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.     

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．     

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.     

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.     

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.     

相关观测融合Kalman估值器及其全局最优性

对于带相关观测噪声和带不同观测阵的多传感器线性离散时变随机控制系统, 用加权最小二乘法(WLS)提出了两种加权观测融合Kalman估值器, 它们包括状态滤波、状态预报和状态平滑. 基于信息滤波器形式下的Kalman滤波器, 证明了在相同初值下, 它们在数值上恒等于相应的集中式观测融合Kalman估值器, 因而具有全局最优性. 但是它们可明显减轻计算负担. 数值仿真例子验证了它们在功能上等价于集中式观测融合Kalman估值器.     

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。     

时滞系统的多源数据融合卡尔曼滤波器研究

对于带观测时滞的线性离散时变随机控制优化问题,提出了观测变换方法,把带观测时滞状态空间模型等效地转换为无观测时滞的状态空间模型,接着应用卡尔曼(Kalman)滤波方法,在线性最小方差最优融合准则下,给出按矩阵、按对角阵和按标量加权三种最优信息融合卡尔曼(Kalman)滤波器,可分为局部最优全局次优的.融合器的精度高于每一个局部Kalman估值器的精度.可以减少用增广状态方法计算负担大的缺点.为了计算最优加权,给出了计算局部估计误差互协方差公式.对于带观测时滞的三传感器目标跟踪系统的Monte Carlo仿真例子证明了算法的有效性.     

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.     

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 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.     

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.     

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.