Comparison and analysis of unmodelled errors in GPS and BeiDou signals

In Global Navigation Satellite Systems (GNSS) positioning, one often tries to establish a mathematic model to capture the systematic behaviors of observations as much as possible. However, the observation residuals still exhibit, to a great extent, as (somewhat systematic) signals. Nevertheless, those systematic variations are referred to as the unmodelled errors, which are difficult to be further modelled by setting up additional parameters. Different from the random errors, the unmodelled errors are colored and time correlated. In general, the larger the time correlations are, the more significant the unmodelled errors. Hence, understanding the time correlations of unmodelled errors is important to develop the theory for processing the unmodelled errors. In this study, we compare and analyze the time correlations caused by unmodelled errors of Global Positioning System (GPS) and BeiDou signals. The time correlations are estimated based on the residuals of double differenced observations on 11 baselines with different lengths. The results show that the time correlation patterns are different significantly between GPS and BeiDou observations. Besides, the code and phase data from the same satellite system are also not the same. Furthermore, the unmodelled errors are affected by not only the baseline length, but also some other factors. In addition, to make use of the time correlations with more efficiency, we propose to fit the time correlations by using exponent and quadratic models and the fitting coefficients are given. Finally, the sequential adjustment method considering the time correlations is implemented to compute the baseline solutions. The results show that the solutions considering the time correlations can objectively reflect the actual precisions of parameter estimates.