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.

中文翻译：

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四元值分布式滤波和控制

本文提出了一个统一的框架，用于通过多代理网络系统对四元数值状态向量过程进行过滤和控制。为了实现这一目标，我们重新审视了传感器网络中的过滤问题，开发了一种用于过滤/跟踪四元数值状态向量过程的分布式卡尔曼滤波算法。分布式四元数卡尔曼滤波器被制定为以允许每个代理保留卡尔曼样式过滤操作和状态向量的中间估计的方式反映最佳集中式方法的操作。本文包括对已开发的分布式四元数卡尔曼滤波算法的综合性能分析，得出二阶误差矩的闭式表达式。更重要的是，由于融合了协方差信息的综合框架并借鉴了所进行的性能分析中的概念，在开发的分布式卡尔曼滤波器和分散控制之间建立了对偶性。这实质上将卡尔曼滤波和线性正交调节器之间的二元性扩展到四元数域和分布式设置。本文中的理论概念通过仿真得到验证。