Theoretical Issues in Adaptive Set-Membership-Based Signal Processing. 1991 YearEnd Report of Progress

摘要

The general purpose of this research is the development and exploration of newset membership-based algorithms for adaptive identification of parametric signal and system models. We are pleased to report progress in several important aspects, both theoretical and applied, of this general scope. The report consists of several preprints of papers in review by respected journals, published and preprinted conference papers, and some other supporting material. A clear understanding of our progress is inherent in the discussion of each item in the following. These discussions are meant to illuminate the directions, rationale, and achievements of our research, with the technical details left to the papers. The items appearing in the following are grouped into papers written for journals, followed by conference papers, descriptions of dissertations in preparation, then documents showing further evidence of research progress. Within each group, the items appear in chronological order. This paper is a generalization of all fundamental results in Optimal Bounding Ellipsoid (OBE) processing to the case of complex signal MIMO models. Such models occur in many important problems including, for example, adaptive beamforming and neural network learning. A suboptimal test for innovation is developed which leads to a class of OBE algorithms which empirically perform as well as those employing optimal checking. This check admits O(m) computational complexity which represents a square root factor improvement over optimal methods, as well as RLS.