Application of Variable Random Walk Process Noise to Improve GPS Tropospheric Path Delay Estimation and Positioning at Local and Global Scales

Accurate positioning using the Global Positioning System (GPS) relies on accurate modeling of tropospheric delays. Estimated tropospheric parameters must vary sufficiently to capture true variations in the delay, otherwise systematic errors propagate into estimated positions, particularly in the vertical component. However, if the allowed tropospheric parameter variation is too large, the propagation of data noise into all parameters is amplified, reducing precision. Here we investigate the optimal choice of tropospheric constraints applied in the GipsyX software, implemented as specified values of random-walk process noise. The commonly adopted default constraint for the zenith wet tropospheric delay (ZWD) is 3 mm/√(hr) (Bar-Sever et al., 1998). Using this default constraint, our investigation reveals spurious wave-like patterns of 5-minute estimates of vertical displacement across the central/eastern United States, coincident with Winter Storm Ezekiel, on November 27, 2019. The amplitudes of these displacements are ~100 mm, and form coherent bands of uplift/subsidence which span hundreds of kilometers. For this event, loosening the constraint to 24 mm/√(hr) suppresses the spurious vertical waves and improves the median station 5-minute vertical repeatability by 44%. More globally, looking at various stations through the year, variability of vertical positions is reduced when selecting a constraint of 6 mm/√(hr). Strong regional variability of the optimal random walk per station is observed and is driven by climactic, geographic, and temporal factors. Further improvement of 10% over the default constraint is achieved when optimizing the constraint to a unique value for each station. The best results are achieved, with 24% improvement, when optimizing the constraint with a daily value for each station. Given that applying the current default value of 3 mm/√(hr) produces pervasive positioning errors in GPS time series, we recommend at least loosening the constraint to 6 mm/√(hr) for ZWD (similarly scaled up for gradient estimation). To account for both regional and temporal variability, while being able to scale to global network analysis, it is recommended to apply annually weighted station specific random-walk constraints.