Showing papers by "Alex Bombrun published in 2010"
TL;DR: In this article, a simplified version of the least square problem is studied in which the only unknowns are the astrometric parameters for a subset of the stars and the continuous three-axis attitude, thus neglecting further calibration issues.
Abstract: The Gaia space astrometry mission (to be launched in 2012) will use a continuously spinning spacecraft to construct a global system of positions, proper motions and absolute parallaxes from relative position measurements made in an astrometric focal plane. This astrometric reduction can be cast as a classical least-squares problem, and the adopted baseline method for its solution uses a simple iteration algorithm. A potential weakness of this approach, as opposed to a direct solution, is that any finite number of iterations results in truncation errors that are difficult to quantify. Thus it is of interest to investigate alternative approaches, in particular the feasibility of a direct (non-iterative) solution. A simplified version of the astrometric reduction problem is studied in which the only unknowns are the astrometric parameters for a subset of the stars and the continuous three-axis attitude, thus neglecting further calibration issues. The specific design of the Gaia spacecraft and scanning law leads to an extremely large and sparse normal equations matrix. Elimination of the star parameters leads to a much smaller but less sparse system. We try different reordering schemes and perform symbolic Cholesky decomposition of this reduced normal matrix to study the fill-in for successively longer time span of simulated observations. Extrapolating to the full mission length, we conclude that a direct solution is not feasible with today’s computational capabilities. Other schemes, e.g., eliminating the attitude parameters or orthogonalizing the observation equations, lead to similar or even worse problems. This negative result appears to be a consequence of the strong spatial and temporal connectivity among the unknowns achieved by two superposed fields of view and the scanning law, features that are in fact desirable and essential for minimizing large-scale systematic errors in the Gaia reference frame. We briefly consider also an approximate decomposition method a la Hipparcos, but conclude that it is either sub-optimal or effectively leads to an iterative solution.
20 citations
01 Dec 2010
TL;DR: Astrometric Global Iterative Solution (AGIS) as discussed by the authors is a framework for combining the available observations per star obtained during Gaia's 5yr lifetime into a single global astrometric solution.
Abstract: Gaia is ESA’s ambitious space astrometry mission with a foreseen launch date in early 2012. Its main objective is to perform a stellar census of the 1000 Million brightest objects in our galaxy (completeness to V=20 mag) from which an astrometric catalog of micro-arcsec level accuracy will be constructed. A key element in this endeavor is the Astrometric Global Iterative Solution (AGIS) - the mathematical and numerical framework for combining the ≍80 available observations per star obtained during Gaia’s 5yr lifetime into a single global astrometric solution. At last year’s ADASS XVIII we presented (O4.1) in detail the fundamental working principles of AGIS, its development status, and selected results obtained by running the system on processing hardware at ESAC, Madrid with large-scale simulated data sets. We present here the latest developments around AGIS highlighting in particular a much improved algebraic solving method that has recently been implemented. This Conjugate Gradient scheme improves the convergence behavior in significant ways and leads to a solution of much higher scientific quality. We also report on a new collaboration aiming at processing the data from the future small Japanese astrometry mission Nano-Jasmine with AGIS. (Less)