source, and E is the unit vector perpendicular to the 
optical axis, and directed along the instantaneous 
scanning velocity. The indices / and k refer to star i at 
time k, respectively. 
In this context one assumes that both classical and 
relativistic apparent places effects are removed a priori 
from the observed star position. In particular, the vector 
F is a function of the 5 astrometric parameters which 
one wants to estimate, namely: F = r(cc,8,p a ,p 6 ,it) , 
Where a and 8 are the stellar coordinates, p a , p§ 
are the stellar proper motions, and 71 the parallax. 
In a more explicit form, the following vectorial 
expression holds: 
r{t) = û b (T)[l+nV R (t-T)]+nü b V T {t-T)+ nû Sun p(t) (4) 
where t is the epoch of observation, T the reference 
epoch, üb =Uf } (<x,b) is the unit vector in the barycentric 
direction to the star, V T and V R are the star barycentric 
tangential and radial velocity (AU/year), ) 
is the unit vector in the direction of V T , ü Sun is the unit 
vector Satellite-Sun, and p is the distance Satellite-Sun 
(AU). 
In analogy with the HIPPARCOS mission, one of the 
key requirements of GAIA is the presence of two FOVs 
separated by a large angle. This peculiarity, which was 
originally devised in order to estimate absolute 
parallaxes by observing couples of widely separated 
stars, allows to easily reconstruct the arcs between 
stars simultaneously observed in the two FOVs. 
Therefore, the data reduction problem can be 
assimilated to that of a global network adjustment of 
arcs on the sphere, irrespective of the satellite attitude. 
However, a correlation analysis performed on this 
model has shown that in the arc approach there is a 
non negligible correlation of about 0.5 among arcs 
having one end in common (Betti et al., 1983). 
On the other end, one can abandon the concept of arcs 
and use the fact that the observations are made in two 
distinct directions separated by a large basic angle, in 
order to determine with sufficient accuracy the spin axis 
attitude at any instant of time. 
In such an approach, the equation (3) is regarded as 
the condition equation, which is linearized as follow: 
5-X/a = &n k * E ik + 5E ik * r ik (5) 
where 6E ik is forced to be in the scanning plane, and 
r ik , Ëjk are zero-order approximations. 
The along satellite velocity 8E k /81 can be modeled by 
a small number of parameters, as it is a very smooth 
motion, while the fact that the same stars are observed 
several times during the mission lifetime, gives the 
necessary redundancy to the linearized 
equation system. 
Noting also that only a small number of attitude 
unknowns is linked in time, since there is a discontinuity 
every time the satellite path is actively corrected, the 
structure of the resulting normal matrix of the system of 
equations has a two-by-two block structure of the type: 
where B and C are block-diagonal, and refer to 
astrometric and attitude unknowns respectively: V and 
its transpose V come from the combination of both 
astrometric and attitude unknowns, and are therefore 
rather full matrices. Given the extremely large 
dimension of the system, numerical strategies must be 
explored in order to make the solution feasible. 
Numerical experiments reported in Sansô et al. (1989) 
on simulated HIPPARCOS data showed that this 
system can be solved using a simple iterative scheme. 
First, the attitude is kept fixed and a solution is made for 
the stellar astrometric parameters only; then the star 
parameters are fixed, and the attitude is adjusted. The 
whole process is iterated until convergence is reached. 
With this scheme, even though only partial knowledge 
of the covariance of the estimated parameters is 
retained, the numerical complexity of the problem is 
drastically reduced since only the block-diagonal sub 
matrices need to be inverted. 
CONCLUSION 
GAIA’s feasibility studies have shown that this mission 
has the potential to perform global astrometry at the 
level of 10 pas. 
Most of the studies carried out for GAIA are also 
relevant to the new generations of ground and space 
instrumentation, which make use of highly accurate 
interferometry as well as active control techniques. 
Further development of the concepts addressed in this 
paper, regarding in particular detection system 
optimization, telemetry data throughput, and data 
reduction, are underway. 
References 
Betti B., Mussio L, Sansô F., 1983, in “The First FAST 
Thinkshop”, ed. P.L. Bernacca, Padova University, pp. 281- 
298 
Bucciarelli B, Lattanzi M., Spagna A., 1997, Proc. ESA Symp. 
Hipparcos Venice ’97, Isola S. Giorgio, Venezia, Battrick B. 
ed., ESA Publ. Division, ESA SP-402, pp. 277-279 
Cesare S., Active Pointing of Large Telescope & Attitude 
Measurement Transfer Systems, Final Presentation, SD-PB- 
AI-0301, October 14, 1998, ESTEC-Noordwijk 
Gai M., Casertano S., Carollo D„ Lattanzi M.G., 1998, 
Location Estimators for Interferometric Fringes, Publ. Astron. 
Soc. Pacific, 110, pp. 848-862 
Gai M„ Bertinetto F., Bisi M., Canuto E., Carollo D., Cesare S., 
Lattanzi M.G., Mana G., Thomas E., Viard T., 1997, GAIA 
Feasibility: Current Research on Critical Aspects, Proc. ESA 
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Battrick B. ed., ESA Publ. Division, ESA SP-402, pp. 835-838 
Lindegren L., M.A.C. Perrymann, 1996, A&AS, 116, 579 
Sansô F„ Betti B., Migliacci F., 1989, ESA SP-1111, Vol. 3, 
The Data Reduction, pp. 437-455 
A'A= 
B 
V 
V’ c 
153