Evaluating the On-Orbit Relative Navigation Performance of Modified Adaptive Kalman Filter with GPS Ambiguity Resolution

For real-time relative positioning of formation-flying nanosatellites in free-space optical communication, this study presents an accurate carrier-phase-based differential global positioning system (CDGPS) technique using a modified adaptive Kalman filter (MAKF) with the least-squares ambiguity decorrelation adjustment (LAMBDA) method as an integer ambiguity resolution (IAR) technique. The proposed relative navigation algorithm aims to enhance the real-time positioning performance of two formation-flying satellites in low-Earth orbit (LEO) and long-baseline environments in the very-high-speed intersatellite link system using an infrared optical terminal and nanosatellite (VISION) mission. To overcome the instability and complexity of calculations caused by distance-based noise in LEO satellites, dual-frequency GPS receivers are required to correct ionospheric delay and implement an onboard filter with single-differenced (SD) data. To improve the efficiency and stability of the MAKF algorithm upon the extended or adaptive Kalman filter system in a low-dynamic scenario, a revised estimation of innovation- and residual-based noise covariance was proposed in this study. The proposed algorithm was verified and evaluated in terms of the pointing and positioning accuracy using software- and hardware-based simulations. According to the software-based assessment, the MAKF improved the 3D relative positioning accuracy by 40% and 5% compared to the EKF and AKF models, respectively, in the mission scenario at a 1,000 km baseline with fixed ambiguities. The proposed algorithm can not only improve the relative navigation performance compared to the EKF and AKF, but also decrease the computational complexity with a simplified adaptation method compared to the AKF model in the low-dynamic scenario, for example, near-solar-minimum environments. The hardware-based simulation results also demonstrated that the relative positioning accuracy of the proposed algorithm was improved by 6% compared to the AKF model at a 1,000 km relative distance with a reduced computational burden.