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Study of fringe tracking for high-precision space-based interferometers

The purpose of the fringe tracking algorithms is to maintain lock on the target star after acquisition and to obtain the most accurate estimate possible of the scientific quantity (or quantities) of interest in the presence of dynamic disturbances to the spacecraft/interferometer ensemble. This study carries out an analysis of the performance and robustness achievable by four candidate estimation techniques when applied to an ultra-high-precision fringe tracking task (5 micro-arcsecond ultimate accuracy). The first class of fringe trackers studied include the Extended Kalman Filter. This class is followed by extensions to second and third order nonlinear filters developed by the authors. The higher order filters have expanded regions of convergence. Third, we consider the use of an invariant filter (IF) to estimate the angle between two target stars (using POINTS as a test case). The IF offers the advantage of improved robustness in the dynamical case, being in effect `invariant' to dynamics. Finally Discrete Bayes Algorithms make use of Bayes' decision rule to propagate the a posteriori distribution of the true parameter and take into account the discrete character of the Poisson photon arrival events. Variations of these algorithms, known as multiple hypotheses trackers, offer great promise for dim star tracking. An exploration of filter performance with respect to several parameters is carried out analytically and selected Monte Carlo simulations are carried out both to verify analytical predictions and to study performance.