Real-Time LEO Satellite Kinematic Orbit Determination Using Code-Carrier Smoothing

Dual-frequency ionosphere-free (IF) combinations, commonly used in real-time low Earth orbit (LEO) kinematic orbit determination, effectively remove ionospheric delay errors but significantly amplify noise in code pseudorange observations, thereby limiting orbit accuracy. To address this limitation and enhance real-time orbit precision, this study investigates a code–carrier smoothing approach integrated into a standard point positioning (SPP)-based kinematic orbit determination (OD) framework.

The Sentinel‑6A satellite’s onboard GNSS code pseudorange observations were processed in real-time mode using least squares estimation (LSE) to estimate the satellite’s position, velocity, and clock offset. Ionospheric effects were mitigated by applying IF combinations derived from GPS (L1/L2) and Galileo (E1/E5) dual-frequency signals. To suppress short-term code noise, a Hatch filter-based code–carrier smoothing technique was implemented, in which noisy code pseudorange measurements were combined with precise carrier-phase measurements to produce stabilized pseudorange observables. A smoothing window constant of 16 epochs was adopted to enable recursive real-time processing.

GNSS observation data in RINEX format and reference SP3 orbit products for the Sentinel‑6A satellite were obtained from the Crustal Dynamics Data Information System (CDDIS) and the European Space Agency (ESA) archives. The dataset consisted of 10-second sampling over a 24-hour period starting at 00:00 UTC on April 20, 2025. Broadcast ephemerides of GPS and Galileo satellites were used for real-time orbit derivation.

The kinematic orbit estimates were evaluated at 10-second intervals using the SP3 orbits as reference truth. Without smoothing, the root-mean-squared errors (RMSEs) were 59.5 cm (radial), 27.9 cm (along-track), and 22.9 cm (cross-track), yielding a 3D RMSE of 69.6 cm. With the Hatch filter applied, the corresponding RMSEs improved to 50.0 cm, 23.1 cm, and 18.1 cm, resulting in a 3D RMSE of 58.0 cm. These results represent improvement rates of 16.0%, 17.2%, 21.0%, and 16.7% in the radial, along-track, cross-track, and 3D directions, respectively.

The findings confirm that Hatch filter-based code–carrier smoothing effectively reduces pseudorange noise and improves the precision of real-time kinematic orbit determination for LEO satellites.