| The partially linear model (PLM) is a flexible extension of both the linear model and nonparametric model of time series. The vector partially linear model (VPLM) is an extension of PLM when there are a set of observations at one time point from several sources. Smoothing spline is one of the popular approaches for PLM estimation. This thesis extends the smoothing spline approach to a few VPLMs and presents algorithms to compute the estimates. Then, we apply the smoothing spline based vector partially linear model (SSBVPLM) approach to Global Positioning System (GPS) applications. In an unfavorable environment, the accuracy of position estimates, which are usually computed by the least squares (LS) method based on the linear model, can be impaired due to system errors. In order to account the system errors, we use the vector partially linear models instead of the linear models. We apply the SSBVPLM estimation techniques to kinematic and static relative positioning, based on both code and carrier phase measurements. The simulations show that the SSBVPLM approach can yield more accurate position estimates than the LS approach. |
