R available bits need to be distributed among the N sensors in the WSN for the next time step. The optimal solution for the bit allocation problem can be obtained by using a combinatorial search which may become computationally prohibitive for large N and R. Therefore, we develop two new suboptimal bit allocation algorithms which are based on convex optimization and approximate dynamic programming (A-DP). We compare the mean squared error (MSE) and computational complexity performances of convex optimization and A-DP with other existing suboptimal bit allocation schemes based on generalized Breiman, Friedman, Olshen, and Stone (GBFOS) algorithm and greedy search. Simulation results show that, A-DP, convex optimization and GBFOS yield similar MSE performance, which is very close to that based on the optimal exhaustive search approach and they outperform greedy search and nearest neighbor based bit allocation approaches significantly. Computationally, A-DP is more efficient than the bit allocation schemes based on convex optimization and GBFOS, especially for a large sensor network.

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.

Energy-Aware Sensor Selection in Field Reconstruction

In this letter, a new sparsity-promoting penalty function is introduced for sensor selection problems in field reconstruction, which has the property of avoiding scenarios where the same sensors are successively selected. Using a reweighted ℓ1 relaxation of the ℓ0 norm, the sensor selection problem is reformulated as a convex quadratic program. In order to handle large-scale problems, we also present two fast algorithms: accelerated proximal gradient method and alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approaches.

Sparsity-aware field estimation via ordinary Kriging

In this paper, we consider the problem of estimating a spatially varying field in a wireless sensor network, where resource constraints limit the number of sensors selected in the network that provide their measurements for field estimation. Based on a one-to-one correspondence between the selected sensors and the nonzero elements of Kriging weights, we propose a sparsity-promoting ordinary Kriging approach where we minimize the Kriging error variance while penalizing the number of nonzero Kriging weights. This yields a combinatorial optimization problem, which is intractable in general. To solve the proposed non-convex optimization problem, we employ the alternating direction method of multipliers (ADMM) and the reweighted ℓ1 minimization method, respectively. Numerical results are provided to illustrate the effectiveness of our proposed approaches that provide a balance between the estimation accuracy and the number of selected sensors.

An approximate dynamic programming based non-myopic sensor selection method for target tracking

In this paper, we study the non-myopic sensor selection problem for target tracking in wireless sensor networks based on quantized sensor data. Using the conditional posterior Cramér-Rao lower bound (C-PCRLB) as a sensor selection metric, we formulate and solve a non-myopic sensor selection problem using an approximate dynamic programming (A-DP) algorithm. Given a constraint on the total number of selected sensors allowed while observing the target over a time window, simulation results show that the proposed non-myopic sensor selection scheme based on A-DP is computationally very efficient and yields better tracking performance than the myopic sensor selection scheme.

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 a low computational complexity, same as the Fisher information (FI)-based sensor selection scheme, and gives an estimation performance similar to the mutual information-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 tradeoffs 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.

Adaptive non-myopic quantizer design for target tracking in wireless sensor networks

In this paper, we investigate the problem of non-myopic (multi-step ahead) quantizer design for target tracking using a wireless sensor network. Adopting the alternative conditional posterior Cramér-Rao lower bound (A-CPCRLB) as the optimization metric, we theoretically show that this problem can be temporally decomposed over a certain time window. Based on sequential Monte-Carlo methods for tracking, i.e., particle filters, we design the local quantizer adaptively by solving a particle-based non-linear optimization problem which is well suited for the use of interior-point algorithm and easily embedded in the filtering process. Simulation results are provided to illustrate the effectiveness of our proposed approach.