具有对称性的嵌入式非线性系统的全局最小能量状态估计
Global Minimum Energy State Estimation for Embedded Nonlinear Systems with Symmetry
AI总结：
针对非线性系统状态估计中局部最优与全局稳定难以兼顾的问题，提出利用嵌入坐标和最小能量范式的全局最优观测器，在单位四元数姿态估计中验证了其始终最优且大初始误差下仍可收敛的性能。
摘要：
为某一应用选择非线性状态估计器时，通常需要在局部最优性（如扩展卡尔曼滤波器所提供的）与（准/半）全局渐近稳定性（如基于李雅普诺夫原理的构造性观测器设计所提供的）之间进行权衡。本文针对一类非线性系统，提出了一种兼具全局性与最优性的滤波器设计方法。具体而言，这类系统满足：状态流形可嵌入欧几里得空间，测量函数在嵌入空间中呈线性，且存在同步误差构造。本文利用最小能量滤波器设计范式，借助嵌入坐标精确求解全局最优解，推导得到了一种新型观测器。通过将三维非线性系统嵌入四维欧几里得空间，将该观测器应用于单位四元数姿态估计问题进行了验证。仿真结果表明，状态估计始终保持最优，即便初始误差极大也能收敛。
英文摘要：
Choosing a nonlinear state estimator for an application often involves a trade-off between local optimality (such as provided by an extended Kalman filter) and (almost-/semi-) global asymptotic stability (such as provided by a constructive observer design based on Lyapunov principles). This paper proposes a filter design methodology that is both global and optimal for a class of nonlinear systems. In particular, systems for which there is an embedding of the state-manifold into Euclidean space for which the measurement function is linear in the embedding space and for which there is a synchronous error construction. A novel observer is derived using the minimum energy filter design paradigm and exploiting the embedding coordinates to solve for the globally optimal solution exactly. The observer is demonstrated through an application to the problem of unit quaternion attitude estimation, by embedding the 3-dimensional nonlinear system into a 4-dimensional Euclidean space. Simulation results demonstrate that the state estimate remains optimal for all time and converges even with a very large initial error.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
