Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

The global positioning system (GPS) has become an essential tool for the high precision navigation and positioning. The quality of GPS positioning results mainly depends on the model’s formulations regarding GPS observations, including both a functional model, which describes the mathematical relationships between the GPS measurements and unknown parameters, and a stochastic model, which reflects the physical properties of the measurements. Over the past two decades, the functional models for GPS measurements have been investigated in considerable detail. However, the stochastic models of GPS observation data are simplified, assuming that all the GPS measurements have the same variance and are statistically independent. Such assumptions are unrealistic. Although a few studies of GPS stochastic models were performed, they are restricted to short baselines and short time session lengths. In this paper, the stochastic modeling for GPS long-baseline and zenith tropospheric delay (ZTD) estimates with a 24-h session is investigated using the residual-based and standard stochastic models. Results show that using the different stochastic modelling methods, the total differences can reach as much as 3–6 mm in the baseline component, especially in the height component, and 10 mm in the ZTD estimation. Any misspecification in the stochastic models will result in unreliable GPS baseline and ZTD estimations. Using the residual-based stochastic model, not only the precision of GPS baseline and ZTD estimation is obviously improved, but also the baseline and ZTD estimations are closer to the reference value.