广义系统降阶信息融合状态估值器

【作者】 陶贵丽；

【导师】 邓自立；

【作者基本信息】 黑龙江大学 ， 控制理论与控制工程， 2006， 硕士

【摘要】 对于带多传感器的广义线性离散定常随机系统，基于奇异值分解，应用线性变换，可将广义系统化为两种典范型，其中每种典范型由两个非广义子系统组成。对于原始状态、变换后状态和子系统状态分别提出了三种不同的加权融合方法。而每种融合方法分别通过按矩阵加权、按标量加权和按对角阵加权三种线性最小方差最优信息融合准则实现。应用经典Kalman滤波方法和白噪声估计理论，在三种不同的加权融合方法下，分别提出了广义系统在两种典范型下的降阶信息融合时变和稳态Kalman估值器，它们可统一处理融合滤波、预报和平滑问题，为了计算最优加权，提出了局部估值误差方差阵和协方差阵的计算公式。对每种加权融合方法，证明了带矩阵权的Kalman融合器的精度高于带标量权的Kalman融合器的精度，而带对角阵权的Kalman融合器的精度位于前两者之间，且每种融合器精度都高于局部估值器精度。大量的Monte Carlo数值仿真例子说明了其有效性和正确性，且说明了带不同类权的融合估值器的精度无显著区别。因而采用带标量权或带对角阵权的融合器可显著减小计算负担，便于实时应用。更多还原

【Abstract】 For the linear discrete time-invariant stochastic descriptor system with multisensor, based on the singular value decomposition, by the linear transformation, the descriptor system can be transformed into two canonical forms, where each canonical form consists of two reduced-order non-descriptor subsystems. Three different weighted fusion approaches are presented for the original state, transformed state, and subsystems’ state, respectively. Each weighted fusion approach is realized via three rules weighted by matrices, diagonal matrices, and scalars, respectively. Using the classical Kalman filtering method and white noise estimation theory, by the three different weighted fusion approaches, the reduced-order information fusion time-varying and steady-state descriptor Kalman estimators are presented for the descriptor system under the two canonical forms, respectively. They can handle the fused filtering, smoothing and prediction problems in a unified framework.The formulas of computing the variance and cross-covariance matrices among local estimation errors are presented, which are applied to compute the optimal weights. It is proved that for each weighted fusion approach, 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 between both of them, and the accuracy of each fuser is higher than that of local estimators. Many Monte Carlo simulation examples show their effectiveness, and show that the accuracy distinction for fused estimators with different kinds of weights is not obvious, so that the fusers更多还原