Joint GRACE-FO Orbit and Gravity Field Determination Using GPS Ambiguity-resolved Carrier-phase and KBR Observations

Summary The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission continues the legacy of satellite gravimetry in monitoring Earth’s mass redistribution. Equipped with dual-frequency Global Positioning System (GPS) receivers and a K-Band Ranging (KBR) system, it enables precise orbit determination and high-resolution gravity field recovery. While integer ambiguity resolution (IAR) has proven effective for GPS-based orbit determination, its impact on time-variable gravity field recovery remains unclear. Here we develop a dynamic framework that jointly estimates GRACE-FO satellite orbits and monthly gravity fields by integrating GPS and KBR observations, in which single-differenced integer ambiguities are fixed and constrained into the normal equations as pseudo-observations with micrometer-level constraint precision. Using GRACE-FO onboard data from July to December 2019, we compare ambiguity-fixed and ambiguity-float solutions in terms of post-fit residuals, orbit accuracy, and gravity field quality. IAR improves three-dimensional orbit precision to ∼1.2 cm RMS, with along- and cross-track components enhanced by up to 52 per cent and 71 per cent, respectively. Satellite Laser Ranging validation confirms ∼1.2 cm agreement. Gravity field solutions from float ambiguities agree closely with official Science Data System (SDS) RL06.1 models up to degree 96, whereas IAR-based solutions maintain consistency only to about degree 40 and exhibit irregular oscillations beyond this range, particularly near orbital resonance conditions around order 45. At higher degrees, these oscillations are accompanied by intensified north–south striping in equivalent water height maps. Covariance diagnostics reveal increased off-diagonal correlations between spherical harmonic coefficients under IAR, indicating weakened spectral orthogonality and potential leakage of high-degree noise. These results indicate that ambiguity-fixed gravity solutions do not consistently outperform float-based solutions beyond spherical harmonic degree 40 in the near-polar orbiting GRACE-FO constellation.