靶向谱修正迭代法

The iteration method by targeted correcting characteristic value

病态的存在对测量数据处理影响较大,会降低参数估计的可靠性。谱修正迭代法是修正法矩阵所有谱并迭代计算,结果是无偏估计。而一般病态问题是法矩阵的几个谱奇异,因而存在谱多余修正的问题。针对该问题,文中提出靶向谱修正迭代法,即只修正法矩阵奇异的谱。将迭代矩阵中的单位阵变成靶向矩阵,靶向矩阵由法矩阵较小特征值对应的特征向量构造的对称矩阵,并用算例验证该方法的有效性与可行性。结果表明,随谱修正参数增大,结果更优且迭代次数更少。

The presence of morbid effects on the measurement data processing will reduce the reliability of the parameter estimation.The iteration by correcting characteristic value corrects all the characteristic value of matrix and iterate.The result is unbiased estimation.The general morbid problem is a few characteristic value strange of the matrix and thus there exists a problem of characteristic value superfluous amendments.For this problem,the paper proposes an iteration method by targeted correcting characteristic value,that is,only corrects strange characteristic value of the matrix.The unit matrix in the iterative matrix is transformed into target matrices,which is the symmetric matrix constructed by the eigenvector corresponding to the smaller eigenvalues of the matrix and then used examples to verify the validity and feasibility of the method.The result shows that the results of the method will be better and the number of iterations will be fewer with the characteristic value correction parameters increase.