补偿最小二乘估计在重力测量中的应用

在测量数据处理中,系统误差总是作为有害成分设法予以消除或补偿,但随着测绘科技的进一步发展,也有一些研究者将系统误差或非参数信号看作非随机变量,利用补偿最小二乘等方法,提取系统误差,从而对它有更多地了解,以满足高精度测量的需要。而本文在系统误差为随机变量的情况下,利用补偿最小二乘法研究半参数模型。得到了参数及非参数的估计;接着,讨论了估计量的若干统计特性;最后,用补偿最小二乘法研究重力测量中的重力异常问题,得到了重力异常的估计值,相同于用最小二乘配置法所得的结果,从而说明本文方法的有效性。

Application of penalized least squares estimation in gravimetry

During surveying data processing,systematic error is always eliminated and compensated as harmful component.With the further development of science and technique of surveying and mapping,however,a few researchers extract systematic error or nonparametric signal by penalized least squares method or others when it is not random variable,thus there is more understanding of it so as to satisfy the need of high precise surveying.While systematic error is random variable in the paper,consider the semiparametric regression model by using the penalized least squares method,estimators of parameter and nonparameter are got.Then,some properties of estimators are discussed.And that,using the penalized least squares method,gravity anomaly in gravimetry are studied,estimations of gravity anomaly are achieved,which are the same with the results from least squares collocation,it demonstrates that the method is valid.