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If an orbit is fitted from combined RV and astrometric data, the orbit shouldbe physically consistent with both data sets. The Keplerian orbit of a planetis a highly nonlinear function of seven parameters. The astrometric orbitproblem can be partially linearized via transformation to four linearparameters (related four Thiele-Innes constants) plus three nonlinearparameters: eccentricity, period and periastron time. The RV orbit problem canbe partially linearized via transformation to two additional linear parametersplus the same three nonlinear parameters. Unfortunately, the two linearparameters from RV are not linearly related to the four linear parameters fromastrometry. Because of this difficulty, currently available algorithms forfitting combined RV and astrometric data to multiple-planet systems employ atleast five nonlinear parameters per planet. We have developed a new algorithmfor fitting orbits of multiple planet systems from combined data sets of radialvelocity and astrometric measurements. The new algorithm satisfies theRV-astrometry consistency requirement, while using three nonlinear parametersper planet. We expect the reduction in nonlinearity to give the algorithm asignificant advantage in computation speed over existing algorithms. In thiswork, we describe the algorithm, which has been validated in the context of arecent double-blind planet detection simulation study.

A new algorithm for fitting orbits of multiple-planet systems to combined RV and astrometric data