Optimal attitude and position determination from line-of-sight measurements

In this paper an optimal solution to the problem of determining both vehicle attitude and position using line-of-sight measurements is presented. The new algorithm is derived from a generalized predictive filter for nonlinear systems. This uses a one time-step ahead approach to propagate a simple kinematics model for attitude and position determination. The new algorithm is noniterative and is computationally efficient, which has significant advantages over traditional nonlinear least squares approaches. The estimates from the new algorithm are optimal in a probabilistic sense since the attitude/position covariance matrix is shown to be equivalent to the Cramér-Rao lower bound. Also, a covariance analysis proves that attitude and position determination is unobservable when only two line-of-sight observations are available. The performance of the new algorithm is investigated using line-of-sight measurements from a simulated sensor incorporating Position Sensing Diodes in the focal plane of a camera. Results indicate that the new algorithm provides optimal attitude and position estimates, and is robust to initial condition errors.