RIA: Coupled State-Space Filtering with Applications

本研究的目的是开发模块化和并行化的算法，在自适应滤波，鲁棒估计，控制和结构矩阵计算的问题。 这项工作的主要动机是需要正确识别，建模和利用可能存在于特定问题中的方便结构，以开发计算有效的解决方案。 所提出的工作的一个内在的和相关的部分是首先确定共同的成分，以及明确澄清，控制，信号处理和数学学科中存在的几个问题之间的相互关系和相互作用。 在这方面，拟议的研究开发了一个统一的观点，同时解决了各种看似无关的问题，估计，控制，自适应滤波和矩阵计算。 它表明，在这些领域的许多应用程序的解决方案，原来共享一个关键的和令人惊讶的简单成分，即计算矩阵的三角因子，表现出结构。 这一特定事实的意义，更一般地说，作为一个整体，拟议的研究，是它使几个很好理解的概念，从矩阵理论和线性代数被应用，以简化推导各种算法，提出新的计算效率的变体，并利用新的形式的结构。 所提出的研究包括理论研究和算法实现。 在这项工作中开发的技术在几个领域中有应用，包括，除其他外，新的窗口计划自适应RLS滤波，分析基于梯度的算法，模块化和平方根算法的工具变量方法，鲁棒估计和控制。 同样重要的是制定一种系统和统一的方法。

The purpose of this research is to develop modular and parallelizable algorithms for problems in adaptive filtering, robust estimation, control, and structured matrix computations. A major motivation for this work is the need to properly identify, model, and exploit convenient structures that might exist in a particular problem in order to develop a computationally effective solution. An intrinsic and relevant part of the proposed work is to first identify common ingredients, as well as to explicitly clarify, the interrelations and interplays that exist among several problems in the disciplines of control, signal processing, and mathematics. In this regard, the proposed research develops a unifying point of view that simultaneously addresses a variety of seemingly unrelated problems in estimation, control, adaptive filtering, and matrix computations. It shows that the solutions to many applications in these areas turn out to share a key and surprisingly simple ingredient, namely, that of computing the triangular factors of matrices that exhibit structure. The significance of this particular fact and, more generally, of the proposed research as a whole, is that it enables several well-understood concepts from matrix theory and linear algebra to be applied in order to simplify the derivation of a variety of algorithms, to propose new computationally efficient variants, and to exploit new forms of structure. The proposed research consists of theoretical investigations and algorithm implementations. The techniques developed in this work have applications in several areas including, among others, new windowing schemes for adaptive RLS filtering, analysis of gradient- based algorithms, and modular and square-root algorithms for instrumental variable methods, robust estimation, and control. Equally important is the development of a systematic and unifying methodology.