Refined functional model of precise orbit determination to capture the dynamics of receiver-dependent biases of low earth orbit satellite

High-precision applications supported by Low Earth Orbit (LEO) satellites rely heavily on accurate spatiotemporal references—comprising both orbit and clock offset—typically established through Precise Orbit Determination (POD). Conventional POD models often assume that Receiver Dependent Biases (RDBs), both the Receiver Code Bias (RCB) and Receiver Phase Bias (RPB), remain stable over short time span, which is not necessarily true in real situation. In this paper, we refine the conventional POD model by explicitly parameterizing the time-varying difference between the RCB and RPB, referred as Dynamic RDB (DRDB), and then a DRDB-Assimilated (float) model is proposed. Moreover, a constrained DRDB-Assimilated model is presented by physically modelling the DRDB behavior with particularly considering the thermal environment of LEO. Using data from a commercial SAR LEO satellite, both models successfully captured the evident DRDB variations ranging approximately from − 25 to 25 m, following an asymmetric periodic trend closely tied to the relative motion among the Sun, Earth, and satellite. With respect to the conventional model, both new models can achieve the comparable orbit accuracies at the centimeter level, but substantial improvements in timing performance. Both models reduced arc-boundary receiver clock discontinuities, from tens of nanoseconds to sub-nanosecond levels. In terms of frequency stability, the constrained DRDB-Assimilated model showed the similar short-term stability to the conventional one but notable improvements in medium- and long-term stability (beyond 10² s). These research findings underscore the importance of processing RDBs dynamics in LEO POD and highlight the constrained DRDB-Assimilated model as a robust model to obtain accuracy orbits and time for LEO satellites.