<p>This paper presents a novel multiplicative particle swarm optimization algorithm (MPSO) for optimization on the space of quaternions. It uses multiplicative quaternion kinematics to propagate quaternion particles, rather than the generic additive kinematics used in the traditional particle swarm optimization algorithm. The performance of the MPSO is demonstrated on the problem of attitude determination from light curves, which presents many challenges to traditional filtering-based attitude estimation approaches. The MPSO is shown to be able to successfully determine the attitude and angular velocity of an object from a set of multi-observer light-curve measurements. The MPSO is compared to other optimization approaches for this problem, and equal or superior performance is demonstrated on a variety of test cases. It is shown that the MPSO can be used to initialize conventional filters in order to successfully estimate attitude in situations where pure filtering would fail.</p>