非线性卡尔曼滤波器的非线性卡尔曼滤波器设计指南
Design Guidelines for Nonlinear Kalman Filters via Covariance Compensation
AI总结：
本文提出了一种理论框架，通过协方差补偿概念，为非线性卡尔曼滤波器的设计提供了三个指导原则，以提高估计精度。
摘要：
非线性卡尔曼滤波器（KF）的非线性扩展，如扩展卡尔曼滤波器（EKF）和无迹卡尔曼滤波器（UKF），是复杂动态系统状态估计中不可或缺的工具，但非线性KF提供鲁棒和准确估计的条件仍不明确。本文提出了一种理论框架，识别某些非线性KF成功和失败的原因，并建立其改进的指南。框架的核心是协方差补偿的概念：非线性KF预测的协方差与EKF协方差之间的偏差。通过这一定义和详细理论分析，我们推导出三个非线性KF的设计指南：（i）对正交变换的不变性；（ii）在EKF基准之上足够的协方差补偿；（iii）选择补偿幅度以有利于低估信心。理论分析和实证验证证实，遵循这些原则显著提高估计精度，而文献中常用的固定参数选择往往不优。本文的所有定理的代码和证明可在https://github.com/Shida-Jiang/Guidelines-for-Nonlinear-Kalman-Filters获取。
英文摘要：
Nonlinear extensions of the Kalman filter (KF), such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are indispensable for state estimation in complex dynamical systems, yet the conditions for a nonlinear KF to provide robust and accurate estimations remain poorly understood. This work proposes a theoretical framework that identifies the causes of failure and success in certain nonlinear KFs and establishes guidelines for their improvement. Central to our framework is the concept of covariance compensation: the deviation between the covariance predicted by a nonlinear KF and that of the EKF. With this definition and detailed theoretical analysis, we derive three design guidelines for nonlinear KFs: (i) invariance under orthogonal transformations, (ii) sufficient covariance compensation beyond the EKF baseline, and (iii) selection of compensation magnitude that favors underconfidence. Both theoretical analysis and empirical validation confirm that adherence to these principles significantly improves estimation accuracy, whereas fixed parameter choices commonly adopted in the literature are often suboptimal. The codes and the proofs for all the theorems in this paper are available at https://github.com/Shida-Jiang/Guidelines-for-Nonlinear-Kalman-Filters.
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。
