LISA is the proposed ESA-NASA gravitational wave detector in the 0.1 mHz -
0.1 Hz band. LISA Pathfinder is the down-scaled version of a single LISA arm.
The arm -- named Doppler link -- can be treated as a differential
accelerometer, measuring the relative acceleration between test masses. LISA
Pathfinder -- the in-flight test of the LISA instrumentation -- is currently in
the final implementation and planned to be launched in 2014. It will set
stringent constraints on the ability to put test masses in geodesic motion to
within the required differential acceleration of 3\times10^{-14} m s^{-2}
Hz^{-1/2} and track their relative motion to within the required differential
displacement measurement noise of 9\times10^{-12} m Hz^{-1/2}, around 1 mHz.
Given the scientific objectives, it will carry out -- for the first time with
such high accuracy required for gravitational wave detection -- the science of
spacetime metrology, in which the Doppler link between two free-falling test
masses measures the curvature. This thesis contains a novel approach to the
calculation of the Doppler response to gravitational waves. It shows that the
parallel transport of 4-vectors records the history of gravitational wave
signals. In practice, the Doppler link is implemented with 4 bodies in LISA and
3 bodies in LISA Pathfinder. To compensate for noise sources a control logic is
implemented during the measurement. The closed-loop dynamics of LISA Pathfinder
can be condensed into operators acting on the motion coordinates, handling the
couplings, as well as the cross-talks. The scope of system identification is
the optimal calibration of the instrument. This thesis describes some data
analysis procedures applied to synthetic experiments and shows the relevance of
system identification for the success of LISA Pathfinder in demonstrating the
principles of spacetime metrology for all future space-based missions.Comment: PhD thesis defended at University of Trento on 26th March 2012.
Advisors: Stefano Vitale, Mauro Hueller. Committee: Eugenio Coccia (Univ. of
Rome, Tor Vergata), Philippe Jetzer (Univ. of Z\"urich), Eric Plagnol
(APC-CNRS, Paris), Rita Dolesi (Univ. Of Trento