按对角阵加权信息融合Kalman滤波器

为了克服按矩阵加权信息融合非稳态Kalman滤波器的在线计算负担大的缺点,和按标量加权融合Kalman滤波器精度较低的缺点,应用现代时间序列分析方法,提出了按对角阵加权的线性最小方差多传感器信息融合稳态Kalman滤波器.它等价于状态分量按标量加权信息融合Kalman滤波器,实现了解耦信息融合Kalman滤波器.它的精度和计算负担介于按矩阵和按标量加权融合器两者之间,且便于实时应用.为了计算最优加权,提出了计算稳态滤波误差方差阵和协方差阵的Lyapunov方程.一个三传感器的雷达跟踪系统的仿真例子说明了其有效性.     

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.     

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．     

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.     

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.     

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.     

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.     

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。     

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.     

带多层融合结构的广义系统 Kalman 融合器

对带多传感器的线性离散随机广义系统, 用奇异值分解将其化为两个降阶耦合子系统, 应用现代时间序列分析方法, 基于自回归滑动平均 (Autoregressive moving average, ARMA) 新息模型和白噪声估计理论, 提出了带三层融合结构的分布式稳态 Kalman 融合器, 它由两个加权融合器和两个复合融合器组成. 第一层给出子系统状态融合器, 实现了每个子系统分量解耦融合; 第二层给出变换后状态融合器, 实现了两个子系统的解耦融合; 第三层给出原始状态融合器, 它可统一处理状态融合滤波、平滑和预报问题. 为计算最优加权阵, 给出了计算局部估计误差互协方差阵公式, 证明了它的精度比每个局部估值器精度高. Monte Carlo 的仿真实例说明了其有效性.     

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.     

Optimal Fusion Reduced-Order Kalman Filters Weighted by Scalars for Stochastic Singular Systems

Based on the optimal fusion algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion reduced-order Kalman filter with scalar weights is presented for discrete-time stochastic singular systems with multiple sensors and correlated noises. It has higher accuracy than any local filter does. Compared with the distributed fusion filter weighted by matrices, it has lower accuracy but has reduced computational burden. Computation formula of cross-covariance matrix of the filtering errors between any two sensors is given. An example with three sensors shows the effectiveness.