Adaptive Attitude Estimation for Multiple-Surface Object Using Light Curve Glints

Abstract

Light curve inversion enables the estimation of orbit, attitude, optical properties, and shape of space objects. Because a light curve is the temporal evolution of a scalar apparent magnitude, the estimation problem can be ill-posed owing to the non-uniqueness of the attitude that reproduces a given light curve. The initial estimate in Kalman filtering can therefore be sensitive, and, depending on the object properties, observation geometry, and number of estimated parameters, an inaccurate initial estimate may lead to divergence of the filter. A previous study uses a sudden change of light curves, called glint, to constrain the range of attitude estimate. The current paper extends the attitude estimation method using glint for multiple-surface objects. Such objects have multiple attitudes to yield glint, and the attitude estimate is not uniquely determined. To address this issue, this paper employs the interacting multiple model (IMM) algorithm that runs multiple parallel filters with model interaction in the estimation sequence. Each filter assumes that the glint occurs on the corresponding surface. The mode probability is updated by the likelihood of each filter, determining the correctness of the hypotheses. Furthermore, the mixing step in the IMM allows interaction among the filters through a transition probability matrix, enabling adaptation to the time-varying glint source. Numerical simulations are conducted for a box satellite in a geosynchronous orbit. Monte Carlo trials with initial attitude errors of up to 80~deg show that the proposed method improves the convergence rate from 10\% for a single surface filter to 73%, and the mixing step is shown to be essential, since the convergence rate drops to 40% when it is removed.