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LISA, the Laser Interferometer Space Antenna, and its technology-demonstrating precursor LISA Pathfinder, form an ESA/NASA collaborative project, selected as an ESA Cornerstone and included in NASAs Beyond Einstein initiative.The primary objective of the LISA mission is to detect and observe gravitational waves emitted from Massive Black Holes and galactic binaries in the low-frequency band which ranges from 0.1 mHz up to 1 Hz with a goal of extending the measurements down to 30 µHz. The underlying measurement principle is a laser interferometry system built up with three satellites that are flying in a triangular constellation with an edge length of 5 million km.The interferometric measurements of LISA are only possible once the three laser links between the three spacecraft of the LISA constellation are established. This phase is addressed as the constellation acquisition for LISA. LISA constellation acquisition is challenging, given the weak signal received by the spacecraft 5 million km away, inherent limits of the attitude sensors accuracy, orbit determination accuracy issues and the time required to phase-lock the incoming and outgoing laser signals. In order to counteract all these adverse constraints and make the LISA constellation acquisition possible, the laser pointing must satisfy challenging performance requirements during the whole duration of the acquisition phase. This thesis proposes a strategy for the acquisition control of the LISA formation based on the use of a Kalman filter: it pre-processes the measurement data providing enhanced signals for the controller, which has the very same structure used in the science mode. The Kalman filter is designed such that it realizes a continuous blend of the sensors data, providing a massive disturbance rejection. Simulations and sensitivity analysis are performed in order to demonstrate the feasibility of the proposed approach.