Flight performance of aerial robotic vehicles is critically dependent on the quality of the state estimates provided by onboard sensor systems. The attitude estimation problem has been extensively studied over the last ten years and the development of low complexity, high performance, robust non-linear observers for attitude has been one of the enabling technologies fueling the growth of small scale aerial robotic systems. The velocity aided attitude estimation problem, that is simultaneous estimation of attitude and linear velocity of an aerial platform, has only been tackled using the non-linear observer approach in the last few years. Prior contributions have lead to non-linear observers for which either there is no stability analysis or for which the analysis is extremely complex. In this paper, we propose a simple relaxation of the state space, allowing scaled rotation matrices R ∈ ℝ3×3 such that RXT = uI where X = uR̂ and u > 0 is a positive scalar, along with additional observer dynamics to force u → 1 asymptotically. With this simple augmentation of the observer state space, we propose a non-linear observer with a straightforward Lyapunov stability analysis that demonstrates almost global asymptotic convergence along with local exponential convergence. Simulations as well as experimental results are provided to demonstrate the performance of the proposed observer.
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