Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems, when the model parameters and the noise variances are unknown, the consistent fused estimators of the model parameters and noise variances are obtained, based on the system identification algorithm, correlation method and least squares fusion criterion. Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter, a self-tuning weighted measurement fusion Kalman filter is presented. Using the dynamic error system analysis (DESA) method, the convergence of the self-tuning weighted measurement fusion Kalman filter is proved, i.e., the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization. Therefore, the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality. One simulation example for a 4-sensor target tracking system verifies its effectiveness.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. For the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises, and with unknown ARMA model parameters and noise statistics, the on-line AR model parameter estimator based on the Recursive Instrumental Variable (RIV) algorithm, the on-line MA model parameter estimator based on Gevers–Wouters algorithm and the on-line noise statistic estimator by using the correlation method are presented. Using the Kalman filtering method, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented based on the self-tuning Riccati equation. It is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steady-state white noise deconvolution estimator in a realization by using the dynamic error system analysis (DESA) method, so that it has the asymptotic global optimality. The simulation example for a 3-sensor system with the Bernoulli–Gaussian input white noise shows its effectiveness.     

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.     

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．     

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...     

快速信息融合Ka lman 滤波器

应用现代时间序列分析方法,在标量加权线性最小方差融合准则下,提出一种多传感器快速信息融合稳态Kalman滤波器.基于ARMA新息模型计算稳态Kalman滤波器增益,提出了计算传感器之间的滤波误差方差阵和协方差阵的Lyapunov方程,它可用迭代法求解,并证明了迭代解的指数收敛性.与基于Riccati方程按矩阵加权的信息融合Kalman滤波器相比,可明显减小计算负担,便于实时应用,可用于设计含未知噪声统计系统的信息融合自校正Kalman滤波器.最后以目标跟踪系统的一个仿真例子说明了其有效性.     

自校正信息融合Wiener预报器及其收敛性

对带相关观测噪声和未知噪声统计的多传感器系统,用相关方法得到噪声统计在线估值器.在按分量标量加权线性最小方差最优信息融合准则下,用现代时间序列分析方法,基于滑动平均(moving average)新息模型的辨识,提出了自校正解耦融合Wiener预报器.用动态误差系统分析(dynamic error system anallysis)方法证明了自校正融合wiener预报器收敛于最优融合Wiener预报器,因而它具有渐近最优性.它的精度比每个局部自校正Wienet预报器精度都高.它的算法简单,便于实时应用.一个目标跟踪系统的仿真例子说明了其有效性.     

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.

     

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.     

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.     

目标跟踪系统自校正解耦融合Wiener平滑器

针对带未知模型参数和噪声的多传感器目标跟踪系统,为了解决信号的平滑问题,分别利用系统辨识及相关方法得到未知模型参数和噪声方差的局部估值,并对这些局部估值求平均值作为它们的融合估值。然后将具有高可靠性的在线融合估值代入到基于现代时间序列的最优解耦融合Wiener平滑器中即可得自校正解耦融合,使自校正融合Wiener平滑器收敛于相应的最优融合Wiener平滑器,并具有渐近最优性。从而证明自校正平滑器能够很好地解决未知模型参数和噪声统计系统的平滑问题。最后利用Matlab软件仿真验证了该自校正解耦融合Wiener平滑器算法的有效性。     

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.