Frequency decomposition of astrometric signature of planetary systems

We present theoretical analysis of the astrometric searches for extrasolar planets with the Space Interferometry Mission (SIM). Particularly, we derive a model for the 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 on simulated SIM astrometric measurements of $\upsilon$ Andromedae planetary system. We demonstrate that our approach allows successfull determination of its orbital elements.