Efficient Fitting of Multiplanet Keplerian Models to Radial Velocity and Astrometry Data

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 −1 and μas 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 RV data for 55 Cnc.