A practical re-weighting scheme of data fitting: application to asteroids orbit determination with Gaia
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911580625567744 |
|---|---|
| author | Vavilov, Dmitri. E. Liu, Ziyu. Hestroffer, Daniel. Desmars, Josselin. |
| author_facet | Vavilov, Dmitri. E. Liu, Ziyu. Hestroffer, Daniel. Desmars, Josselin. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A practical re-weighting scheme of data fitting: application to asteroids orbit determination with Gaia Vavilov, Dmitri. E. Liu, Ziyu. Hestroffer, Daniel. Desmars, Josselin. Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics 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. |
| title | A practical re-weighting scheme of data fitting: application to asteroids orbit determination with Gaia |
| topic | Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2604.08820 |