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

Abstract

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 fo...