Improved time-correlated noise modeling for GNSS terrestrial reference frame realization via square root information filter

Realizing a Terrestrial Reference Frame (TRF) with an accuracy of 1 mm and a long-term stability of 0.1 mm/yr is a longstanding goal of the geodesy field. To achieve this, selecting an appropriate stochastic model to accurately characterize the nonlinear coordinate variations of geodetic stations is essential for TRF realization. However, the commonly used Random Walk (RW) model in filtering is not the optimal noise model for time-correlated noise in Global Navigation Satellite System (GNSS) coordinates. In this study, we replace the RW model with a first-order autoregressive (AR[1]) process to model the GNSS time-correlated noise and implement a GNSS TRF solution aligned with ITRF2020 via the Square Root Information Filter (SRIF). We found that the AR[1] process used in this study has a higher cut-off frequency than the RW model, allowing it to retain a larger portion of the input flicker noise. Consequently, the GNSS time-correlated noise modelled by AR[1] more closely approximates true flicker noise than that modelled by RW. When time-correlated noise is modelled by AR[1], the median RMS of coordinate residuals is decreases to 0.3 and 2.0 mm in the horizontal and up components, respectively. Moreover, the AR[1] process can capture short-term correlations in time-correlated noise parameters, thereby enhancing the accuracy of short-term (approximately 11 weeks) TRF coordinate predictions. These findings demonstrate the potential of incorporating time-correlated noise using AR[1] in GNSS data assimilation, with implications for both multi-technique global TRF realization and regional GNSS TRF solutions.