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