Resource Management for Distributed Estimation via Sparsity Promoting Regularization

Recent advances in wireless communications and electronics have enabled the development of low cost, low power, multifunctional sensor nodes that are small in size and communicate untethered in a sensor network. These sensor nodes can sense, measure, and gather information from the environment and, based on some local processing, they transmit the sensed data to a fusion center that is responsible for making the global inference. Sensor networks are often tasked to perform parameter estimation; example applications include battlefield surveillance, medical monitoring, and navigation. However, under limited resources, such as limited communication bandwidth and sensor battery power, it is important to design an energy efficient estimation architecture. The goal of this thesis is to provide a fundamental understanding and characterization of the optimal tradeoffs between estimation accuracy and resource usage in sensor networks. In the thesis, two basic issues of resource management are studied, sensor selection/scheduling and sensor collaboration for distributed estimation, where the former refers to finding the best subset of sensors to activate for data acquisition in order to minimize the estimation error subject to a constraint on the number of activations, and the latter refers to seeking the optimal inter sensor communication topology and energy allocation scheme for distributed estimation systems. Most research on resource management so far has been based on several key assumptions, a) independence of observation, b) strict resource constraints, and c) absence of inter sensor communication, which lend analytical tractability to the problem but are often found lacking in practice. This thesis introduces novel techniques to relax these assumptions and provide new insights into addressing resource management problems. The thesis analyzes how noise correlation affects solutions of sensor selection problems, and proposes both a convex relaxation approach and a greedy algorithm to find these solutions. Compared to the existing sensor selection approaches that are limited to the case of uncorrelated noise or weakly correlated noise, the methodology proposed in this thesis is valid for any arbitrary noise correlation regime. Moreover, this thesis shows a correspondence between active sensors and the nonzero columns of an estimator gain matrix. Based on this association, a sparsity promoting optimization framework is established, where the desire to reduce the number of selected sensors is characterized by a sparsity promoting penalty term in the objective function. Instead of placing a hard constraint on sensor activations, the promotion of sparsity leads to trade offs between estimation performance and the number of selected sensors. To account for the individual power constraint of each sensor, a novel sparsity promoting penalty function is presented to avoid scenarios in which the same sensors are successively selected. For solving the proposed optimization problem, we employ the alternating direction method of multipliers (ADMM) which allows the optimization problem to be decomposed into subproblems that can be solved analytically to obtain exact solutions. The problem of sensor collaboration arises when inter sensor communication is incorporated in sensor networks, where sensors are allowed to update their measurements by taking a linear combination of the measurements of those they interact with prior to transmission to a fusion center. In this thesis, a sparsity aware optimization framework is presented for the joint design of optimal sensor collaboration and selection schemes, where the cost of sensor collaboration is associated with the number of nonzero entries of a collaboration matrix, and the cost of sensor selection is characterized by the number of nonzero rows of the collaboration matrix. It is shown that a) the presence of sensor collaboration smooths out the observation noise, thereby improving the quality of the signal and eventual estimation performance, and b) there exists a trade off between sensor selection and sensor collaboration. This thesis further addresses the problem of sensor collaboration for the estimation of time varying parameters in dynamic networks that involve, for example, time varying observation gains and channel gains. Impact of parameter correlation and temporal dynamics of sensor networks on estimation performance is illustrated from both theoretical and practical points of view. Last but not least, optimal energy allocation and storage control polices are designed in sensor networks with energy harvesting nodes. We show that the resulting optimization problem can be solved as a special nonconvex problem, where the only source of nonconvexity can be isolated to a constraint that contains the difference of convex functions. This specific problem structure enables the use of a convex concave procedure to obtain a near optimal solution.