Monte-carlo estimation from observation on stiefel manifold

Partial observation of stochastic processes can occur for various reasons, ranging from faulty sensors to occultation issues. In this paper, we consider the problem of estimating the angular velocity of a rotating system from partial observation corrupted by noise. The system is assumed to evolve on the rotation group SO(n), and only k noisy measurements with k <; n are available. We propose an optimal filter to track the angular velocity. We show that, under some conditions, it is possible to recover the angular velocity of the rotating system and we propose a solution based on a Monte-Carlo method (particle filter). In particular, we show that if the angular velocity is stepwise constant, our algorithm succeed in estimating it. Simulations illustrate the proposed approach.