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.     

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.     

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.     

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.     

带有色观测噪声的广义系统Kalman滤波器

对于带自回归滑动平均(ARMA)有色观测噪声的多传感器为广义离散随机线性系统,应用奇异值分解,将其变换为等价的两个降阶多传感器子系统,提出了广义系统多传感器信息融合状态滤波问题。为了提高精度,采用Kalman滤波方法,在线性最小方差按块对角阵最优加权融合准则下,给出了按矩阵加权解耦的分布式Kalman滤波器,可减少计算负担和改善局部滤波精度。为了计算最优加权,提出了局部滤波误差协方差阵的计算公式。一个Monte Carlo仿真例子说明了方法的有效性。     

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.     

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.     

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...     

广义系统信息融合稳态与自校正满阶Kalman滤波器

基于线性最小方差标量加权融合算法和射影理论,对带多个传感器和带相关噪声的广义系统,提出了分布式标量加权融合稳态满阶Kalman滤波器.推得了任两个传感器子系统之间的稳态满阶滤波误差互协方差阵,其解可任选初值离线迭代计算.所提出的稳态融合滤波器避免了每时刻计算协方差阵和融合权重,减小了在线计算负担.当系统含有未知模型参数时,基于递推增广最小二乘算法和标量加权融合算法,提出了一种两段融合自校正状态滤波器.其中第1段融合获得未知参数的融合估计;第2段融合获得分布式自校正融合状态滤波器.与局部估计和加权平均融合估计相比,所提出的标量加权融合参数估计和自校正状态估计都具有更高的精度.仿真研究验证了其有效性.