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.

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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 αstable signals via multi-agent networks is derived. This not only provides an approximation of the formulated optimal solution, but also a cost-effective algorithm which scales with the size of the network. Moreover, performance of the derived algorithm is analyzed and convergence conditions are established.Index Terms-Sensor networks, distributed adaptive filtering, consensus fusion, fractional differential, α-stable random signals.

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The multi-dimensional nature of quaternions allows for the full characterization of three-phase power systems. This is achieved through the use of quaternions to provide a unified framework for incorporating voltage measurements from all the phases of a three-phase system and then employing the recently introduced H R-calculus to derive a state space estimator based on the quaternion extended Kalman filter (QEKF). The components of the state space vector are designed such that they can be deployed for adaptive estimation of the system phasors. Finally, the proposed algorithm is validated through simulations using both synthetic and real-world data, which indicate that the developed quaternion frequency estimator can outperform its complex-valued counterparts.Index Terms-Three-phase power systems, frequency estimation, smart grid, quaternion-valued signal processing.