  In the past several years, there have been several representative attitude
determination methods developed using derivative-based optimization algorithms.
Optimization techniques e.g. gradient-descent algorithm (GDA), Gauss-Newton
algorithm (GNA), Levenberg-Marquadt algorithm (LMA) suffer from local optimum
in real engineering practices. A brief discussion on the convexity of this
problem is presented recently \cite{Ahmed2012} stating that the problem is
neither convex nor concave. In this paper, we give analytic proofs on this
problem. The results reveal that the target loss function is convex in the
common practice of quaternion normalization, which leads to non-existence of
local optimum.
