Accuracy and covariance analysis of global astrometry with the Space Interferometry Mission

Construction of an all- sky microarcsecond astrometric grid is an essential preliminary step toward global astrometry with the Space Interferometry Mission ( SIM). The general setup of the global astrometry problem is given, and fast, robust algorithms to solve the problem are described. The results of extensive numerical simulations are used to outline the conditions necessary to achieve the performance goal of absolute astrometric accuracy. Rigorous computation of the global covariance matrix makes it possible to correctly interpret and utilize the SIM data. We formulate and resolve the new issue of the basic performance uncertainty of a single astrometric mission.