Efficient fitting of multiplanet Keplerian models to radial velocity and astrometry data

TL;DR

This paper presents a fast, analytic derivative-based method for fitting multi-planet Keplerian models to high-precision radial velocity and astrometry data, improving efficiency and convergence especially for complex systems.

Contribution

It introduces an analytic derivative approach for Levenberg-Marquardt fitting of multi-planet models, enabling faster and more accurate orbital parameter estimation from RV and astrometry data.

Findings

Demonstrated speed-up and convergence improvements in fitting five-planet systems.

Applied method to published data for 55 Cnc, validating its effectiveness.

Suitable for detecting Earth-massed planets in habitable zones.

Abstract

We describe a technique for solving for the orbital elements of multiple planets from radial velocity (RV) and/or astrometric data taken with 1 m/s and microarcsecond precision, appropriate for efforts to detect Earth-massed planets in their stars' habitable zones, such as NASA's proposed Space Interferometry Mission. We include details of calculating analytic derivatives for use in the Levenberg-Marquardt (LM) algorithm for the problems of fitting RV and astrometric data separately and jointly. We also explicate the general method of separating the linear and nonlinear components of a model fit in the context of an LM fit, show how explicit derivatives can be calculated in such a model, and demonstrate the speed up and convergence improvements of such a scheme in the case of a five-planet fit to published radial velocity data for 55 Cnc.