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Estimating and reacting to 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 key
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 weighting matrices, which enables a seamless embedding of the
MHE as a learnable layer into neural networks for highly effective learning.
Interestingly, we show that the gradients can be computed efficiently using a
Kalman filter in a recursive form. Moreover, we develop a model-based policy
gradient algorithm to train NeuroMHE directly from the quadrotor trajectory
tracking error without needing the ground-truth disturbance data. The
effectiveness of NeuroMHE is verified extensively via both simulations and
physical experiments on quadrotors in various challenging flights. Notably,
NeuroMHE outperforms a state-of-the-art neural network-based estimator,
reducing force estimation errors by up to 76.7%, while using a portable neural
network that has only 7.7% of the learnable parameters of the latter. The
proposed method is general and can be applied to robust adaptive control of
other robotic systems.