Implementation of the global parameters
determination in Gaia's Astrometric Solution (AGIS)
F. Raison*, A. Olias*, D. Hobbs**, L. Lindegren*** European Space Astronomy Centre of ESA, Madrid, Spain,** Lund Observatory, Lund, Sweden.

Abstract
Gaia is ESA's 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 IterativeSolution (AGIS). A core part of AGIS is to determine the accurate spacecraft attitude, geometric instrument calibration and astrometric model parameters for a well-behaved subset of all
the objects (the `primary stars'). In addition, a small number of global parameters will be estimated, one of these being PPN γ. We present here the implementation of the algorithms
dedicated to the determination of the global parameters.

A. Motivation

B. Gaia measurements• The global parameters estimation provide a number of stringent tests of general relativity.
• Gaia is expected to constrain 2 parameters of the PPN formalism: PPN γ, measuring the curvature of space-time through gravitational light deflection.
 PPN β, measuring the degree of nonlinearity in the superposition law of gravity.

• Gaia is a scanning satellite, hence stars transit through the focal plane continuously inthe along-scan direction, CCDs are operated in Time-Delayed Integration (TDI) mode
synchronized with the star motion on the focal plane.
• Due to the large amount of CCDs and the limited downlink bandwidth, the amount ofdata to be gathered has been reduced by defining windows around the selected objects.

• Based on simulations (AGISLab), AGIS could provide a value of PPN γ about 10-6, which
is significantly better than today’s best estimate from the Cassini mission (10-5).

transiting star
0.930 m• Some 700 measurements per
object are expected over the 5 year
mission ( 1012 observations)C. AGIS• The best global match between all measurement data and an observational model
involving the unknown source, attitude, calibration, and global parameters is sought in aleast-square sense using normal equations and a block-iterative solution scheme.

WFS

0.420 mWFSRVS
Radial-Velocity
Spectrometer CCDs

• The "Time of observation" forimage centre relative to CCD
is determined to ~200 mas precision(magnitude 15). They are used as
input in AGIS.

BAM

SMSky
Mapper
CCDs• A Global Update block is used for global parameters determination.

BPBlue Photometer CCDs

• AGIS is the mathematical and numerical scheme that will generate the core astrometricsolution, i.e. the standard astrometric parameters (position, parallax , proper motion, radialvelocity) for all observed celestial objects brighter than G=20 mag with targeted accuracies(e.g. <10 µas [G<10 mag], <25 µas [G=15 mag], <300 µas [G=20 mag]).

AF
Astrometric Field CCDs

Figure courtesy Alex Short

D. Implementation

algorithms

1 Launcher: runs on every node of the cluster.
 starts the appropriate processes.

4 Algorithms:
 Source Update, Attitude Update, Calibration
Update, Global Update (optional).
 Client/Server scheme.
5 Taker: is a (Global)Collector (client) attached to datatrain.
 sends AstroElementaries to the server.

2 Run Manager: controls the overall AGIS processing.
 publishes jobs on the Whiteboard.
 handles multiple iterations.
 checks for convergence of the solution by
consulting the Convergence monitor.

6 Update Server:
 buffers the list of AstroElementaries receivedfrom Collector.
 Processes them accumulating the updateinformation.

3 Data trains:
 pick jobs from the Whiteboard.
 receive objects from the DB(AstroElementaries with “times of observation”).
 pass the objects to the attached algorithms.

This architecture was designed tomaximize the degree of parallelism in theprocessing.

(Global)UpdateServer:
 pass the AE to (Global)UpdateWorker (GlobalGIS).
 one (Global)UpdateServer object is a master and the others are slaves.
 Master will collect all the intermediate results from the slaves.
 Master will ask its (Global)UpdateWorker to perform the final
calculation.

E. Algorithms for Global Update block• Assuming a centered Gaussian observation noise of standard deviation σL theastrometric problem is equivalent to a weighted least-square minimization ofminxJ (x) = ∑ (tLobs − fL (x))

2LwL= ∑ R (x)2WL
σL2 + εL2 L L

sum over observations

In the case of PPN γ, the partial derivatives∂R L∂xi.e.

∂R L∂γare obtained through a general relativity model (Gaia Relativistic Model) that provides asingle consistent relativistic framework for the whole Gaia processing.

statistical weight
Observed-Calculated (Residual)• This scheme performs a special treatment of outliers (involving the down-weighting
function wL and the fraction ε of data having a larger standard deviation).
• The solution vector x=(g1, g2, .... , gn) gives the optimal agreement between theobservational model f and the actual observations• What is really solved in practice is a system of normal equations system for the updates∆x to the parameters x:∂R L
 ∂R L ∂R L∑ ∂x ∂x ′ W L  ⋅ ∆x = −∑ ∂x R LWL
 L
L

⇔

N ⋅ ∆x = b

N is a symmetric n×n matrix, b is an array of length n = number of parameters

F. Preliminary Results• So far, the ~10-5 level of accuracy was reached with: PPN γ as first global parameter.
 <parallax> as a second parameter to reduce the impact of the statistical correlation
between PPN γ and the parallax.
 167 x 106 AstroElementaries ( 2 x 106 simulated sources).
 Starting value: PPN γ =1.1
 Simulated true value: PPN γ =1.0
• Improved implementation and a larger set of simulated observations should allow toreach the expected 10-6 level of accuracy.