Reduced-Parameter Recalibration of SGP4 Using Precise Orbit Ephemerides and Constrained Particle Swarm Optimisation with Processor-in-the-Loop Validation

Two-Line Element (TLE)-based orbit forecasts propagated with Simplified General Perturbations 4 (SGP4) exhibit time-dependent, biased, and spacecraft-specific errors. Previous approaches have reduced these errors by optimising SGP4 parameters against independent GNSS-derived precise orbit ephemerides, but high-dimensional optimisation can impose a significant computational burden on resource-constrained on-board processors. This work proposes a reduced-parameter SGP4 recalibration using bound-constrained Particle Swarm Optimisation (PSO), considering corrections to the initial mean anomaly and mean motion, with B* included as an additional parameter for comparison. The method is evaluated for Sentinel-1A, Sentinel-3A, and Sentinel-6A using GNSS-derived precise orbit products as high-accuracy reference ephemerides, with 1.5, 6, and 24 h fitting arcs and independent forecasts up to 24 h. The results show that forecast improvement depends strongly on the spacecraft and fitting-arc duration: Sentinel-1A achieves the most persistent benefit, with a median Cartesian position-RMSE reduction of 84.66% for the j=2, 24 h fitting and 24 h forecasting configuration, whereas Sentinel-3A improves only over shorter horizons, and Sentinel-6A shows no sustained out-of-sample benefit. Radial-Transverse-Normal (RTN) analysis attributes the successful cases primarily to reductions in transverse-position and radial-velocity errors, consistent with correction of accumulated in-plane phase error. Estimating B* provides no systematic forecasting advantage over the two-parameter correction. Finally, the complete PSO–SGP4 recalibration is validated through Processor-in-the-Loop implementation on STM32H563ZI and STM32F411CE microcontrollers, demonstrating host–embedded numerical consistency and feasibility under constrained computational and memory resources. Validation using actual on-board GNSS navigation solutions, including their characteristic measurement uncertainty and data availability, is left for future work.