  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 its 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 MHE weighting matrices, which enables a seamless embedding of
the MHE as a learnable layer into the neural network 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.
