On the distance to optimality of the geometric approximate minimum-energy attitude filter

This paper studies the near-optimality of the recent geometric approximate minimum-energy (GAME) filter, an attitude filter for estimation on the rotation group SO(3). The GAME filter approximates the minimum-energy (optimal) filtering solution by truncating the derivatives of the associated value function of order higher than 2. In this work, this approximation is pinned down in terms of an analytic expression for a bound on the difference between the cost attained by the GAME filter and the minimum-energy cost. This bound, called the optimality gap, is shown to be small in normal operating conditions. This is further supported by simulations.