Solution of Structured Total Least Norm and Parameter Estimation Problems

点击翻译按钮获取中文摘要

A solution to an over determined linear system, where there may be errors in both the data matrix and the target vector, is required in many important applications in sciences and engineering. Recently, a new technique called Structured Total Least Norm (STLN) has been developed for obtaining the solution that preserves any affine structure, after the data are perturbed to account for the errors. It also permits the error to be minimized in various norms. The STLN algorithm is being investigated and developed into an efficient and practical solution method for many applications. Its computational performance is being studied and a more complete convergence theory is under development. Significant algorithmic and improvements are being made in order to efficiently handle large-scale problems and special structures. A particular study is being conducted to apply the STLN method to the model reduction by Hankel norm approximation problem. The effect of different norms are being explored. The STLN algorithm is being extended to solve more general problems where the structured matrix is a differentiable function of parameters to be estimated, and its performance is to be compared to other parameter estimation methods such as Prony's method.