自校正多传感器观测融合Kalman估值器及其收敛性分析

对于带未知噪声方差的多传感器系统,应用加权最小二乘(WLS)法得到了一个加权融合观测方程,且它与状态方程构成一个等价的观测融合系统.应用现代时间序列分析方法,基于观测融合系统的滑动平均(MA)新息模型参数的在线辨识,可在线估计未知噪声方差,进而提出了一种加权观测融合自校正Kalman估值器,可统一处理自校正融合滤波、预报和平滑问题,并用动态误差系统分析方法证明了它的收敛性,即若MA新息模型参数估计是一致的,则它按实现或按概率1收敛到全局最优加权观测融合Kalman估值器,因而具有渐近全局最优性.一个带3传感器跟踪系统的仿真例子说明了其有效性.     

Self-tuning measurement fusion Kalman predictors and their convergence analysis

For multisensor systems with unknown parameters and noise variances, three self-tuning measurement fusion Kalman predictors based on the information matrix equation are presented by substituting the online estimators of unknown parameters and noise variances into the optimal measurement fusion steady-state Kalman predictors. By the dynamic variance error system analysis method, the convergence of the self-tuning information matrix equation is proved. Further, it is proved by the dynamic error system analysis method that the proposed self-tuning measurement fusion Kalman predictors converge to the optimal measurement fusion steady-state Kalman predictors in a realisation, so they have asymptotical global optimality. Compared with the centralised measurement fusion Kalman predictors based on the Riccati equation, they can significantly reduce the computational burden. A simulation example applied to signal processing shows their effectiveness.     

带未知有色观测噪声的自校正融合Kalman滤波器

对于带未知有色观测噪声的多传感器线性离散定常随机系统, 未知模型参数和噪声方差的一致的融合估值器用递推增广最小二乘法(RELS)和求解相关函数方程得到. 将这些估值器代入到最优解耦融合Kalman滤波器中, 得出了自校正解耦融合Kalman滤波器, 并用动态方差误差系统分析(DVESA)和动态误差分析(DESA)方法证明了它收敛于最优解耦融合Kalman滤波器, 因而具有渐近最优性. 一个带3传感器跟踪系统的仿真例子说明了其有效 性.     

WMF self-tuning Kalman estimators for multisensor singular system

For the multisensor linear stochastic singular system with unknown noise variances, the weighted measurement fusion (WMF) self-tuning Kalman estimation problem is solved in this paper. The consistent estimates of these unknown noise variances are obtained based on the correlation method. Applying the WMF method and the singular value decomposition (SVD) method yields the WMF reduced-order subsystems. Based on these consistent estimates of unknown noise variances and the new non-singular systems, the WMF self-tuning Kalman estimators of the state components and white noise deconvolution estimators are presented. Then the WMF self-tuning Kalman estimators of the original state are presented, and their convergence has been proved by dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example of 3-sensors circuits systems verifies the effectiveness, the accuracy relationship and the convergence.     

基于Riccati方程的自校正解耦融合Kalman滤波器

对于带未知噪声方差的多传感器系统,用相关方法给出了噪声方差的在线估值器,进而基于Riccati方程和按分量标量加权最优融合规则,提出了自校正分量解耦信息融合Kalman滤波器.用动态误差系统分析方法证明了自校正融合Kalman滤波器按实现收敛于最优融合Kalman滤波器,因而具有渐近最优性.一个3传感器跟踪系统的仿真例子说明了其有效性.     

自校正对角阵加权信息融合Kalman预报器

For the multisensor systems with unknown noise statistics, using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation models, and based on the solution of the matrix equations for correlation function, estimators of the noise variances are obtained, and under the linear minimum variance optimal information fusion criterion weighted by diagonal matrices, a self-tuning information fusion Kalman predictor is presented, which realizes the self-tuning decoupled fusion Kalman predictors for the state components. Based on the dynamic error system, a new convergence analysis method is presented for self-tuning fuser. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. It is strictly proved that if the parameter estimation of the MA innovation models is consistent, then the self-tuning fusion Kalman predictor will converge to the optimal fusion Kalman predictor in a realization, or with probability one, so that it has asymptotic optimality. It can reduce the computational burden, and is suitable for real time applications. A simulation example for a target tracking system shows its effectiveness.     

含未知参数的自校正融合Kalman滤波器及其收敛性

对于带未知模型参数和噪声方差的多传感器系统,基于分量按标量加权最优融合准则,提出了自校正解耦融合Kalman滤波器,并应用动态误差系统分析(Dynamic error system analysis,DESA)方法证明了它的收敛性.作为在信号处理中的应用,对带有色和白色观测噪声的多传感器多维自回归(Autoregressive,AR)信号,分别提出了AR信号模型参数估计的多维和多重偏差补偿递推最小二乘(Bias compensated recursive least-squares,BCRLS)算法,证明了两种算法的等价性,并且用DESA方法证明了它们的收敛性.在此基础上提出了AR信号的自校正融合Kalman滤波器,它具有渐近最优性.仿真例子说明了其有效性.     

按对角阵加权自校正信息融合Kalman预报器及其收敛性分析

对于带未知噪声统计的多传感器系统，应用现代时间序列分析方法，基于滑动平均(MA)新息模型的在线辨识和相关函数矩阵方程的解，得到了噪声方差估值器，且在按对角阵加权线性最小方差最优信息融合准则下，提出了自校正信息融合Kalman预报器.它实现了状态分量的自校正解耦融合Kalman预报器.基于动态误差系统，提出了自校正融合器的一种新的收敛性分析方法.提出了按实现收敛新概念，它比以概率1收敛弱.严格证明了:假如MA新息模型参数估计是一致的，则自校正融合Kalman预报器将按实现或按概率1收敛到最优融合Kalman预报器，因而它具有渐近最优性.它可减小计算负担，且便于实时应用. 一个3传感器跟踪系统的仿真例子证明了其有效性.     

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.     

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.     

自校正解耦信息融合Wiener状态估值器

对含未知噪声方差阵的多传感器系统,用现代时间序列分析方法.基于滑动平均(MA)新息模型的在线辨识和求解相关函数矩阵方程组,可得到估计噪声方差阵估值器,进而在按分量标量加权线性最小方差最优信息融合则下,提出了自校正解耦信息融合Wiener状态估值器.它的精度比每个局部自校正Wiener状态估值器精度高.它实现了状态分量的解耦局部Wiener估值器和解耦融合Wiener估值器.证明了它的收敛性,即若MA新息模型参数估计是一致的,则它将收敛于噪声统计已知时的最优解耦信息融合Wiener状态估值器,因而它具有渐近最优性.一个带3传感器的目标跟踪系统的仿真例子说明了其有效性.     

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.     

Convergence of self-tuning Riccati equation with correlated noises

For the linear discrete time-invariant stochastic system with correlated noises,and with unknown model parameters and noise statistics,substituting the online consistent estimators of the model paramet...     

自校正信息融合Kalman平滑器

对含未知噪声统计的多传感器系统,用现代时间序列分析方法,基于滑动平均(MA)新息模型的在线辨识和求解相关函数矩阵方程组,得到了噪声统计的在线估值器,进而在按矩阵加权线性最小方差最优信息融合准则下,提出了自校正信息融合Kalman平滑器,提出了一种按实现收敛性新概念,证明了自校正Kalman融合器按实现收敛于最优Kalman融合器,因而它具有渐近最优性．同单传感器自校正Kalman平滑器相比,它可提高平滑精度,一个目标跟踪系统的仿真例子说明了其有效性．     

带未知模型参数和衰减观测率系统自校正分布式融合估计

研究了带未知模型参数和衰减观测率多传感器线性离散随机系统的信息融合估计问题.在模型参数和衰减观测率未知的情形下,应用递推增广最小二乘(Recursive extend least squares,RELS)算法和加权融合估计算法提出了分布式融合未知模型参数辨识器;应用相关函数对描述衰减观测现象的随机变量的数学期望和方差...     

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.

     

Self-tuning decoupled information fusion Wiener state component filters and their convergence

For the multisensor systems with unknown noise variances, using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation models, and based on the solution of the matrix equations for correlation function, the on-line estimators of the noise variances are obtained, and under linear minimum variance optimal information fusion criterion weighted by scalars for state components, a class of self-tuning decoupled fusion Wiener filters is presented. It realizes the self-tuning decoupled local Wiener filters and self-tuning decoupled fused Wiener filters for the state components. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. The dynamic error system analysis (DESA) method is presented, by which the problem of convergence in a realization for self-tuning fusers is transformed into the stability problems of non-homogeneous difference equations, and the decision criterions of the stability are also presented. It is strictly proved that if the parameter estimation of the MA innovation models is consistent and if the measurement process is bounded in a realization or with probability one, then the self-tuning fusers will converge to the optimal fusers in a realization or with probability one, so that they have the asymptotic optimality. They can deal with the systems with the non-stationary or Gaussian measurement processes. They can reduce the computational burden, and are suitable for real time applications. A simulation example for a target tracking system with 3-sensor shows their effectiveness.     

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.     

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 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.