Boundedness of the Kalman Filter Revisited

Qinghua Zhang; Liangquan Zhang

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Boundedness of the Kalman Filter Revisited

机译：卡尔曼滤波器的界限重新审视

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The boundedness of the Kalman filter, as the first cornerstone of its stability analysis, has been proved in the classical literature through upper bounds of non-recursive filters in the sense of the trace of the state estimation error covariance. In this paper, an upper bound of the Kalman filter prediction error covariance is established in the sense of matrix positive definiteness, based on a bounded recursive non-optimal filter. The boundedness of the error covariance is a prerequisite for the definition of a Lyapunov function involved in the state estimation error dynamics stability analysis.

机译：作为其稳定性分析的第一个基石的卡尔曼滤波器的界限已经在经典文献中通过在状态估计误差协方差的迹线的痕迹中通过非递归滤波器的上限被证明。在本文中，基于有界递归非最佳滤波器，在矩阵正绝对的意义上建立了卡尔曼滤波预测误差协方差的上限。错误协方差的界限是在状态估计误差动态稳定性分析中涉及的Lyapunov函数定义的先决条件。

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《IFAC PapersOnLine》 |2021年第7期|共5页
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Qinghua Zhang; Liangquan Zhang;
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Kalman filterboundednessstabilityprediction error;

机译：卡尔曼referreferboundednesstystilityPrediction错误;

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专利

1. Kalman Filtering With Intermittent Observations: On the Boundedness of the Expected Error Covariance [J] . Rohr E.R., Marelli D., Fu M. Automatic Control, IEEE Transactions on . 2014,第10期

机译：带有间歇性观察的卡尔曼滤波：关于期望误差协方差的有界性
2. Nonlinear filtering for sequential spacecraft attitude estimation with real data: Cubature Kalman Filter, Unscented Kalman Filter and Extended Kalman Filter [J] . Garcia R. V., Pardal P. C. P. M., Kuga H. K., Advances in space research . 2019,第2期

机译：用于使用实际数据进行连续航天器姿态估计的非线性滤波：Cubature Kalman滤波，Unscented Kalman滤波和Extended Kalman滤波
3. Nonlinear filtering for sequential spacecraft attitude estimation with real data: Cubature Kalman Filter, Unscented Kalman Filter and Extended Kalman Filter [J] . Garcia R. V., Pardal P. C. P. M., Kuga H. K., Journal of neurosurgical sciences . 2019,第2期

机译：具有真实数据的连续航天器姿态估计的非线性滤波：Cubature Kalman滤波器，Unscented Kalman滤波器和扩展卡尔曼滤波器
4. Boundedness of covariance estimates of extended Kalman filtering with directional measurements and linear state dynamics [C] . Sugathadasa, S., Martin, . 2001

机译：具有方向测量和线性状态动力学的扩展卡尔曼滤波协方差估计的有界性
5. Hybrid - Nudging Ensemble Kalman Filter and Ensemble Adjustment Kalman Filter Approach to Subsurface Water Contaminant Transport Modeling. [D] . Hokey, Wisdom Mawuli. 2016

机译：混合-集成整体卡尔曼滤波和整体调整卡尔曼滤波方法在地下水污染物运移建模中的应用。
6. An Improved Interacting Multiple Model Filtering Algorithm Based on the Cubature Kalman Filter for Maneuvering Target Tracking [O] . Wei Zhu, Wei Wang, Gannan Yuan 2016

机译：基于Cubature卡尔曼滤波的机动目标跟踪的交互式多模型滤波改进算法。
7. Comparative Study between the Discrete-Frequency Kalman Filtering and the Discrete-Time Kalman Filtering with Application in Noise Reduction in Speech Signals [O] . Leandro Aureliano da Silva, Gilberto Arantes Carrijo, Eduardo Silva Vasconcelos, 2018

机译：不同频率卡尔曼滤波与分立时Kalman滤波的比较研究，在语音信号中的噪声减少中的应用
8. Nonlinear Filtering, the Link between Kalman and Extended Kalman Filters. [R] . Emara-Shabaik, H. E. 1982

机译：非线性滤波，卡尔曼与扩展卡尔曼滤波器之间的联系。

Boundedness of the Kalman Filter Revisited

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