摘要
本文对变形分析与预测模型中的线性回归分析法、时间序列分析模型、灰色系统分析模型中的病态问题进行了理论分析和数值模拟。通过对变形观测资料施加干扰噪声,采用最小二乘原理,得出了三种模型中每一个参数与干扰噪声的数值关系表达式。指出在变形解释和变形预测中,用这三种模型进行建模分析时必须先检查信息矩阵A=XTX的病态程度,采取有效方法减轻A=XTX的病态程度后方可使用这三种模型。
Firstly, theoretical analysis and numerical simulation of ill-posed problem have been done for linear regression analysis, time series analysis model and gray system model in deformation analysis and forecasting model. Then, by imposing interference noise on deformation observational data, the numerical expression relation between every three model parameters and the noise interference is derived based on least square principle. Finally, The paper points out that if one use any of the three models for modeling analysis to explain the deformation and deformation forecast, it is required to inspect the information matrix A = X^TX no matter it is illposed or not, and to reduce ill-condition of A = X^TX with effective method before using these three models.
出处
《测绘科学》
CSCD
北大核心
2008年第6期47-49,共3页
Science of Surveying and Mapping
基金
湖南省科技计划项目(编号:2008SK3054)
关键词
变形分析
病态
线性回归分析
时间序列
灰色模型
deformation analysis
ill-posed
linear regression analysis
time series
gray model
