【作者】 赵洪国；

【导师】 王英健；

【作者基本信息】 长沙理工大学 ， 计算机应用技术， 2005， 硕士

【摘要】 自从Wiener 滤波以来,估计问题包括滤波、预测、平滑已经成为控制、通信领域关键的研究课题。但是Wiener 滤波很难实现信号的实时处理,而Kalman 滤波正好弥补了这一缺陷,当信号含有噪声时,Kalman 滤波可以在最小均方差条件下给出信号的最佳估计,而且是在时域中采用递推方式下进行,因此速度快,便于实现。　传统的Kalman 滤波算法是建立在H 2估计准则基础之上的,它要求精确已知的系统模型。但是在实际情况下,系统中存在着随机不确定性。本论文将研究一类随机不确定系统的鲁棒Kalman 滤波问题,其中这里所说的随机不确定性是指状态矩阵和观测矩阵中存在着随机扰动矩阵。如果我们仍然按照传统的Kalman 滤波进行估计,则会造成估计效果较差或引起发散。　本论文将分别从具有时滞和非时滞两个方面对系统模型中系统矩阵和观测矩阵含有随机扰动阵的系统模型作出进一步的研究与分析,提出处理随机扰动阵的处理方法。针对时滞系统的估计和控制问题,我们知道对连续系统常用的方法有偏微分方程或线性矩阵不等式等方法。对于离散时间系统最直接的方法是采用增广状态方法。但是当系统模型的维数很高时,延迟很大时,这种方法会导致计算量的增加。本论文将采用新息重组的新技术,鲁棒Kalman 滤波器的计算将建立在与系统相同的两个同维数的黎卡提方程之上,与同类算法相比,该算法是无偏的,并且易于计算和计算量小。　新息重组的主要思想是:通过重新组织不同观测方程的观测值,导出重组的新息序列。并且证明重组的新息序列是不相关的白噪声序列,它完全不同于传统的Kalman 滤波新息序列。利用重组的新息序列和Hilbert 空间上的预测递推公式导出其鲁棒Kalman 滤波公式。　　　　仿真实例证明,该鲁棒Kalman 滤波方法是有效的、可行的。新息重组的新方法可以为时滞的鲁棒估计问题提供了基本的理论依据,同时展望了其应用的前景。更多还原

【Abstract】 The problem of estimation includes filtering, prediction and smoothing and has been one of the key research topics of control community since the seminal paper by Wiener. But wiener filtering cannot be used in the real time signal processing. Kalman filtering just can fetch up the default, which can give the optimum estimation of signal under the condition of the minimums mean-square. And this method works in the time domain; the processing speed is fast, which make it be use in the real time signal processing. The standard kalman filtering is based on H 2 estimative criterion and need accurate model of system. But there exists stochastic uncertainties in the model of system in case of reality. This paper deals with the problem of robust kalman filtering for a class of stochastic uncertain system, where the uncertainties that satisfy the random uncertain matrices that exist in state matrices and observer matrices. If we still estimate according to the tradinonal kalman filtering, the estimative result will be relatively bad or cause scatteration. We will make further research and analysis for the linear stochastic uncertain system model from two respects separately in this thesis. One is system with time delay; another is system with non-time delay. To the problem of estimation and controlling for system with time delay, we know that there are some methods. for continuous time linear system ,such as prejudicial differential equation、linear matrix inequality ,etc. For discrete time linear systems, the most direct method is augmented system. That is to say, it can only be calculated based on an augmented system. But these methods lead to increasing of calculation when the dimension or time delay in the system is very great. We will adopt a new method in this thesis. The robust kalman filtering will based on two Riccati equations with the same dimension as system. Compared with other existing robust filtering, it is very simple and effective to calculate and is unbiased to the linear stochastic uncertain system. Main idea of the re-organized innovation: We will renew to organize innovation, which comes from different observer measurements, and introduce a re-organized innovation sequence. We also prove that it the innovation sequence which is an uncorrelated white noise and different from the innovation in kalman filtering formulation. Thus robust kalman filtering is derived based on an innovation analysis method together with projection in Hilbert space. In the end a stimulant example shows that the robust filtering method is effective and feasible. The new theory of re-organized innovation will give basic foundation for the problem of robust estimation in the linear system with time-delay. The application prospect of this method is prognosticated at the same time.更多还原