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Regional Stochastic Models for NOAA-Based Residual Tropospheric Delays

Real-time and near real-time precise GPS positioning requires shorter GPS solution convergence time. Residual tropospheric delay, which exists as a result of the limitations of existing tropospheric correction models, is a limiting factor for quick GPS solution convergence. This paper proposes a new approach to tropospheric delay modelling, which overcomes the limitations of existing models. In this approach, the bulk of the tropospheric delay is accounted for using the NOAA-generated tropospheric correction model, while the residual tropospheric delay component is accounted for stochastically. First, the NOAA tropospheric correction model is used to generate daily time series of zenith total tropospheric delays (ZTDs) at ten IGS reference stations spanning North America for many days in 2006. The NOAA ZTDs are then compared with the new highly-accurate IGS tropospheric delay product to obtain daily residual time series at 5 minute intervals. Finally, the auto-covariance functions of the daily residual tropospheric delay series are estimated at each of the ten reference stations and then used to find the best empirical covariance function in the least squares sense. Of the three potential covariance functions examined, it is shown that the exponential cosine function gives the best fit most of the time, while the second-order Gauss-Markov model gives the worst fit. The first-order Gauss-Markov fits are close to those of the exponential cosine. Additionally, the model coefficients seem to be season independent, but change with geographical location.