Quaternion-Valued Distributed Filtering and Control

This article presents a unified framework for filtering and control of quaternion-valued state vector processes through multiagent 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 article 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 essentially extends the duality between Kalman filtering and linear quadrature regulators to the quaternion domain and distributed setting. The theoretical concepts in this article are verified via simulations.