  We consider the problem of jointly estimating the attitude and spin-rate of a
spinning spacecraft. Psiaki (J. Astronautical Sci., 57(1-2):73--92, 2009) has
formulated a family of optimization problems that generalize the classical
least-squares attitude estimation problem, known as Wahba's problem, to the
case of a spinning spacecraft. If the rotation axis is fixed and known, but the
spin-rate is unknown (such as for nutation-damped spin-stabilized spacecraft)
we show that Psiaki's problem can be reformulated exactly as a type of
tractable convex optimization problem called a semidefinite optimization
problem. This reformulation allows us to globally solve the problem using
standard numerical routines for semidefinite optimization. It also provides a
natural semidefinite relaxation-based approach to more complicated variations
on the problem.

Optimization and Control