Receiver-Side Physics-Informed Residual Digital Twin for Predictive Fine Tracking in Inter-Satellite Optical Links

Track the beam at actuation time

After coarse acquisition and point-ahead compensation, a receiver must suppress residual line-of-sight motion within its fine-tracking range. Sensor noise, vibration and actuator latency mean that an accurate estimate of the beam’s current angle may already be out of date when a steering correction takes effect.

The architecture combines quadrant-photodetector sensing, an extended Kalman filter (EKF), nominal LOS dynamics, a residual predictor and a delayed fine-steering-mirror (FSM) command queue. The EKF estimates uncompensated LOS motion using the known correction currently applied to the optics. An FSM command changes the optical pointing geometry; it does not accelerate the spacecraft or enter the physical LOS transition.

Manuscript · Sections I–II; Fig. 1; Eqs. (1)–(14)

Learn the mismatch and preserve the physical model

A constant-angular-rate model supplies the nominal transition. A normalized autoregressive ridge regressor learns only its residual mismatch, using consecutive synchronized EKF posterior estimates from separate calibration traces. It does not receive the true simulated state during fitting.

The predictor rolls the nominal transition and a bounded learned residual forward over the command delay. Pending commands remain known optical offsets. The same nominal EKF, gain, actuator authority and measurement noise are retained across reactive, nominal-predictive and PIR-Twin modes, isolating the contribution of improved forecasting.

Tuning uses a separate 2 s trace. Four independent 5 s calibration traces yield 18000 valid transition samples after discarding the initial 0.5 s of each trace. The learned weights are fixed before testing on ten unseen 2 s realizations.

Manuscript · Section III; Eqs. (15)–(34); Section IV-A

Controlled simulation results

The model uses a 1000 km link at 1550 nm, a 30 mm beam waist and a 16.45 µrad Gaussian half-angle, with a 100 mm receive aperture. Fine tracking operates at 1 kHz, nominally with a 2 ms delay and ±50 µrad per-axis correction authority. The independently generated LOS trajectories include bias, drift, vibration and randomized low-frequency tones.

At the nominal 2 ms delay, Table I reports mean two-axis pointing RMS of 25.7 ± 0.6 µrad open loop, 2.12 ± 0.08 µrad reactive, 2.11 ± 0.08 µrad nominal predictive, and 1.82 ± 0.11 µrad PIR-Twin. The reported ± values are sample standard deviations across ten test seeds. The manuscript reports a 14.1% improvement over reactive tracking from its unrounded results.

Actuation-time prediction RMSE falls from 1.95 ± 0.01 µrad for reactive tracking to 1.62 ± 0.05 µrad for PIR-Twin. Its equivalent Gaussian angular penalty falls from 0.125 to 0.088 dB, with similar applied-command amplitudes. This optical-quality proxy is not a measured received-power or communications-throughput result.

Manuscript · Section IV-A–C; Table I; Eqs. (35)–(41)

Robustness and boundaries

The fixed residual model has the lowest mean pointing error across the tested 1–12 ms delays and 1×, 1.5× and 2× time-varying LOS-motion amplitudes. At 12 ms under nominal motion, pointing RMS is 12.56 µrad for nominal prediction, 6.33 µrad reactive and 5.94 µrad PIR-Twin. The stronger-motion tests increase the reported 2 ms improvement over reactive tracking to 20.7% and 23.7%, without retraining.

These are controlled numerical results. The QPD observation assumes sufficiently large detector area, negligible quadrant gaps and fixed normalized measurement covariance. The actuator is represented by an effective fixed delay and finite angular authority. The work does not demonstrate on-orbit hardware, field robustness to every disturbance, or end-to-end data-rate gains.

Manuscript · Section II-B; Section IV-D; Fig. 2; Section V