Solution of Structured Total Least Norm and Parameter Estimation Problems

一个超定线性系统的解，其中 在数据矩阵和目标向量中都可能存在误差， 在科学和工程的许多重要应用中需要。 最近，一种新的技术被称为结构化总体最小范数（STLN 为了获得保留任何仿射结构的解，在数据 都在为这些错误而烦恼 它还允许错误是 在各种规范中最小化。 STLN算法正在研究中， 已发展成为一种高效实用的解决方案， 应用. 它的计算性能正在研究中， 完全收敛理论正在发展之中。 重要的算法和 正在进行改进，以便有效地处理 大型问题和特殊结构。 一项特别的研究正在 将STLN方法应用于Hankel范数近似的模型降阶 问题. 正在探讨不同规范的影响。 STLN 算法被扩展到解决更一般的问题，其中结构化的 矩阵是待估计参数的可微函数，并且 其性能将与其它参数估计方法进行比较， Prony的方法

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.