CASIA OpenIR  > 毕业生  > 硕士学位论文
Alternative TitleReduced Rank Estimation and MinimalPositive Realizaiton
Thesis Advisor郁文生
Degree Grantor中国科学院研究生院
Place of Conferral中国科学院自动化研究所
Degree Discipline控制理论与控制工程
Keyword降秩估计 自适应滤波 有限冲激响应(fir) 正系统 最小实现 Reduced-rank Estimation Adaptive Filter Fir Positive Systems Minimal Positive Realization
Abstract降秩估计的基本含义是在估计过程中用降秩矩阵来近似被估计的信道矩阵。降秩估计和滤波在信号处理与通信系统中有广泛的应用,尤其是在处理数据和模型冗余、抗噪声和模型误差的鲁棒性以及高效计算方面发挥重要的作用。另一方面,正系统是一类变量在非负范围内取值的系统,也有着大量实际应用的背景:工业过程中的化学反应和蒸馏过程、仓储系统、以及水和大气的污染模型等。针对降秩估计问题和系统最小正实现问题,本文展开了深入的研究,涉及到该领域中许多基本问题,例如,降秩估计与滤波的自适应算法、有限冲激响应(FIR)结构的降秩估计问题以及三阶系统最小正实现问题。在本文中,主要的工作和贡献有:1° 首先,简单回顾了降秩估计和正系统理论的研究状况,对两类问题给出基本的描述。2° 其次,将降秩估计与自适应滤波结合给出两种自适应的降秩估计算法――交替的最小均方法(ALMS)与交替的递推最小二乘法(ARLS)。由于这两种方法不需要信号的任何统计信息,也不需要奇异值分解等复杂的计算,所以在计算效率上有很大提高。仿真例子说明两种方法的有效性。3° 第三,在第二章的基础上,讨论FIR结构的降秩估计问题。首先在时域内分析二阶情况,进而给出一种处理任意阶系统降秩估计的方法。另一方面,从频域角度出发,给出一种适用非平稳信号的任意阶降秩估计方法。仿真说明了几种方法都是有效的。4° 第四章讨论了三阶系统最小正实现问题。给出一类三阶系统存在三阶最小正实现的充分条件,并结合已有结果,在合理假设下对此问题给出了充分必要条件。最后的数值例子也说明我们给出的参数条件是容易检验的,在证明过程中给出的构造方法是便于应用的。论文最后对所取得的研究成果进行了总结。
Other AbstractReduced-rank estimation, which is important for a wide range of signalprocessing and communication systems where data or model reduction, robust-ness against noise or model errors, or high computational e–ciency is desired,is to approximate the channel matrix by a reduced rank one. Meanwhile, pos-itive systems require all variables be nonnegative, which have been widely usedin industrial processes involving chemical reactors, distillation columns, storagesystems and water and atmospheric pollution models this paper, we focus on the reduced rank estimation and minimal positiverealizations and discuss some basic problems, such as, adaptive reduced-rank esti-mation algorithms, reduced-rank estimation for FIR systems and minimal positiverealization for third-order systems. The main contribution of this thesis includes:1° Firstly, researches on reduced-rank estimation and positive systems are re-viewed.2° Secondly, combining the adaptive filtering and reduced-rank estimation,two adaptive reduced-rank estimation algorithms are developed(ALMS andARLS). Since these two methods don’t need any statistical information orSVD, lots of computation is saved. Simulations show that these algorithms effective.3° Thirdly, based on the 2nd chapter, reduced-rank estimation for FIR systemsis discussed. We start from 2nd-order systems, then develop a method forarbitrary order FIR reduced-rank estimation. On the other hand, we givean approach based on frequency domain to deal with the situation that theinput signal is nonstationary. Simulations show satisfying performances ofthese methods.4° In the fourth chapter, a su–cient condition for 3rd-order systems’ mini-mal positive realization is given. With the existing results, this su–cientcondition can turn to be necessary. The numerical examples prove thatthe condition o?ered can be tested easily and the constructive method forminimal positive realization is applicable.A conclusion is given finally.
Other Identifier200228014603533
Document Type学位论文
Recommended Citation
GB/T 7714
于源. 降秩估计与系统最小正实现[D]. 中国科学院自动化研究所. 中国科学院研究生院,2005.
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