Regression and hypothesis tests for multivariate GNSS state time series

A satellite based observation system can continuously or repeatedly generate a user state vector time series that may contain useful information. One typical example is the collection of International GNSS Services (IGS) station daily and weekly combined solutions. Another example is the epoch-by-epoch kinematic position time series of a receiver derived by a GPS real time kinematic (RTK) technique. Although some multivariate analysis techniques have been adopted to assess the noise characteristics of multivariate state time series, statistic testings are limited to univariate time series. After review of frequently used hypotheses test statistics in univariate analysis of GNSS state time series, the paper presents a number of T-squared multivariate analysis statistics for use in the analysis of multivariate GNSS state time series. These T-squared test statistics have taken the correlation between coordinate components into account, which is neglected in univariate analysis. Numerical analysis was conducted with the multi-year time series of an IGS station to schematically demonstrate the results from the multivariate hypothesis testing in comparison with the univariate hypothesis testing results. The results have demonstrated that, in general, the testing for multivariate mean shifts and outliers tends to reject less data samples than the testing for univariate mean shifts and outliers under the same confidence level. It is noted that neither univariate nor multivariate data analysis methods are intended to replace physical analysis. Instead, these should be treated as complementary statistical methods for a prior or posteriori investigations. Physical analysis is necessary subsequently to refine and interpret the results.