Simulation of Kalman-filter fringe tracking with on-sky measurements of the PRIMA Fringe Sensor Unit
GRAVITY is a second generation instrument for the VLTI that will combine four telescopes in the K band. To achieve astrometric precision of 10μas and angular resolution of 4mas for objects with magnitude up to K=16 in the science beam, its fringe tracker will stabilize fringes to 350nm rms on a reference star as faint as K=10. To efficiently correct both atmospheric piston and longitudinal vibrations, we developed a controller based on Kalman filtering, which is a predictive algorithm providing optimized commands based on a model of the disturbances. In order to validate the Kalman algorithm as a fringe tacker for GRAVITY, we performed numerical simulations of 2-telescope fringe tracking with a Kalman controller with on-sky measurements from the PRIMA Fringe Sensor Unit (FSU). We find that tracking with the Kalman controller is more efficient than with the PRIMA FSU for all archive data provided by ESO. We deduced an average gain of 170nm rms over the residual OPD using the PRIMA FSU.