Covariance Analysis of Astrometric Alignment Estimation Architectures for Precision Dual Spacecraft Formation Flying

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Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing precision dual spacecraft formation flying to enable a “virtual” telescope. Using precision dual spacecraft alignment, very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Proposed science missions include astrophysics concepts with spacecraft separations from 1000 km to 25,000 km, such as the Milli-Arc-Second Structure Imager (MASSIM) X-ray telescope and the New Worlds Observer exoplanet mission as well as, heliophysics concepts for solar coronagraphs and X-ray imaging with smaller separations (50m - 500m). All of these proposed missions require advances in precision formation flying of two spacecraft. In particular, very precise astrometric alignment control and estimation is required for accurate inertial pointing of the virtual telescope, which is required to perform the orders of magnitude improvement in the science imaging. The work presented in this paper focuses on analysis of proposed navigation systems and architectures for achieving precise dual spacecraft astrometric alignment. First, the dynamics of dual spacecraft relative motion, within a restricted n-body problem framework, are shown to reduce to a simple linear form and are used in estimation filter design and error analysis for deep space mission applications, such as MASSIM. This model is augmented with simplified measurement process models of relevant measurement types. These include inertial sensors, such as accelerometers and rate gyros, as well as optical alignment sensors, such as star and laser beacon trackers. A consider-state covariance analysis tool is developed from these process models and used to study the performance of proposed estimation architectures for the MASSIM application, specifically focusing on the transverse alignment between the two spacecraft with the goal of achieving mm-scale transverse alignment accuracy.