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Robust integrated covariance intersection fusion Kalman estimators for networked mixed uncertain time-varying systems
IMA Journal of Mathematical Control and Information ( IF 1.5 ) Pub Date : 2020-05-13 , DOI: 10.1093/imamci/dnaa009
Yuan Gao 1 , Zili Deng 1
Affiliation  

Abstract
For the multisensor time-varying networked mixed uncertain systems with random one-step sensor delays and uncertain-variance multiplicative and linearly dependent additive white noises, a new augmented state method with fictitious noises is presented, by which the original system is transformed into a standard system without delays and with uncertain-variance fictitious white noises. According to the minimax robust estimation principle and the Kalman filtering theory, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the local and integrated covariance intersection (ICI) fused robust time-varying Kalman estimators (filter, predictor and smoother) are presented respectively in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their robustness is proved by the extended Lyapunov equation method, and their accuracy relations are compared based on the traces of the variance matrices and the covariance ellipsoids, respectively. Specially, a universal ICI fusion robust Kalman filtering method of integrating the local robust estimators and their conservative cross-covariances is presented. It overcomes the drawbacks of the original covariance intersection (CI) fusion method and improves robust accuracy of the original CI fuser. A simulation example applied to two-mass spring system shows the effectiveness of the proposed methods and results.


中文翻译:

网络混合不确定时变系统的鲁棒积分协方差相交融合卡尔曼估计

摘要
针对多传感器时变网络混合不确定系统,该系统具有随机单步传感器延迟,不确定方差可乘和线性相关的加性白噪声,提出了一种新的具有虚拟噪声的增强态方法,将原始系统转化为标准系统没有延迟,并且具有不确定性的虚拟白噪声。根据minimax鲁棒估计原理和Kalman滤波理论,基于具有不确定噪声方差的保守上限的最坏情况系统,局部和积分协方差交点(ICI)融合了鲁棒时变Kalman估计器(滤波器,预测器和平滑器)分别以这样一种方式表示:确保它们的实际估计误差方差对于所有允许的不确定性都具有相应的最小上限。通过扩展的Lyapunov方程方法证明了它们的鲁棒性,并分别基于方差矩阵和协方差椭球的轨迹比较了它们的精度关系。特别地,提出了一种集成局部鲁棒估计量及其保守互协方差的通用ICI融合鲁棒卡尔曼滤波方法。它克服了原始协方差相交(CI)融合方法的缺点,并提高了原始CI热熔器的鲁棒性。应用于两质量弹簧系统的仿真例子表明了所提出方法和结果的有效性。通过扩展的Lyapunov方程方法证明了它们的鲁棒性,并分别基于方差矩阵和协方差椭球的轨迹比较了它们的精度关系。特别地,提出了一种集成局部鲁棒估计量及其保守互协方差的通用ICI融合鲁棒卡尔曼滤波方法。它克服了原始协方差相交(CI)融合方法的缺点,并提高了原始CI热熔器的鲁棒性。应用于两质量弹簧系统的仿真例子表明了所提方法和结果的有效性。通过扩展的Lyapunov方程方法证明了它们的鲁棒性,并分别基于方差矩阵和协方差椭球的轨迹比较了它们的精度关系。特别地,提出了一种集成局部鲁棒估计量及其保守互协方差的通用ICI融合鲁棒卡尔曼滤波方法。它克服了原始协方差相交(CI)融合方法的缺点,并提高了原始CI热熔器的鲁棒性。应用于两质量弹簧系统的仿真例子表明了所提出方法和结果的有效性。提出了一种集成局部鲁棒估计量及其保守互协方差的通用ICI融合鲁棒卡尔曼滤波方法。它克服了原始协方差相交(CI)融合方法的缺点,并提高了原始CI热熔器的鲁棒性。应用于两质量弹簧系统的仿真例子表明了所提方法和结果的有效性。提出了一种集成局部鲁棒估计量及其保守互协方差的通用ICI融合鲁棒卡尔曼滤波方法。它克服了原始协方差相交(CI)融合方法的缺点,并提高了原始CI热熔器的鲁棒性。应用于两质量弹簧系统的仿真例子表明了所提方法和结果的有效性。
更新日期:2020-05-13
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