Astrometric Systematic Errors as a Limiting Factor in Stellar-Aberration-Based Autonomous Navigation

Motivation and approach

Stellar-aberration-based navigation (StarNAV) estimates spacecraft velocity from velocity-induced changes in the apparent angular separations between stars. Achieving metre-per-second velocity sensitivity requires milliarcsecond-level angular measurements, so uncertainty in the transformation from focal-plane coordinates to celestial directions must be assessed alongside sensor noise and astrometric catalog errors.

We select 477,502 Gaia DR3 stars with $G<10$ mag and propagate their positions and covariances to J2026.0. Using HEALPix with $N_{\mathrm{side}}=64$, we divide the sky into 49,152 fields of approximately $0.84,\mathrm{deg}^{2}$ each, representing the adopted approximately one-degree field scale. The median field contains about eight reference stars. We compare nine plate models to quantify the effects of model complexity, reference-star density, and spatial distribution on plate-solution uncertainty.

Main results

• Under the plate-constant-variance metric, the four-parameter linear model is the most stable option for the adopted sparse fields. The median propagated positional uncertainty is 0.95 mas, and the 95th percentile is 1.7 mas.
• More complex models are more sensitive to limited reference-star counts and uneven spatial distributions. Additional distortion terms can increase variance or cause poorly conditioned solutions.
• Using the first-order scaling $\delta v \sim c,\delta\theta$, the reported angular-uncertainty range of 0.6–1.7 mas corresponds to an approximate velocity-error scale of 0.9–2.5 m/s, with a median of about 1.4 m/s.
• Low plate-constant variance does not guarantee adequate correction of real optical distortion. A linear model can leave nonlinear distortion biases that are not included in the variance calculation.

The velocity conversion is an order-of-magnitude estimate of the plate-solution contribution, not a prediction or lower bound for the complete navigation solution. Future StarNAV systems should jointly account for plate-solution uncertainty, residual distortion bias, measurement geometry, sensor noise, and catalog errors.