Frequency decomposition of astrometric signature of planetary systems

We present a theoretical analysis of astrometric searches for extrasolar planets with the Space Interferometry Mission (SIM). In particular, we derive a model for future measurements with SIM and discuss the problem of reliable estimation of orbital elements of planets. For this purpose we propose a new method of data analysis and present a numerical test of its application to simulated SIM astrometric measurements of the upsilon And planetary system. We demonstrate that our approach allows for successful determination of its orbital elements. Most of the proposed approach can be adopted for other astrometric missions.