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

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... nimum-energy cost. This bound, called the optimality gap, is shown to be small in normal operation conditions. This is further supported by simulations. II. PRELIMINARIES The rotation group is denoted by SO(3). SO(3) = {X ∈ R 3×3 | X X = I, det(X) = 1}, CONFIDENTIAL. Limited circulation. For review only.