Filtering attitude series data and extracting angular rates with moving-window least-squares polynomial fitting

Abstract Data series of attitudes determined using vector measurements are widely available in many satellite missions. These data series are reprocessed to provide filtered attitude estimates with improved accuracies. A moving-window polynomial fitting method is employed. First, the attitude data within a moving window are transformed to small-magnitude relative attitudes with respect to a chosen reference frame. Second, these relative attitudes, often unit-norm quaternions, are reparameterized as Gibbs vectors. Third, the parameters of the empirically chosen polynomials representing the kinematics of the relative Gibbs vectors within the moving window are estimated with least-squares method. Fourth, filtered attitudes can be readily constructed with the Gibbs vectors calculated with the polynomial model at any time instant not necessarily those of the data points. Furthermore, with the Gibbs vectors and their derivatives calculated using the polynomial model, the angular rates can be readily extracted also at any time instant, as byproducts. Experiments with simulation and real data are conducted; and the results show the performance of the proposed method in terms of both attitude filtering and angular rates extraction.