A practical re-weighting scheme of data fitting: application to asteroids orbit determination with Gaia

TL;DR

The paper introduces a simple reweighting scheme for weighted least squares that improves asteroid orbit determination by effectively handling heterogeneous observational uncertainties, especially with Gaia data.

Contribution

It presents a practical, three-step reweighting method to enhance the consistency and accuracy of parameter estimation in the presence of mixed-precision data.

Findings

Reweighted solutions better match older data for several asteroids.

Increasing Gaia observation uncertainties improves fit quality, highlighting systematic biases.

Reweighting reduces impact probability estimates for near-Earth asteroid 2024 YR4.

Abstract

The method of weighted least squares is widely used in parameter estimation problems such as asteroid orbit determination. A key difficulty is the treatment of observational uncertainties, especially when combining heterogeneous datasets with differing precision. We propose a simple reweighting scheme that adjusts the contribution of each measurement group to ensure a statistically consistent least-squares solution. It consists of three steps: (i) estimating error standard deviations for each observational subset, (ii) rescaling their weights by the corresponding variances, and (iii) a weighted least-squares fit with the adjusted weights. We apply this to heliocentric orbit fitting of asteroids using ground-based astrometry and high-precision Gaia measurements. We validated the method by fitting each orbit to a restricted set and comparing with the complete set of measurements. For 7 objects, the reweighted solutions provide significantly improved agreement with older data. The most dramatic case is asteroid (21) Lutetia, where increasing the effective uncertainty of Gaia observations by a factor of 17 yields a substantially better fit, indicating the importance of accounting for systematic biases in high-precision datasets. We further apply the scheme to near-Earth asteroid 2024 YR4, grouping observations by visual magnitude. The reweighted orbit produces smaller uncertainty regions and a more stable solution, reducing predicted impact probabilities by roughly an order of magnitude. All computed probabilities remain below 0.5%, under the 1% International Asteroid Warning Network (IAWN) alert threshold. This reweighting procedure provides a practical way to combine heterogeneous measurements, improving the reliability of orbit determination and impact-risk assessment. The method is general and can be readily applied to other parameter estimation problems involving mixed-precision data.