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.     

带丢失观测和不确定噪声方差系统改进的鲁棒协方差交叉融合稳态Kalman滤波器

对带丢失观测和不确定噪声方差的线性定常多传感器系统,引入虚拟噪声将原系统转化为仅带不确定噪声方差的系统.根据极大极小鲁棒估值原理,用Lyapunov方程方法提出局部鲁棒稳态Kalman滤波器及其实际方差最小上界,并利用保守的局部滤波误差互协方差,提出一种改进的鲁棒协方差交叉(covariance intersection,CI)融合稳态Kalman滤波器及其实际方差最小上界.证明了所提出的鲁棒局部和融合滤波器的鲁棒性,并证明了改进的CI融合器鲁棒精度高于原始CI融合鲁棒精度,且高于每个局部滤波器的鲁棒精度.一个仿真例子验证所提出结果的正确性和有效性.     

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.     

基于Kalman滤波的自回归滑动平均信号信息融合Wiener滤波器

应用Kalman滤波方法,在按矩阵加权线性最小方差最优信息融合规则下,提出了带白色观测噪声的多通道ARMA信号的多传感器信息融合Wiener滤波器.它可统一处理信息融合滤波、平滑和预报问题.为了计算最优加权阵,提出了计算局部滤波误差互协方差阵的公式.同单传感器情形相比,可提高估计精度.一个带三传感器的目标跟踪系统的仿真例子说明了其有效性.     

多传感器时滞系统信息融合最优Kalman滤波器

基于线性最小方差最优加权融合估计算法,对多传感器的离散线性状态时滞随机系统,给出了一种非增广分布式加权融合最优Kalman滤波器.推导了状态时滞系统任两个传感器子系统之间的滤波误差互协方差阵的计算公式.它与状态增广加权融合滤波器具有相同的精度.与每个传感器的局部滤波器相比,分布式融合滤波器具有更高的精度.与状态和观测增广最优滤波器相比,具有较小的精度.但避免了增广所带来的高维计算和大的空间存储,可减小计算负担.仿真例子验证了其有效性.     

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.     

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.     

快速对角阵权系数协方差交叉融合容积卡尔曼滤波器

针对互协方差信息未知的多传感器系统,本文提出了一种快速对角阵权系数协方差交叉融合算法(FDCI).本文首先提出了一种对角阵权系数协方差交叉融合(DCI)方案,并证明了所提出DCI算法在融合估计精度上高于经典批处理CI融合(BCI)算法.在此基础之上,针对非线性等复杂的互协方差未知的多传感器系统,提出FDCI算法,并证明了所提出FDCI算法的无偏性及鲁棒精度. FDCI融合算法虽然在融合估计精度上低于DCI,但FDCI无需进行多权系数的非线性代价函数的优化问题,进而大大降低了计算负担,提高了系统的实时性.最后,结合容积卡尔曼滤波算法(CKF)提出了快速对角阵权系数协方差交叉融合容积卡尔曼滤波算法.仿真实例验证了所提出算法的正确性和有效性.     

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.     

带有色观测噪声系统多传感器标量加权最优信息融合稳态Kalman滤波器

基于标量加权多传感器线性最小方差最优信息融合准则,对被多传感器观测的带有色观测噪声的离散线性随机控制系统,提出了一种具有两层融合结构的标量加权信息融合稳态Kalman滤波器,它等价于相应的带相关噪声系统的最优信息融合稳态Kalman预报器.最优信息融合稳态预报器可在所有局部预报器达到稳态时,通过一次融合获得,且任两个子系统之间的稳态预报误差互协方差阵可通过任选初值迭代求得,并证明了它的收敛性.通过将它应用到带三个传感器的雷达跟踪系统验证了其有效性.     

The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers

For multisensor systems with exactly known local filtering error variances and cross-covariances, a covariance intersection (CI) fusion steady-state Kalman filter without cross-covariances is presented. It is rigorously proved that it has consistency, and its accuracy is higher than that of each local Kalman filter and is lower than that of the optimal Kalman fuser with matrix weights. Under the unbiased linear minimum variance (ULMV) criterion, it is proved that the accuracy of the fuser with matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrix weights is in between both of them, and the accuracies of all three weighting fusers and the CI fuser are lower than that of centralized Kalman fuser, and are higher than that of each local Kalman filter. The geometric interpretations of the above accuracy relations are given based on the covariance ellipsoids. A Monte-Carlo simulation example for tracking system verifies correctiveness of the proposed theoretical accuracy relations, and shows that the actual accuracy of the CI Kalman fuser is close to that of the optimal Kalman fuser, so that it has higher accuracy and good performance. When the actual local filtering error variances and cross-covariances are unknown, if the local filtering estimates are consistent, then the corresponding robust CI fuser is also consistent, and its robust accuracy is higher than that of each local filter.     

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.     

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.     

The covariance intersection fusion estimation algorithm weighted by diagonal matrix based on genetic simulated annealing algorithm and machine learning

This paper is concerned with covariance intersection (CI) fusion for multi-sensor linear time-varying systems with unknown cross-covariance. Firstly, a CI fusion weighted by diagonal matrix (DCI) is proposed, and it is proved to be unbiased and robust and has higher accuracy than classical CI fusion. Secondly, the genetic simulated annealing (GSA) algorithm is used for multi-parameter optimization problem caused by diagonal matrix weights. Considering the serious time-consuming problem in optimization process of the GSA algorithm, Back Propagation (BP) network is used to obtain the optimal weights. Eventually, the DCI based on GSA algorithm and BP network is proposed. The proposed algorithm has higher accuracy and better stability than classic CI fusion algorithms. Simulation analyses verify the effectiveness and correctness of the conclusion.     

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.     

Robust integrated sequential covariance intersection fusion Kalman filters and their convergence and stability for networked sensor systems with five uncertainties

For networked sensor systems (NSSs) with hard and soft sensors including five uncertainties, two universal approaches of solving the robust fusion estimation problems are presented. It includes an integrated sequential covariance intersection (SCI) fusion minimax robust Kalman filtering approach with cross-covariance information and a generalized Lyapunov equation approach with four pairs of Lyapunov equations. Applying them, the robust local and SCI fused time-varying and steady-state Kalman filters are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. The equivalent batch SCI fusers are also presented. Their robustness and accuracy relations are proved, and the sensitivity of the SCI fuser with respect to the fused orders of sensors is analyzed. Applying the dynamic error system analysis method and the dynamic variance error system analysis method, a new convergence and absolute asymptotic stability theory of robust fusion Kalman filtering is presented. The classical Kalman filtering convergence and stability theory is developed. Compared with the original covariance intersection fuser, they significantly reduced the computational complexity and burden. Compared with the optimal and conservative SCI fusers, they significantly improved the robust accuracies. They are suitable to deal with asynchronous or random delayed data and are suitable for real-time applications. A simulation applied to the two-mass spring damper mechanical system shows their effectiveness.