Reduced-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 et.al..In 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.
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