In this thesis, we consider the problem of decentralized estimation under communication constraints in the context of Collaborative Signal and Information Processing. Motivated by sensor network applications, a high volume of data collected at distinct locations and possibly in diverse modalities together with the spatially distributed nature and the resource limitations of the underlying system are of concern. Designing processing schemes which match the constraints imposed by the system while providing a reasonable accuracy has been a major challenge in which we are particularly interested in the tradeoff between the estimation performance and the utilization of communications subject to energy and bandwidth constraints. One remarkable approach for decentralized inference in sensor networks is to exploit graphical models together with message passing algorithms. In this framework, after the so-called information graph of the problem is constructed, it is mapped onto the underlying network structure which is responsible for delivering the messages in accordance with the schedule of the inference algorithm. However it is challenging to provide a design perspective that addresses the tradeoff between the estimation accuracy and the cost of communications. Another approach has been performing the estimation at a fusion center based on the quantized information provided by the peripherals in which the fusion and quantization rules are sought while taking a restricted set of the communication constraints into account. We consider two classes of in-network processing strategies which cover a broad range of constraints and yield tractable Bayesian risks that capture the cost of communications as well as the penalty for estimation errors. A rigorous design setting is obtained in the form of a constrained optimization problem utilizing the Bayesian risks. These processing schemes have been previously studied together with the structures that the solutions exhibit in the context of decentralized detection in which a decision out of finitely many choices is made. We adopt this framework for the estimation problem. However, for the case, computationally infeasible solutions arise that involve integral operators that are impossible to evaluate exactly in general. In order not to compromise the fidelity of the model we develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in-network processing strategies and the solution schemes to the design problem. Doing that, we can produce approximating strategies for decentralized estimation networks under communication constraints captured by the framework including the cost. The proposed Monte Carlo optimization procedures operate in a scalable and efficient manner and can produce results for any family of distributions of concern provided that samples can be produced from the marginals. In addition, this approach enables a quantification of the tradeoff between the estimation accuracy and the cost of communications through a parameterized Bayesian risk.

This dissertation lays out a multi-static radar system with mobile receivers. The transmitter is at a known location emitting a radar signal that bounces off a target. The echo is received by a team of UAVs that are capable of estimating both time-delay and Doppler from the received signal. Several methods for controlling the movement of mobile sensor platforms are presented to improve target tracking performance. Two optimization criteria are derived for the problem, both of which require some type of search procedure to find the desired solution. Simulations are used to show the benefit of using closed-loop sensor control for the special case of an EKF tracking filter. In addition, a simpler closed-form approach based on one of the algorithms is also presented and is shown to have performance similar to that obtained using the optimal algorithms. To decentralize the estimation in the UAV network, an information consensus filter (ICF) is presented. In the ICF each agent maintains a local estimate, which is shown to be unbiased and conservative with respect to the local covariance matrix estimate. The ICF does not take into account unknown track-to-track correlation that occurs when local independent estimates pass through a common process model. However, it does eliminate the redundancy incurred when communicating information through general network topologies, including graphs containing loops. In the ICF a discrete-time consensus filter is used to handle the communication of information between nodes (UAVs) in the network. Communication is local in that each agent can only communicate with local neighbors and not the entire network. A second-order discrete-time consensus protocol is developed. Necessary and sufficient conditions are given that ensure the team of agents achieves consensus using the second-order protocol. Using insights from the analysis of the ICF an extension is made by adding an observation buffer to the ICF. The new filter is called the information consensus filter with an observation buffer (ICFOB). The track-to-track correlation occurring from independent estimates passing through a common process model does not affect the ICFOB as it does other decentralized estimation methods. The ICFOB is shown to be equivalent to a centralized filter that has access to every measurement in a network. There are two caveats to this equivalency. First, at any point in time, the prior ICFOB estimate is equal to the prior centralized filter estimate found by fusing the observations that are taken before those stored in the buffer. The a posteriori estimates using observations in the buffer are not equal to estimates from the centralized filter since the agents have not finished disseminating those observations throughout the sensor network. Second, the ICFOB needs to know the number of active sensors in the network. The number of sensors is global information; therefore, the ICFOB is not fully decentralized. If the number of sensors is not known, the local estimates are conservative.