高斯线性模型正则估计的Cramér-Rao下界

Cram r-Rao lower bound for regular estimation of linear Gaussian models

该文针对正则化高斯模型中参数估计的Cramér-Rao下界(CRB)开展研究,提出了一种新型CRB.在线性高斯模型的设计矩阵单位正交的假设下,给出L_1类正则估计的方差及CRB的显式表达,并进行数值计算.进一步地,推导了正则估计的CRB取等条件:在线性高斯模型中,取得CRB的估计均为线性估计量;在正则项可微的假设下,仅二次多项式正则项可令估计取得CRB.最后,针对带稀疏特征的估计提出sparse CRB,将其与现有的CRB比较,从理论和实践两方面说明了其优势.

The Cram r-Rao lower bound of parameter estimation in regularization Gaussian model is studied,and a new CRB is proposed.Under the assumption of unit orthogonality of the design matrix of the linear Gaussian model,the explicit expressions of the variance and CRB of the L1 type regular estimates are given,and numerical calculations are carried out.Furthermore,this article derives the CRB equivalence condition for regular estimation:in a linear Gaussian model,the estimates obtained for CRB are all linear estimators;under the assumption that the regularization term is differentiable,only the regularization term of a quadratic polynomial can make the estimation obtain CRB.Finally,sparse CRB is proposed for estimation with sparse features,and its advantages are illustrated both theoretically and practically by comparing it with existing CRBs.