# Neural Moving Horizon Estimation for Robust Flight Control

arXiv: https://arxiv.org/abs/2206.10397 · HTML: https://mlsanity.com/paper/2206.10397/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 65 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Autonomous Drone Racing with Deep Reinforcement Learning](https://mlsanity.com/paper/2103.08624/) (2021)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [NeuroBEM: Hybrid Aerodynamic Quadrotor Model](https://mlsanity.com/paper/2106.08015/) (2021)
- [Model-Based Meta-Reinforcement Learning for Flight with Suspended Payloads](https://mlsanity.com/paper/2004.11345/) (2020)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions](https://mlsanity.com/paper/2003.02992/) (2020)
- [Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactions](https://mlsanity.com/paper/2012.05457/) (2020)
- [Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors](https://mlsanity.com/paper/2109.04210/) (2021)
- [Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking](https://mlsanity.com/paper/2206.03305/) (2022)
- [Safe Feedback Motion Planning: A Contraction Theory and L1-Adaptive Control Based Approach](https://mlsanity.com/paper/2004.01142/) (2020)
- [Reinforcement Learning based on MPC/MHE for Unmodeled and Partially Observable Dynamics](https://mlsanity.com/paper/2103.11871/) (2021)
- [Differentiable Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2108.03212/) (2021)
- [L1 Adaptive Augmentation for Geometric Tracking Control of Quadrotors](https://mlsanity.com/paper/2109.06998/) (2021)
- [Learning-based Moving Horizon Estimation through Differentiable Convex Optimization Layers](https://mlsanity.com/paper/2109.03962/) (2021)
- [A Lyapunov function for robust stability of moving horizon estimation](https://mlsanity.com/paper/2202.12744/) (2022)
- [Energy Tank-Based Policies for Robust Aerial Physical Interaction with Moving Objects](https://mlsanity.com/paper/2202.06755/) (2022)

## Built on by (most cited first, 5 of 5)

- [Towards End-to-End GPS Localization with Neural Pseudorange Correction](https://mlsanity.com/paper/2401.10685/) (2024)
- [Proto-MPC: An Encoder-Prototype-Decoder Approach for Quadrotor Control in Challenging Winds](https://mlsanity.com/paper/2401.15508/) (2024)
- [Radar and Event Camera Fusion for Agile Robot Ego-Motion Estimation](https://mlsanity.com/paper/2506.18443/) (2025)
- [NeRC: Neural Ranging Correction through Differentiable Moving Horizon Location Estimation](https://mlsanity.com/paper/2508.14336/) (2025)
- [Temporal Learning for End-Effector Position Estimation under Aerodynamic Disturbances in Aerial Continuum Manipulation](https://mlsanity.com/paper/2609.28716/) (2026)

## Abstract (arXiv)

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.