广义系统最优与自校正分布式信息融合估值器

【作者】 马静；

【导师】 孙书利；

【作者基本信息】 黑龙江大学 ， 控制理论与控制工程， 2007， 硕士

【摘要】 广义系统广泛出现在机器人、电网络和经济管理等实际系统中，广义系统的状态估计问题在系统设计与控制中具有重要的意义。本文研究了广义系统分布式信息融合状态估计算法，包括广义系统降阶信息融合估值器的设计、广义系统满阶信息融合估值器的设计以及带未知噪声统计和／或未知模型参数的广义系统降阶、满阶滤波器的设计。对带多传感器和带相关噪声的广义离散随机线性系统，通过多种非奇异变换，将广义系统转化为不同的降阶子系统标准形，基于线性最小方差最优加权融合算法和射影理论，针对不同的降阶子系统标准型，分别提出了分布式降阶信息融合Kalman估值器和Wiener估值器(包括滤波器、预报器和平滑器)。推导了任两个局部估计误差之间的互协方差阵的计算公式，以及两个降阶子系统之间的局部估计误差互协方差阵的计算公式。当各局部传感器子系统存在稳态滤波时，证明了任两个局部估计误差之间的互协方差阵所满足的方程解的收敛性，即其解可通过带任意初值迭代计算。给出了多传感器降阶信息融合稳态Kalman估值器。并且，降阶信息融合稳态Kalman估值器可在各局部子系统达到稳态时仅通过一次融合求得融合权重，与非稳态情形相比避免了每时刻计算融合权重，可明显减小在线计算负担。将带噪声在同时刻相关的广义系统转化为噪声在同时刻和邻近时刻相关的非广义系统，基于这个非广义系统提出了基于每个传感器的局部满阶Kalman估值器(包括滤波器和平滑器)。基于线性最小方差最优加权融合算法，对带多个传感器的广义系统给出了分布式最优加权满阶Kalman估值器。推导出任两个传感器子系统之间的估计误差互协方差阵所满足的方程。在系统可检和可稳的条件下，证明了局部传感器子系统估计误差方差阵所满足的Riccati方程解的收敛性，进而对多传感器系统证明了任两个传感器子系统之间的互协方差阵所满足的Riccati方程解的收敛性。并给出了满阶信息融合稳态估值器。当系统含有未知噪声统计信息时，基于相关函数给出了一种分布式辨识方法，提出了自校正降阶和满阶信息融合滤波器。当系统含有未知模型参数时，通过直接辨识ARMA新息模型参数，给出了信息融合参数估计算法和自校正降阶、满阶信息融合滤波器。当系统同时含有未知模型参数和噪声统计时，给出了具有三段融合结构的自校正降阶和满阶信息融合滤波器。更多还原

【Abstract】 The descriptor systems extensively exist in some practical applications such asrobot, electronic network and economic systems, and so on. The state estimationproblem for descriptor systems has very important significance in systems design andcontrol. In this paper, we investigate the distributed information fusion state estimationalgorithms for descriptor systems, including the design of reduced-order informationfusion estimators, full-order information fusion estimators and self-tuning reduced-orderfilter and full-order filter for descriptor systems with unknown noises statistics and/orunknown model parameters.For descriptor discrete-time stochastic linear systems with multiple sensors andcorrelated noises, by some non-singular transformations, the descriptor system istransferred to four reduced-order subsystems canonical forms. Based on the optimalfusion estimation algorithm in the linear minimum variance sense and projection theory,distributed reduced-order information fusion Kalman estimators and Wiener estimators,including filter, predictor and smoother, are presented for different canonical forms,respectively. The computation formulas for error covariance matrices between any twolocal estimation errors and two reduced-order subsystems are derived. Convergences ofsolutions of equations that cross-covariance matrices between any local estimationerrors satisfy are proven when steady-state Kalman filter exists for each sensor system,i.e., the solution can be computed by the iteration with an arbitrary initial value. Thedistributed steady-state reduced-order information fusion Kalman estimators are given.Furthermore, the reduced-order information fusion steady-state Kalman estimators canbe obtained by fusing once after all local subsystems reach the steady state. Comparingwith non-steady-state information fusion estimators, computations of fusion weights areavoided at each time step, so the online computational burden can be reduced obviously. A descriptor system with correlated noises at the same time is transferred to theequivalent non-descriptor system with correlated noises at the same and neighboringtime. The local full-order Kalman filter and smoother are presented for thisnon-descriptor system. Further, based on the optimal weighted fusion estimationalgorithms in the linear minimum variance sense, the distributed optimal weightedfusion full-order Kalman estimators are presented for the descriptor system withmultiple sensors. The estimation error cross-covariance matrices between any two localestimation errors are derived. Under the condition that the system is detectable andstabilizable, convergence of solution of Riccati equation that variance matrix of localestimation error satisfies is proved. Further, convergences of solutions of equations thatcross-covariance matrices between any local estimation errors satisfy are proven for thesystem with multiple sensors. Also, the full-order information fusion steady-stateestimators are given.When system has unknown noise statistics, a distributed identification approach fornoise statistic information is presented based on correlation functions and self-tuningreduced- and full-order information fusion filters are given. When the system model isunknown, information fusion estimators for model parameters and self-tuning reduced-and full-order information fusion filters are given by identifying ARMA innovationmodel parameter. When the system model parameters and noise statistics are unknown,the self-tuning reduced- and full-order information fusion filters with the three-stagefusion structures are given.更多还原