指数混合模型非线性最小二乘法的参数分辨率探讨  

Discussion on the Parameter Resolution of Nonlinear Least Square Method for Exponential Mixed Model

作　　者：陶玉潘 余旌胡[1] 丁义明 Tao Yupan;Yu Jinghu;Ding Yiming(College of Science,Wuhan University of Technology,Wuhan 430070,China;Mathematics Research Center,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学理学院,武汉430070 [2]武汉理工大学数学研究中心,武汉430070

出　　处：《统计与决策》2020年第17期24-27,共4页Statistics & Decision

摘　　要：文章以两分量指数衰减模型为例,给出求解模型参数非线性最小二乘法分辨率的定义。为衡量此类相近信号能否分开提供一个标准,也为评价非线性最小二乘法在估计此模型准确度的度量提供一个新方法。实验表明:信噪比越大,参数分辨率精度越高;均匀取点比均匀对数取点得到更好的参数估计;固定信噪比时,在合适样本区间和样本数量下,局部分辨率与整体分辨率是一致的;参数分辨率与噪声的四分之一次方满足正线性关系。This paper takes the two-component exponential decay model as an example to give the definition of the resolution of the nonlinear least square method for solving the model parameters.It provides a criterion to measure whether the similar signals can be separated or not,and a new approach to evaluating the accuracy of the model by the non-linear least square method.Experiments show that the accuracy of parameter resolution becomes higher with the increase of SNR;uniform point selection is better than uniform logarithmic point selection which could obtain better parameter estimation;when the SNR is fixed,the local resolution is consistent with the overall resolution under the appropriate sample interval and sample number;the parameter resolution and the 1/4 power of noise satisfy the positive linear relation.

关 键 词：两分量指数模型 参数分辨率 非线性最小二乘法 信噪比 

分 类 号：O212[理学—概率论与数理统计]