This work presents a unified framework for distributed filtering and control of state-space processes. To this end, a distributed Kalman filtering algorithm is developed via decomposition of the optimal centralized Kalman filtering operations. This decomposition is orchestrated in a fashion so that each agent retains a Kalman style filtering operation and an estimate of the state vector. In this setting, the agents mirror the operations of the centralized Kalman filter in a distributed fashion through embedded average consensus fusion of local state vector estimates and their associated covariance information. For rigor, closed-form expressions for the mean and mean square error performance of the developed distributed Kalman filter are derived. More importantly, in contrast to current approaches, due to the comprehensive framework for fusion of the covariance information, a duality between the developed distributed Kalman filter and decentralized control is established. Thus, resulting in an effective and all inclusive distributed framework for filtering and control of state-space processes over a network of agents. The introduced theoretical concepts are validated using simulations that indicate a precise match between simulation results and the theoretical analysis. In addition, simulations indicate that performance levels comparable to that of the optimal centralized approaches are attainable.

This work presents a unified framework for filtering and control of quaternion-valued state vector processes through multi-agent networked systems. To achieve this goal, the filtering problem in sensor networks is revisited, where a distributed Kalman filtering algorithm for filtering/tracking quaternion-valued state vector processes is developed. The distributed quaternion Kalman filter is formulated to mirror the operations of an optimal centralized approach in a fashion that will allow each agent to retain a Kalman style filtering operation and an intermediate estimate of the state vector. The work includes a comprehensive performance analysis of the developed distributed quaternion Kalman filtering algorithm, resulting in a closed- form expression for the second-order error moment. More importantly, due to the comprehensive framework for fusion of the covariance information and drawing upon concepts from the conducted performance analysis, a duality between the developed distributed Kalman filter and decentralized control is established.

This work revisits the problem of distributed adaptive filtering in multi-agent sensor networks. In contrast to classical approaches, the formulation relaxes the Gaussian assumption on the signal and noise to the generalized setting of $\alpha$ -stable distributions that do not possess second- and higher-order statistical moments. Most importantly, the considered scenario allows for different characteristic exponents throughout the network. Drawing upon ideas from correntropy-type local similarity measures and fractional-order calculus, a novel class of distributed fractional-order correntropy adaptive filters, that are robust against the jittery behavior of $\alpha$ -stable signals, is derived and their convergence criterion is established. The effectiveness of the proposed algorithms, as compared to existing distributed adaptive filtering techniques, is demonstrated via simulation examples.

Recent advances in sensor and communication technologies have made the deployment of sensor networks in a variety of roles feasible, including smart grid management applications and collaborative target tracking solutions. While most research in distributed adaptive signal processing is conducted in the real and complex domains, inherently in many real-world applications the data sources are three-dimensional. This scenario is ideally suited for quaternions in terms of both convenience of representation and mathematical tractability. In this paper, we expand the concept of distributed Kalman filtering to the quaternion domain in order to develop a robust distributed quaternion Kalman filtering algorithm for data fusion over sensor networks dealing with three-dimensional data. For rigor, the mean and mean square behavior of the algorithm are analyzed. Finally, the developed algorithm is used to estimate the nominal system frequency in power distribution networks and for collaborative target tracking applications.

A cost-effective framework for distributed adaptive filtering of α-stable signals over sensor networks is proposed. First, the filtering paradigm of α-stable signals through multiple observations made over a network of sensors is revisited and an optimal solution is formulated. Then, an adaptive gradient descent based algorithm for distributed real-time filtering of α-stable signals via multiagent networks is derived. This not only provides an approximation of the formulated optimal solution, but also a cost-effective algorithm that scales with the size of the network. Moreover, performance of the derived algorithm is analyzed and convergence conditions are established.

Distributed Kalman filtering techniques enable agents of a multiagent network to enhance their ability to track a system and learn from local cooperation with neighbors. Enabling this cooperation, however, requires agents to share information, which raises the question of privacy. This paper proposes a privacy-preserving distributed Kalman filter (PP-DKF) that protects local information of agents by restricting and obfuscating the information exchanged. The derived PP-DKF embeds two state-of-the-art average consensus techniques that guarantee agent privacy. The resulting PP-DKF utilizes noise injection-based and decomposition-based privacy-preserving techniques to implement a robust distributed Kalman filtering solution against perturbation. We characterize the performance and convergence of the proposed PP-DKF and demonstrate its robustness against the injected noise variance. We also assess the privacy-preserving properties of the proposed algorithm for two types of adversaries, namely, an external eavesdropper and an honest-but-curious (HBC) agent, by providing bounds on the privacy leakage for both adversaries. Finally, several simulation examples illustrate that the proposed PP-DKF achieves better performance and higher privacy levels than the distributed Kalman filtering solutions employing contemporary privacy-preserving techniques.