Gravitational waves detection is a challenging scientific objective, faced by scientist in the last 100 years, when Einstein theorized their existence. Despite multiple attempts, it was only in 2016 that the first observation of a gravitational wave was officially announced. The observation, worth a Nobel Prize, was made possible thanks to a worldwide collaboration of three large ground-based detectors. When detecting gravitational waves from ground, the noisy environment limits the frequency bandwidth of the measurement. Thus, the type of cosmic events that are observable is also limited. For this reason, scientists are developing the first gravitational waves detector based in space, which is a much quieter environment, especially in the sub-Hertz bandwidth. The space-based detector is named laser interferometer space antenna (LISA) and its launch is planned for 2034. Due to the extreme complexity of the mission, involving several new technologies, a demonstrator of LISA was launched and operated between 2015 and 2017. The demonstrator mission, called LISA Pathfinder (LPF), had the objective to show the feasibility of the gravitational waves observation directly from space, by characterizing the noise affecting the relative acceleration of two free falling bodies in the milli-Hertz bandwidth. The mission was a success, proving the expected noise level is well below the minimum requirement. The free-falling bodies of LPF, called test masses (TMs), were hosted inside dedicated electrode housings (EH), located approximately 30 cm apart inside the spacecraft. When free falling, each TM stays approximately in the center of the EH, thus having milli-meter wide gaps within the housing walls. Due to the presence of such large gaps, the TMs were mechanically constrained by dedicated mechanisms (named CVM and GPRM) in order to avoid damaging the payload during the launch phase and were released into free fall once the spacecraft was in orbit. Prior to the start of the science phase, the injection procedure of the TMs into free-fall was started. Such a procedure brought each TM from being mechanically constrained to a state where it was electro-statically controlled in the center of the EH. Surprisingly, the mechanical separation of the release mechanism from the TM caused unexpected residual velocities, which were not controllable by the electrostatic control force responsible for capturing the TM once released. Therefore, both the TMs collided with either the surrounding housing walls or the release mechanism end effectors. It was possible to start the science phase by manually controlling the release mechanism adopting non-nominal injection strategies, which should not be applicable in LISA, due to the larger time lag. So, since any release mechanism malfunctioning may preclude the initialization of LISA science phase, the GPRM was extensively tested at the end of LPF, by means of a dedicated campaign of releases, involving several modifications to the nominal injection procedure. The data of the extended campaign are analyzed in this work and the main conclusion is that no optimal automated release strategy is found for the GPRM flight model as-built configuration that works reliably for both the TMs producing a nominal injection procedure. The analysis of the in-flight data is difficult since the gravitational referencesensor of LPF is not designed for such type of analysis. In particular, the low sampling frequency (i.e., 10 Hz) constitutes a limiting factor when detecting instantaneous events such as collisions of the TM. Despite the difficulties of extracting useful information on the TM residual velocity from the in-flight data, it is found that the main cause of the uncontrollable state of the released TM is the collision of the TM with the plunger, i.e., one of the end-effectors of the GPRM. It is shown that the impact is caused by the oscillation of the plunger or by the elastic relaxation of the initial preload force that holds the TM. At the end of the analysis, some improvements to the design of the release mechanism are brie y discussed, aimed at maximizing the probability of performing a successful injection procedure for the six TMs that will be used as sensing bodies in the LISA experiment.

LISA Pathfinder (LPF) has been a space mission led by ESA with NASA contributions, operating between March 2016 and July 2017. LPF demonstrated the feasibility of setting bodies in space along freely-falling geodetic trajectories, complying with the residual acceleration requirements of the future gravitational-wave observatory LISA. After operations, the LPF Collaboration pointed out that two phenomena, affecting the sub-mHz performance, were not completely understood and needed deeper analyses. This, despite performing better than requirements. Such phenomena are, namely, the low-frequency acceleration noise, and the sub-pN transient acceleration glitches. This thesis work focuses entirely on analyzing these observations, in view of the future mission LISA. Regarding the low-frequency sub-mHz noise, first, we make a preliminary analysis. We investigate its evolution in time, its properties, its stability, and its nature. We find that the low-frequency noise has had a remarkably stable behavior for nearly two years, but noise fluctuations are not compatible with an overall unique noise. We develop results on multivariate spectral estimation. Implementing results from complex-variable statistics, we show that cross-power spectral density matrices follow complex-Wishart probability distributions; we develop a Bayesian tool for the posterior inference of spectral parameters. We develop decorrelation tools to understand the measured noise's physical origin. In particular, we aim at finding, if any, correlations between the main acceleration measurement and synchronously measured time series. Then, we summarize the most recent understanding of the LPF acceleration performance. We expand previous analyses about the LPF outgassing environment, through the analysis of the white "Brownian" noise, and the long-term quasi-static acceleration drift observed on LPF, proposing a physical model. We extensively analyze the second phenomenon impacting low-frequency performances, the acceleration transient glitches. We show that LPF glitches spanned a wide range of amplitudes, transferring impulses between a few fN s, to some nN s, and showing durations ranging from a few seconds to hours. We show that LPF glitches fall into two rather distinct categories: fast transients in the interferometric motion readout and long-lasting sub-pN force transient events, acting on the test masses. We present an analysis of the physical and statistical properties of both, including a cross-investigation with other time series and other dynamical variables, and examine the possible sources of glitches, identifying the most likely ones.