Exponential Modeling with Unknown Model Order Using Structured Nonlinear Total Least Norm

A new algorithm called Structured Nonlinear Total Least Norm (SNTLN) has recently been developed for obtaining an approximate solution to the structured overdetermined nonlinear system. Both theoretical justification and computational testing show that SNTLN is an efficient method for solving structured overdetermined systems. In this paper, we present a method based on SNTLN for estimating the parameters of exponentially damped sinusoidal signals in noise when the model order is unknown. It is compared to two other existing methods to show its robustness in recovering correct values of parameters when the model order is unknown, in spite of some large errors in the measured data.     

Analysis of the Structured Total Least Squares Problem for Hankel/Toeplitz Matrices

The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) approach when structured matrices are involved and a similarly structured rank deficient approximation of that matrix is desired. In many of those cases the STLS approach yields a Maximum Likelihood (ML) estimate as opposed to, e.g., TLS.In this paper we analyze the STLS problem for Hankel matrices (the theory can be extended in a straightforward way to Toeplitz matrices, block Hankel and block Toeplitz matrices). Using a particular parametrisation of rank-deficient Hankel matrices, we show that this STLS problem suffers from multiple local minima, the properties of which depend on the parameters of the new parametrisation. The latter observation makes initial estimates an important issue in STLS problems and a new initialization method is proposed. The new initialization method is applied to a speech compression example and the results confirm the improved performance compared to other previously proposed initialization methods.     

线性流形上矩阵方程AXAT=B的极小Frobenius范数对称正交对称解

利用矩阵对的商奇异值分解,给出了线性流形上矩阵方程AXAT=B存在极小Frobe- nius范数对称正交对称解的充要条件及其解的表达式．     

一类矩阵方程的极小Frobenius范数双对称解

利用矩阵的广义奇异值分解,给出了实矩阵方程ATXA=B存在极小Frobenius范数双对称解的充要条件及其解的表达式.