Effect of Temporal Physical Correlation on Accuracy Estimation in GPS Relative Positioning

Generally, in global positioning system (GPS) carrier phase relative positioning, the mathematical model does not describe the observations completely. This is mainly due to the lack of information about the physical phenomena associated with the GPS observations. As a result, a residual error component remains unmodeled. The analysis of a large number of data series representing baselines of various lengths showed that, in GPS carrier phase relative positioning, the residual errors are positively correlated over a time period of about 20 min. Not accounting for this temporal correlation could have significant effects on the resulting station coordinates and their accuracy measures. A simple way of accounting for the temporal correlation could be done through an empirical covariance function—namely, an exponential model. Although this stochastic modeling of the residual errors yields a fully populated covariance matrix for the GPS carrier phase double difference observations, its inverse takes a simple form of a block diagonal matrix. A modified sequential least-squares adjustment algorithm, which takes the temporal correlation into account, is presented in this paper. It is shown that neglecting the temporal correlation has little effect on the resulting station coordinates. Neglecting temporal correlation, however, leads to an overly optimistic covariance matrix. As the sampling interval increases, the effect of the temporal correlation on the accuracy estimation becomes less significant, as would be expected.