不确定性平差算法在沉降灰色模型中的应用  

Application of Uncertainty Adjustment Algorithm in Settlement Grey Model

作　　者：肖兆兵 宋迎春[1] 谢雪梅[1] XIAO Zhaobing;SONG Yingchun;XIE Xuemei(School of Geosciences and Info-Physics,Central South University,Changsha 410083,China)

机构地区：[1]中南大学地球科学与信息物理学院,湖南长沙410083

出　　处：《测绘地理信息》2019年第1期48-51,共4页Journal of Geomatics

基　　金：国家自然科学基金(41674009;41574006)

摘　　要：在沉降模型GM(1,1)中考虑不确定性的影响,利用残差中不确定度的传播规律,建立了使残差中最大不确定度最小的min-max准则,得到了带有不确定性的GM(1,1)模型算法,提高参数解算的准确性,最后将预测结果与实测沉降数据对比。结果表明,带不确定性的平差算法(leastsquare with uncertainty,ULS)与最小二乘平差(leastsquares,LS)和整体最小二乘平差(total least-square,TLS)相比,其预测结果更接近实际测量数据,说明了不确定性平差算法在沉降灰色模型中应用的有效性。In order to rid the uncertainty effects of settlement GM(1,1)model,a new uncertainty-based GM(1,1)model is obtained by applying the propagation law of uncertainty in residual error to establish the min-max criterion that can make the maximal uncertainty minimal,thus improving the accuracy of parameters calculation.The Comparison of the forecasting results with settlement observation data shows that the results of the least-squares with uncertainty(ULS)are closer to measurement data compared with least-square(LS)and total least-square(TLS),it also indicates the effectiveness of application of uncertainty adjustment algorithm in settlement grey model.

关 键 词：不确定性 平差模型 参数估计 GM(1 1)模型 minmax准则 

分 类 号：P207[天文地球—测绘科学与技术] P221