Solution Strategies for an Extension of Wahba's Problem to a Spinning Spacecraft

Several methods have been devised to estimate the optimal attitude quaternion and angular velocity for an axially symmetric spacecraft given only a time series of vector attitude measurements and a rigid-body model of the spacecraft dynamics. These methods solve a generalization of the Wahba problem that is applicable to a lowcomplexity spinning spacecraft such as a sounding rocket. They have the advantages of enabling rate estimation without gyros and avoiding the divergence issues of an extended Kalman filter. Measurements at different times are combined via the closed-form quaternion state transition matrix that makes use of Euler equations for a rigid body. The problem takes the form of six ormore nonlinear equations in six or seven unknowns, and these equations can be partially solved analytically to facilitate a numerical solution of the remainder. Representative simulation results illustrate both the merits of these solution strategies and some of the practical issues that arise during implementation.