带不确定参数和噪声方差的鲁棒观测融合Kalman滤波器

对带不确定参数和噪声方差的多传感器定常系统,引入虚拟白噪声补偿不确定参数,可将其转化为带已知参数和不确定噪声方差系统.应用极大极小鲁棒估值原理和加权最小二乘法,基于带噪声方差保守上界的最坏情形保守系统,提出了鲁棒加权观测融合Kalman滤波器,并证明了它与集中式融合鲁棒Kalman滤波器是等价的,且融合器的鲁棒精度高于每个局部滤波器鲁棒精度.一个Monte-Carlo仿真例子说明了如何寻求不确定参数的鲁棒域和如何搜索保守性较小的虚拟噪声方差上界.     

不确定离散系统具有H∞性能界的鲁棒LQG状态反馈控制

研究了含有范数有界参数不确定线性离散系统具有H∞性能界的鲁棒LQG状态反 馈控制问题,考虑了有限时域时变及无限时域时不变两种情形.所得的控制器对于所有可容 许的参数不确定都能满足给定的H∞性能界,且为最坏情形H∞性能指标提供了一个最优上 界.对于无限时域时不变情形,该控制器还能保证闭环系统渐近稳定.结果仅需求解一含有 一个尺度参数的Riccati方程.     

不确定噪声方差定常系统保性能鲁棒Kalman滤波器

对带不确定噪声方差线性定常系统鲁棒Kalman滤波,提出一般的统一的保性能鲁棒性概念.用Lyapunov方程方法,提出两类保性能极大极小鲁棒稳态Kalman滤波器.一类是寻求不确定噪声方差最大扰动域(鲁棒域),使得对于扰动域内的所有扰动,确保系统滤波精度偏差的最大下界是零,最小上界是所预置的精度偏差指标;另一类是在预置噪声方差有界扰动域内,寻求滤波精度偏差的最大下界和最小上界.通过引入不确定噪声方差扰动的参数化表示,问题转化为相应的非线性与线性最优化问题,可分别用Lagrange乘数法和线性规划(LP)方法求解.应用于跟踪系统的仿真例子验证了所提结果的正确性和有效性.     

离散系统状态和参数鲁棒滤波分离算法

提出了一种离散系统的鲁棒分离滤波方法.为了对状态向量进行较准确估计,将鲁棒滤波器分为:1)零误差状态估计器;2)不确定矩阵估计器;3)鲁棒合成器.零偏差状态估计器是假定系统的不确定部分为零时的状态估计器;其新息作为不确定部分的估计变量,并由此估计系统的不确定部分;最后,根据系统不确定部分估计误差的上下界,用鲁棒合成器对状态向量的估计值进行鲁棒修正.为了在合成器中得到鲁棒滤波的逼近计算式,通过变换状态估计误差的协方差阵,得到了系统矩阵不确定部分的误差上界不等式逼近,并且得到了估计误差协方差阵逆阵的下界不等式逼近,从而给出了鲁棒合成滤波的完整算法.     

线性不确定系统鲁棒滤波器设计

分别研究了一类线性不确定连续和离散系统的鲁棒保成本滤波器的设计问题.采用保 成本滤波器(guaranteed cost filter)的设计思想,用线性矩阵不等式的形式给出鲁棒保成本滤波 器存在的简便检验条件,由LMI的解直接得到滤波器各参数的值.对鲁棒保成本滤波器存在的 系统,进一步优化成本矩阵,获得了最优鲁棒保成本滤波器.最后给出一个仿真实例,结果验证 了方法的有效性.     

具有脉冲模的奇异摄动系统鲁棒稳定分析与仿真研究

本文研究了当摄动参数为零时存在脉冲模的奇异摄动系统的鲁棒稳定性问题，得到了使系统鲁棒稳定的摄动参数上界，给出了一个数值仿真例子。     

带丢失观测和不确定噪声方差系统改进的鲁棒协方差交叉融合稳态Kalman滤波器

对带丢失观测和不确定噪声方差的线性定常多传感器系统,引入虚拟噪声将原系统转化为仅带不确定噪声方差的系统.根据极大极小鲁棒估值原理,用Lyapunov方程方法提出局部鲁棒稳态Kalman滤波器及其实际方差最小上界,并利用保守的局部滤波误差互协方差,提出一种改进的鲁棒协方差交叉(covariance intersection,CI)融合稳态Kalman滤波器及其实际方差最小上界.证明了所提出的鲁棒局部和融合滤波器的鲁棒性,并证明了改进的CI融合器鲁棒精度高于原始CI融合鲁棒精度,且高于每个局部滤波器的鲁棒精度.一个仿真例子验证所提出结果的正确性和有效性.     

基于仿射控制输入的输入状态稳定非线性预测控制

针对有扰动的约束非线性系统,提出了一种基于仿射控制输入的反馈预测控制策略.采用无穷范数定义有限时域代价函数,对其进行极大极小优化得到预测控制律,并应用输入状态稳定分析了闭环系统的鲁棒稳定性,同时还给出了确定容许扰动上界的方法.最后,数值仿真说明本文的预测控制策略是有效的.     

离散不确定系统分布式鲁棒融合滤波器设计

针对一类离散多传感器动态模型的不确定系统,将鲁棒滤波理论与数据融合技术相结合,基于参数依赖Lyapunov函数,研究该离散系统的鲁棒融合滤波器设计问题。在集中式鲁棒融合滤波器的基础上,探讨了分布式加权融合滤波器的设计方法,通过仿真实验比较了鲁棒融合滤波器的性能。结果表明,利用该分布式加权融合算法,不仅对于解决当系统模型中存在参数不确定性时的滤波问题有较好的鲁棒性能和较低的计算量,而且在多传感器系统中对于满足不同精度鲁棒融合滤波器的设计需要具有较大的灵活性。     

线性广义系统的最优和鲁棒满阶平滑器

对于线性离散随机广义系统,利用增广状态方法将平滑器问题转化为增广状态的滤波器问题.基于极大似然线性估计准则,提出了最优的满阶平滑器,其中增广状态滤波器的误差方差阵满足广义Riccati方程.当线性离散广义系统的过程噪声和观测噪声的方差不确定时,基于极大极小鲁棒设计原理和最优满阶平滑算法,得到了鲁棒满阶平滑器.应用动态误差方差分析方法证明了其鲁棒性,即鲁棒平滑误差方差阵存在一个上界方差矩阵.数值仿真例子验证了其有效性和正确性.     

Design and analysis of discrete-time robust Kalman filters

In this paper, the problem of finite and infinite horizon robust Kalman filtering for uncertain discrete-time systems is studied. The system under consideration is subject to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of linear filters having an error variance with an optimized guaranteed upper bound for any allowed uncertainty. A novel technique is developed for robust filter design. This technique gives necessary and sufficient conditions to the design of robust quadratic filters over finite and infinite horizon in terms of a pair of parameterized Riccati equations. Feasibility and convergence properties of the robust quadratic filters are also analyzed.     

Finite‐horizon robust Kalman filtering for uncertain discrete time‐varying systems with state‐delay

A finite‐horizon robust estimator design approach is developed for a class of discrete time‐varying uncertain systems with state‐delay. It extends the Kalman filter to the case in which the considered system is subject to norm‐bounded uncertainties in both state and output matrices. The state and gain matrices of the designed filter are optimized to give a minimal upper bound such that the estimation error variance is guaranteed to lie within a certain bound for all admissible uncertainties. A simulation example is presented to show the effectiveness of the proposed approach by comparing to the traditional Kalman filtering method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

区间系统的离散鲁棒Kalman滤波

着重研究区间系统的鲁棒滤波问题.通过等价变换,将区间系统转换为对应的矩阵 范数不确定系统,并据此导出区间系统的鲁棒滤波算法.该算法为一离散验后(a posteriori) 滤波算法,它能保证区间系统的滤波误差有界.理论分析和实际计算结果表明,本算法能达到 比验前(a priori)滤波小得多的滤波误差的方差上界.     

Robust nonlinear filter for nonlinear systems with multiplicative noise uncertainties,unknown external disturbances,and packet dropouts

This study is concerned with the robust nonlinear filtering problem for nonlinear discrete‐time stochastic system with multiplicative noise uncertainties, unknown external disturbances, and packet dropouts. The focus of this paper is to design a filter with predictor–corrector structure such that the upper bound on the state estimation error variance is minimized in the presence of multiplicative noise, unknown external disturbances, and packet dropouts. Thus, a robust nonlinear filter based on the method to obtain the upper bound on variances of multiplicative noises, unknown disturbances, and packet dropouts is designed. Further stability analysis shows that the proposed filter has robustness against multiplicative noises, unknown external disturbances, and packet dropouts. Simulation results show that the proposed filter is more effective than extended Kalman filter and other robust extended Kalman filter. Copyright © 2017 John Wiley & Sons, Ltd.     

满意滤波在航迹辨识中的应用

利用线性矩阵不等式(LMI,linear matrix inequalities)方法,首先研究了Kalman滤波 的稳态误差方差和滤波增益的解法,并根据满意控制的思想,提出了具有误差方差上界约束的 滤波问题,然后研究了误差方差上界约束下对系统测量噪声具有最大容许强度的满意鲁棒滤 波.本文的研究成果已被应用于某型C3I系统中的航迹辨识.     

Robust Kalman filtering for discrete time-varying uncertain systemswith multiplicative noises

In this paper, a robust finite-horizon Kalman filter is designed for discrete time-varying uncertain systems with both additive and multiplicative noises. The system under consideration is subject to both deterministic and stochastic uncertainties. Sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete Riccati difference equations. A numerical example is given to show the applicability of the presented method     

不确定系统改进的鲁棒协方差交叉融合稳态Kalman预报器

针对带随机参数和噪声方差两者不确定性的线性离散多传感器系统,利用虚拟噪声补偿随机参数不确定性,原系统可转化为仅带不确定噪声方差的系统.根据极大极小鲁棒估值原理,用Lyapunov方程方法提出局部鲁棒稳态Kalman预报器及其误差方差最小上界,并利用保守的局部预报误差互协方差,提出改进的鲁棒协方差交叉（Covariance intersection,CI）融合稳态Kalman预报器及其误差方差最小上界.克服了原始CI融合方法要求假设已知局部估值及它们的保守误差方差的缺点和融合误差方差上界具有较大保守性的缺点.证明了鲁棒局部和融合预报器的鲁棒性,并证明了改进的CI融合器鲁棒精度高于原始CI融合器鲁棒精度,且高于每个局部预报器的鲁棒精度.一个仿真例子验证了所提出结果的正确性和有效性.     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

基于方差配置不确定系统的鲁棒滤波

实际系统普遍存在不确定性,这种不确定性可能导致滤波发散问题.该文对一类时 变不确定系统讨论了一种指定误差方差上限的状态滤波器的设计,该方法采用两个Riccati 方程,其中第一个Riccati方程用以补偿系统的不确定性,第二个Riccati方程用来配置状态 滤波误差的协方差上限.导出了滤波器的存在条件和滤波器的通解,揭示了该滤波器与稳态 Kalman滤波器之间的内在联系.