具有时滞和测量丢失的离散随机系统最优滤波

发布时间：2018-02-04 17:10

本文关键词： 随机时滞测量丢失噪声最优滤波一致滤波　出处：《哈尔滨理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文研究了具有时滞和测量丢失的离散随机系统的最优滤波问题。在实际系统中,时滞与测量丢失是最常见的问题之一。为了可以更准确地对系统的状态进行估计,我们研究一类具有时滞和测量丢失的系统是很有理论和实际意义的。首先,研究具有乘性噪声和一步随机传感器时滞的离散随机时滞系统的最优滤波问题,系统的过程噪声与测量噪声是不相关的白噪声。利用新息分析方法以及递推射影公式,设计出了在均方意义下滤波误差最小的线性最优滤波器,并给出数值算例来验证滤波器的有效性与可行性。随后,将问题推广到一般情况,即研究具有一步随机多传感器时滞的离散随机时滞系统的最优滤波问题,为简化问题不考虑系统的乘性噪声。类似地,得到了该系统的线性最优滤波器,并通过一组数值算例来验证滤波器的可行性和有效性。其次,研究具有乘性噪声、有限步自相关过程噪声、一步随机传感器时滞和测量丢失的离散随机系统的最优滤波问题,系统的测量噪声是不相关的白噪声。我们基于均方误差最小(minimum mean square error(MMSE))的准则,设计出了估值误差最小的线性最优滤波器,并通过一组数值算例对滤波器的有效性和可行性进行了验证。最后,研究了具有测量丢失的非线性离散随机系统基于分布式无损(无迹)卡尔曼滤波(Distributed Unscented Kalman Filtering(DUKF))的一致算法,系统的过程噪声与测量噪声是不相关的白噪声。通过无损(无迹)变换(Unscented Transformation(UT))的方法设计出具有测量丢失的非线性离散随机系统的DUKF,根据一致信息(Consensus on Information(CI))的方法可以得到基于DUKF的一致算法,通过数值算例说明所设计滤波算法的一致性。
[Abstract]:In this paper, the optimal filtering problem for discrete stochastic systems with time delay and measurement loss is studied. Time delay and measurement loss are one of the most common problems. In order to estimate the state of the system more accurately, it is of great theoretical and practical significance to study a class of systems with time delay and measurement loss. The optimal filtering problem for discrete stochastic time-delay systems with multiplicative noise and one-step stochastic sensor delays is studied. The process noise and measurement noise of the system are white noise which is irrelevant. Using innovation analysis method and recursive projective formula, a linear optimal filter with minimum filtering error in the sense of mean square is designed. Numerical examples are given to verify the validity and feasibility of the filter. Then, the problem is extended to the general situation, that is, the optimal filtering problem for discrete stochastic time-delay systems with one-step stochastic multi-sensor delay is studied. In order to simplify the problem without considering the multiplicative noise of the system, the linear optimal filter of the system is obtained, and the feasibility and validity of the filter are verified by a set of numerical examples. The optimal filtering problem for discrete stochastic systems with multiplicative noise, finite step autocorrelation process noise, one-step stochastic sensor delay and measurement loss is studied. The measurement noise of the system is an irrelevant white noise. We base on the criterion of minimum mean square error (MMSE) with minimum mean square error (MSE). A linear optimal filter with minimum estimation error is designed, and the validity and feasibility of the filter are verified by a set of numerical examples. The distributed lossless (unscented) Kalman filter for nonlinear discrete stochastic systems with measurement loss is studied. Distributed Unscented Kalman filtering algorithm. The process noise and the measurement noise of the system are white noises which are irrelevant. Unscented Transformation by Lossless (Unscented Transformation). The DUKF of nonlinear discrete stochastic system with measurement loss is designed. A consistent algorithm based on DUKF can be obtained based on consensus information. A numerical example is given to illustrate the consistency of the proposed filtering algorithm.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713

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