COMPACT FINITE BURN TARGETING AND RECONSTRUCTION ALGORITHM

A method is presented for targeting a spacecraft through a rocket moto r burn of finite duration to match a desired final state. Variational equations are numerically integrated to yield the Jacobian of the fina l state with respect to the finite burn model parameters. An innovativ e application of the Euler axis and angle parameterization of attitude Is used to model the direction of thrust. This parameterization avoid s the traditional singularities associated with right ascension and de clination angles. Marquardt's method is used in the differential corre ction of the nonlinear model parameters. At each iteration singular va lue decomposition is used to solve the weighted normal equations for t he finite bun model parameters, which minimize the weighted least squa res 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 reduced-order model simulates an inertially fixed thrust vector. Th e compact size and speed of this algorithm has made it possible to imp lement on a laptop personal computer. An application of this algorithm to real-time telemetry antenna pointing for the Advanced Range Instru mentation Aircraft is presented.