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Estimating and reacting to external disturbances is crucial for robust flight control of quadrotors. Existing estimators typically require significant tuning for a specific flight scenario or training with extensive ground-truth disturbance data to achieve satisfactory performance. In this paper, we propose a neural moving horizon estimator (NeuroMHE) that can automatically tune the MHE parameters modeled by a neural network and adapt to different flight scenarios. We achieve this by deriving the analytical gradients of the MHE estimates with respect to the tuning parameters, which enable a seamless embedding of an MHE as a learnable layer into the neural network for highly effective learning. Most interestingly, we show that the gradients can be obtained efficiently from a Kalman filter in a recursive form. Moreover, we develop a model-based policy gradient algorithm to train NeuroMHE directly from the trajectory tracking error without the need for the ground-truth disturbance data. The effectiveness of NeuroMHE is verified extensively via both simulations and physical experiments on a quadrotor in various challenging flights. Notably, NeuroMHE outperforms the stateof-the-art estimator with force estimation error reductions of up to 49.4% by using only a 2.5% amount of the neural network parameters. The proposed method is general and can be applied to robust adaptive control for other robotic systems.

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