在连续离散扩展卡尔曼波器的SPD多元组上基于日志-欧几里德度量的协差传播
Jiaolong Wang1, Chengxi Zhang1, Shunyi Zhao1
1Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, Jiangsu, China.
ISA transactions
|April 27, 2024
概括
本研究为连续离散扩展卡尔曼波器 (CDEKF) 引入了一个Log-Euclidean度量 (LEM),以改进共变性集成. 这种新方法通过考虑对称正确数矩阵的里曼结构来提高非线性系统的估计准确性.
科学领域:
- 控制系统工程 控制系统工程
- 非线性动力学是一种非线性动力学.
- 估计理论 估计理论
背景情况:
- 连续离散扩展卡尔曼波器 (CDEKF) 对于具有混合数据类型的非线性系统至关重要.
- 传统的CDEKF使用欧几里德度量,忽略了共变矩阵的多重结构.
- 这种限制阻碍了复杂动态系统的最佳估计准确性.
研究的目的:
- 为CDEKF使用Log-Euclidean度量 (LEM) 开发一种新的协差整合方案.
- 通过结合里曼几何来解决CDEKF中欧几里德矩阵运算的局限性.
- 为了提高连续动态和离散测量的非线性系统的估计准确性.
主要方法:
- 在对称正定数 (SPD) 矩阵的多重上定义共变量变量.
- 使用Log-Euclidean度量 (LEM) 来传播共变性,以加强整合.
- 实施基于LEM的CDEKF的多重集成方案 (LEM-CDEKF).
主要成果:
- 拟议的LEM-CDEKF有效地整合了SPD多路线上的共变量.
- 这种新方法避免了传统的欧几里德图的固有缺点.
- 与现有方法相比,数值模拟显示出更高的准确性.
结论:
- 基于Log-Euclidean度数的协差整合为CDEKF提供了显著的改进.
- 对于非线性系统,LEM-CDEKF提供了更准确的估计.
- 这种方法在复杂的动态环境中推进了状态估计领域.
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