Abstract
A method is presented for targeting a spacecraft through a rocket motor burn of finite duration to match a desired final state. Variational equations are numerically integrated to yield the Jacobian of the final state with respect to the finite burn model parameters. An innovative application of the Euler axis and angle parameterization of attitude is used to model the direction of thrust. This parameterization avoids the traditional singularities associated with right ascension and declination angles. Marquardt's method is used in the differential correction of the nonlinear model parameters. At each iteration singular value decomposition is used to solve the weighted normal equations for the finite burn model parameters, which minimize the weighted least squares error in the final state. The full-order finite burn model allows the thrust vector to rotate at a constant angular rate within a plane. A reducedorder model simulates an inertially fixed thrust vector. The compact size and speed of this algorithm has made it possible to implement on a laptop personal computer. An application of this algorithm to real-time telemetry antenna pointing for the Advanced Range Instrumentation Aircraft is presented.
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