测绘学报 ›› 2016, Vol. 45 ›› Issue (12): 1396-1405.doi: 10.11947/j.AGCS.2016.20160263

• 大地测量学与导航 • 上一篇    下一篇

无缝线性回归与预测模型

王苗苗, 李博峰   

  1. 同济大学测绘与地理信息学院, 上海 200092
  • 收稿日期:2016-06-14 修回日期:2016-09-06 出版日期:2016-12-20 发布日期:2017-01-02
  • 通讯作者: 李博峰 E-mail:bofeng_li@tongji.edu.cn
  • 作者简介:王苗苗(1989-),女,博士生,研究方向为GNSS数据处理和理论应用。E-mail:5wmmgps@tongji.edu.cn
  • 基金资助:
    国家自然科学基金(41374031;41574023);测绘地理信息公益性行业科研专项(HY14122136)

Seamless Linear Regression and Prediction Model

WANG Miaomiao, LI Bofeng   

  1. College of Surveying and Geo-informatics, Tongji University, Shanghai 200092, China
  • Received:2016-06-14 Revised:2016-09-06 Online:2016-12-20 Published:2017-01-02
  • Supported by:
    National Natural Science Fund of China (Nos.41374031,41574023);China Special Fund for Surveying,Mapping and Geo-information Research in the Public Interest (No.HY14122136)

摘要: 建立回归模型常采用最小二乘方法并忽略自变量观测误差。尽管同时顾及自变量和因变量观测误差的总体最小二乘方法近年来得到了广泛研究,但在模型预测时,依然忽略了待预测自变量的观测误差。对此,本文提出了一种严格考虑所有变量观测误差的无缝线性回归和预测模型,该模型将回归模型的建立和因变量预测联合处理,在建立回归模型过程中对待预测自变量的观测误差进行估计并修正,从而提高了模型预测效果。理论证明,现有的几种线性回归模型都是无缝线性回归和预测模型的特例。试验结果表明,无缝线性回归和预测模型的预测效果优于现有的几种模型,尤其在变量观测误差相关性较大时,无缝模型对预测效果的改善更为显著。

关键词: 无缝线性回归模型, 模型预测, 误差估计, 误差相关性

Abstract: The regression model was traditionally established by using the least squares (LS) method where the errors of independent variables were ignored. Although the weighted total least squares (TLS) method that captures errors of both dependent and independent variables was extensively studied for regression analysis in recent years, it still neglects the errors of independent variables when predicting the corresponding dependent variables.This paper puts forward a seamless linear regression and prediction model which estimates regression parameters and predicts dependent variables simultaneously by considering the errors of all variables.In the seamless model, the errors of independent variables in the prediction model are predicted and corrected to improve the prediction accuracy.The several existing regression models are theoretically proved to be the special cases of the proposed seamless model. The experimental results show that the proposed seamless model outperforms the other existing models in the sense of prediction accuracy, especially when the error correlation of variables is significant.

Key words: seamless linear regression model, model prediction, observation error estimation, error correlation

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