基于敏感度分析的病态性诊断

Ill conditioning diagnostics based on sensitivity analysis

如何针对测量实际,削弱或克服测量平差系统病态性的危害,取得更为准确的参数估值和可靠的平差成果,是当前测量工程数据处理中面临的一个重要课题,而给出更合理的诊断指标是进行病态性诊断研究的重点。本文采用矩阵微分法,通过对法矩阵的逆阵、均方误差以及最小二乘估计进行敏感度分析,提出了病态性问题的一种新的诊断技术——敏感度分析诊断法。

The resarch on covering the bad effects of ill conditioning to obtain more accurate and stable estimation of the unknown parameters is important in surveying engineering data processing field.So the ill-conditioning diagnostics should be studied firstly.Since ill conditioning is concerned with the sensitivity (or insensitivity) of a given relation to perturbations in underlying data, a new diagnostic technique is proposed, which is based on the sensitivity analysis of the inverse matrix of the normal matrix, the MSE and the 'length' of the LS estimator to the design matrix.