Robust weighted fusion Kalman estimators for multisensor systems with multiplicative noises and uncertain‐covariances linearly correlated white noises

This paper addresses the design of robust weighted fusion Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include the same multiplicative noises perturbations both on the systems state and measurement output and the uncertain noise variances. The measurement noises and process noise are linearly correlated. By introducing two fictitious noises, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case systems with the conservative upper bounds of the noise variances, the four robust weighted fusion time‐varying Kalman estimators are presented in a unified framework, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, scalar weights, and a modified robust covariance intersection fusion estimator. The robustness of the designed fusion estimators is proved by using the Lyapunov equation approach 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. The corresponding robust local and fused steady‐state Kalman estimators are also presented, a simulation example with application to signal processing to show the effectiveness and correctness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay,missing measurements,and uncertain‐variance multiplicative and additive white noises

The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.     

Robust centralized and integrated covariance intersection fusion Kalman estimators for networked mixed‐uncertain systems

For networked mixed uncertain time‐varying systems with uncertain noise variances, random one‐step measurement delay, state‐dependent and noise‐dependent multiplicative noises, and linearly dependent additive white noises, the robust local, centralized, and distributed fusion estimation problems are addressed. Three new approaches are presented, which include a new augmented state approach with fictitious white noises, an extended Lyapunov equation approach with two Lyapunov equations, and a universal integrated covariance intersection (ICI) fusion approach of integrating the minimax robust local Kalman estimators and their conservative cross‐covariances. They constitute a new important methodology of solving robust fusion estimation problems. Applying them, the local, centralized, and distributed ICI fusion time‐varying and steady‐state robust Kalman estimators (predictor, filter, and smoother) are presented in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, convergence, and accuracy relations are proved. Specially, the proposed ICI fusers improve the robust accuracies of the original covariance intersection fusers, and overcome their drawbacks, such that the local estimators and their conservative variances are assumed to be known, and the conservative cross‐variances are ignored. A simulation example with application to a vehicle suspension system shows the effectiveness of the proposed approaches and results.     

带不确定方差乘性和加性噪声系统鲁棒加权 融合稳态Kalman估值器

本文研究带不确定方差乘性和加性噪声和带状态相依及噪声相依乘性噪声的多传感器系统鲁棒加权融合估计问题.通过引入虚拟噪声补偿乘性噪声的不确定性,将原系统化为带确定参数和不确定加性噪声方差的系统,进而利用Lyapunov方程方法提出在统一框架下的按对角阵加权融合极大极小鲁棒稳态Kalman估值器(预报器、滤波器和平滑器),其中基于预报器设计滤波器和平滑器,并给出每个融合器的实际估值误差方差的最小上界.证明了融合器的鲁棒精度高于每个局部估值器的鲁棒精度.应用于不间断电源(uninterruptible power system,UPS)系统鲁棒融合滤波的仿真例子说明了所提结果的正确性和有效性.     

Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

This paper is concerned with robust weighted state fusion estimation problem for a class of time-varying multisensor networked systems with mixed uncertainties including uncertain-variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, four weighted state fusion robust Kalman estimators (filter, predictor and smoother) are presented in a unified form that the robust filter and smoother are designed based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust local and fused steady-state Kalman estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method. Finally, a simulation example applied to uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results.     

网络化不确定系统集中式融合鲁棒稳态估值器

对于一类在状态转移阵和系统观测阵中带相同的状态依赖乘性噪声、带噪声依赖乘性噪声、一步随机观测滞后、丢包和不确定噪声方差的多传感器网络化系统,文章研究其鲁棒集中式融合稳态滤波问题.应用增广方法将系统转换为带随机参数矩阵、相同过程和观测噪声的集中式融合系统.应用去随机化方法和虚拟噪声技术,系统进一步转化为仅带不确定噪声方差的集中式融合系统.根据极大极小鲁棒估计原理,本文提出了鲁棒集中式融合稳态Kalman估值器(预报器、滤波器和平滑器),证明了所提出的集中式融合估值器的鲁棒性,给出了鲁棒局部与集中式融合估值器之间的精度关系.本文提出了应用于多传感器多通道滑动平均(MA)信号估计的一个实例,给出了相应的鲁棒局部和集中式融合信号估值器.仿真实验验证了所提出方法的有效性和正确性.     

具有噪声方差及多种网络诱导不确定系统鲁棒Kalman估计

对不确定噪声方差乘性噪声,同时带观测缺失、丢包和一步随机观测滞后三种网络诱导特征的混合不确定网络化系统,应用带虚拟噪声的扩维方法和去随机参数方法,将其转化为带不确定虚拟噪声方差的时变系统.基于极大极小鲁棒估计原理,对带虚拟噪声方差保守上界的最坏情形系统,设计了鲁棒时变和稳态Kalman估值器.对所有容许的不确定性,保证实际Kalman估计误差方差有最小上界.应用扩展的Lyapunov方程方法和矩阵分解方法证明了所设计估值器的鲁棒性.证明了实际和保守估值器的精度关系,以及时变和稳态估值器间的按实现收敛性.应用于F-404航空发动机系统的仿真验证了所提出结果的正确性和有效性.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

Information fusion robust guaranteed cost Kalman estimators with uncertain noise variances and missing measurements

ABSTRACT

For multisensor systems with uncertain noise variances and missing measurements, it can be converted into one only with uncertain noise variances by introducing fictitious measurement white noises. According to the minimax robust estimation principle and parameterisation representation of perturbances of uncertain noise variances, based on the worst-case system with conservative upper bounds of uncertain noise variances, the two classes of guaranteed cost robust weighted fusion Kalman estimators with matrix weights, diagonal matrix weights, scalar weights, and covariance intersection fusion matrix weights are presented. One class is the construction of a maximal perturbance region of uncertain noise variances, in which for all admissible perturbances, the accuracy deviations are guaranteed to remain within the prescribed range. The other class is the finding of minimal upper bound and maximal lower bound of accuracy deviations over the given perturbance region of uncertain noise variances. Two problems can be converted into the optimisation problems with constraints. Their optimal analytical solutions can simply be found respectively by the Lagrange multiplier method and the linear programme method. The guaranteed cost robustness is proved by the Lyapunov equation approach. A simulation example applied to the mass-spring system is provided to demonstrate the correctness and effectiveness of the proposed results.     

不确定多传感器系统鲁棒观测融合Kalman 预报器

对于带不确定模型参数和噪声方差的线性离散时不变多传感器系统, 用虚拟噪声补偿不确定参数, 系统转化为仅带噪声方差不确定性的多传感器系统. 用加权最小二乘法和极大极小鲁棒估计准则, 基于带噪声方差保守上界的最坏情形保守系统, 提出一种鲁棒加权观测融合稳态Kalman 预报器, 并应用Lyapunov 方程方法证明了它的鲁棒性, 同时给出了与鲁棒局部和集中式融合Kalman 预报器的精度比较. 最后通过一个仿真例子说明了如何搜索参数扰动的鲁棒域, 并验证了所提出的理论结果的正确性和有效性.

     

带不确定协方差线性相关白噪声系统改进的鲁棒协方差交叉融合稳态Kalman 估值器

对于带有不确定协方差线性相关白噪声的多传感器系统, 利用Lyapunov 方程提出设计协方差交叉(CI) 融合极大极小鲁棒Kalman 估值器(预报器、滤波器、平滑器) 的一种统一方法. 利用保守的局部估值误差互协方差, 提出改进的CI 融合鲁棒稳态Kalman 估值器及其实际估值误差方差最小上界, 克服了用原始CI 融合方法给出的上界具有较大保守性的缺点, 改善了原始CI 融合器鲁棒精度. 跟踪系统的仿真例子验证了所提出方法的正确性和有效性.

     

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.     

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 weighted fusion Kalman predictors with uncertain noise variances

In this paper, the problem of designing weighted fusion robust time-varying Kalman predictors is considered for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) rule, based on the worst-case conservative system with the conservative upper bounds of noise variances, the local and five weighted fused robust time-varying Kalman predictors are designed, which include a robust weighted measurement fuser, three robust weighted state fusers, and a robust covariance intersection (CI) fuser. Their actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equation approach. The concept of the robust accuracy is presented, and the robust accuracy relations are proved. The corresponding steady-state robust local and fused Kalman predictors are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman predictors is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. Simulation results show the effectiveness and correctness of the proposed results.     

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.     

带观测滞后和不确定噪声方差的多智能体传感网络鲁棒序贯协方差交叉融合Kalman滤波（英文）

This paper deals with the problem of designing robust sequential covariance intersection(SCI) fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances. The sensor network is partitioned into clusters by the nearest neighbor rule. Using the minimax robust estimation principle, based on the worst-case conservative sensor network system with conservative upper bounds of noise variances, and applying the unbiased linear minimum variance(ULMV) optimal estimation rule, we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources, and guarantee that the actual filtering error variances have a less-conservative upper-bound. A Lyapunov equation method for robustness analysis is proposed, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented and the robust accuracy relations of the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter. A simulation example for a tracking system verifies the robustness and robust accuracy relations.     

带观测滞后和不确定噪声方差的多智能体传感网络鲁棒序贯协方差交叉融合Kalman滤波

针对带观测滞后和不确定噪声方差的分簇多智能体传感网络系统,研究鲁棒序贯协方差交叉融合Kalman滤波器的设计问题.应用最邻近法则,传感网络被分成簇.应用极大极小鲁棒估计原理,基于带噪声方差最差保守上界的最差保守传感网络系统,提出了两级序贯协方差交叉(SCI)融合鲁棒稳态Kalman滤波器,可减小通信和计算负担并节省能量,且保证实际滤波误差方差有一个最小保守上界.一种Lyapunov方程方法被提出用于证明局部和融合滤波器的鲁棒性.提出了鲁棒精度的概念且证明了局部和融合鲁棒Kalman滤波器的鲁棒精度关系.证明全局SCI融合器的鲁棒精度高于每簇SCI融合器的精度且两者的鲁棒精度都高于每个局部鲁棒滤波器的精度.一个跟踪系统的仿真例子证明了鲁棒性和鲁棒精度关系.     

带不确定噪声方差保性能鲁棒集中式融合Kalman 预报器

对于带不确定噪声方差的多传感器系统, 基于极大极小鲁棒估计原理, 提出保证估计性能的集中式融合鲁棒稳态Kalman 预报器. 对于预置的估计精度偏差指标, 利用Lagrange 乘数法求得相应噪声方差的最大扰动域, 使该域中所有可容许的噪声扰动, 其实际精度对鲁棒精度的偏差被保证在预置范围内, 并给出精度偏差的最大下界和最小上界. 应用Lyapunov 方程方法证明了保证估计性能能够被满足. 仿真分析表明了所得结果的正确性和有效性.

     

Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises

In this paper, the problem of distributed weighted robust Kalman filter fusion is studied for a class of uncertain systems with autocorrelated and cross-correlated noises. The system under consideration is subject to stochastic uncertainties or multiplicative noises. The process noise is assumed to be one-step autocorrelated. For each subsystem, the measurement noise is one-step autocorrelated, and the process noise and the measurement noise are two-step cross-correlated. An optimal robust Kalman-type recursive filter is first designed for each subsystem. Then, based on the newly obtained optimal robust Kalman-type recursive filter, a distributed weighted robust Kalman filter fusion algorithm is derived for uncertain systems with multiple sensors. The distributed fusion algorithm involves a recursive computation of the filtering error cross-covariance matrix between any two subsystems. Compared with the centralized Kalman filter, the distributed weighted robust Kalman filter developed in this paper has stronger fault-tolerance ability. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.