Structured Innovation-Based Covariance Calibration for TLE-Driven dSGP4–EKF Orbit Determination

Reliable orbit estimation from position observations depends on both nominal propagation and the specification of process and measurement uncertainty. An offline covariance calibration framework is presented for a TLE-driven differentiable SGP4 extended Kalman filter (dSGP4–EKF). dSGP4 supplies the fixed nominal trajectory, while the sensitivities to six TLE initialization elements define a local Cartesian error transition. Error state re-baselining maintains consistent coordinates across catalog changes. Each condition-specific checkpoint contains six positive scalars: three continuous white noise acceleration scales defining the process covariance Q, and three position noise scales defining the measurement covariance R. One-step-ahead innovation negative log-likelihood calibrates these parameters without ground-truth state supervision. The calibrated parameters are frozen during deployment, which requires no neural network inference. Across three Sentinel satellites, three synthetic Gaussian noise levels, and ten paired realizations, the proposed method achieved macro-average component-wise position and velocity RMSEs of 20.64 m and 0.0463 m s−1, respectively. The corresponding values for a supervised observation-conditioned GRU-Q/R point estimator were 20.42 m and 0.0462 m s−1. The proposed method used six trainable parameters per checkpoint, compared with 8886 for GRU-Q/R, and had a median Day-7 filtering time of 13.37 ms versus 40.35 ms. Re-baselining reduced switch-local errors, while the tested initialization, training seed, and window settings produced limited variation for the proposed method. No numerical divergence was observed during the examined 24-h S1A–25 m runs. The learned scales are effective uncertainty parameters rather than uniquely identifiable physical disturbances. These findings are limited to the controlled synthetic observation protocol.