The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is no constraint on the mutual coherence, so when this regressor is used to estimate sparse parameter vectors of a system, it may yield a large estimation error. This paper aims to tackle this issue for fixed denominator models, which include Laguerre, Kautz, and generalized orthonormal basis function expansion models, for example. The paper proposes an optimal input design method where the achieved Fisher information matrix is fitted to the desired Fisher matrix, together with a coordinate transformation designed to make the regressors in the transformed coordinates have low mutual coherence. The method can be used together with any sparse estimation method and in a numerical study we show its potential for alleviating the problem of model order selection when used in conjunction with, for example, classical methods such as AIC and BIC.

翻译：回归量之间的最大绝对值相关性，即互相干性，在稀疏估计中起着至关重要的作用。由于没有对互相干性的约束，最优输入设计可能导致列高度相关的回归量矩阵；当使用此类回归量估计系统的稀疏参数向量时，可能产生较大的估计误差。本文旨在针对固定分母模型（例如包括拉盖尔、考茨和广义正交基函数展开模型）解决这一问题。本文提出一种最优输入设计方法，通过将获得的费舍尔信息矩阵拟合到期望的费舍尔矩阵，并结合旨在降低变换坐标中回归量互相干性的坐标变换。该方法可与任意稀疏估计方法配合使用，数值研究表明，当与AIC和BIC等经典方法结合时，该方法能够有效缓解模型阶次选择问题。