The Application of Penalized Least Squares Estimation to GPS Height Fitting

Being a harmful component, systematic error should always be eliminated and compensated during the procedure of surveying data processing. With further development in science and technology of surveying and mapping, some researchers extract systematic error by penalized least squares method when such systematic error is not random variable, therefore gain more understanding of systematic error to satisfy the need of high precise surveying. While the systematic error is random variable, as in the paper, we consider the semi-parametric regression model by using the penalized least squares method and get estimators of parameter and non-parameter. Then, the choices of regular matrix R and smoothing parameter a are discussed. Based on research of solving method of the smoothing parameter, a new method of function Xu (a) is proposed. By using the penalized least squares method, we study the height fitting in global positioning system, with results showing that penalized least squares is superior to conventional method in GPS height fitting.