# Learning-based Moving Horizon Estimation through Differentiable Convex Optimization Layers

arXiv: https://arxiv.org/abs/2109.03962 · HTML: https://mlsanity.com/paper/2109.03962/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2021.

## Built on by (most cited first, 3 of 3)

- [Neural Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2206.10397/) (2022)
- [Decision-Oriented Learning with Differentiable Submodular Maximization for Vehicle Routing Problem](https://mlsanity.com/paper/2303.01543/) (2023)
- [LEARNEST: LEARNing Enhanced Model-based State ESTimation for Robots using Knowledge-based Neural Ordinary Differential Equations](https://mlsanity.com/paper/2209.08185/) (2022)

## Abstract (arXiv)

To control a dynamical system it is essential to obtain an accurate estimate of the current system state based on uncertain sensor measurements and existing system knowledge. An optimization-based moving horizon estimation (MHE) approach uses a dynamical model of the system, and further allows for integration of physical constraints on system states and uncertainties, to obtain a trajectory of state estimates. In this work, we address the problem of state estimation in the case of constrained linear systems with parametric uncertainty. The proposed approach makes use of differentiable convex optimization layers to formulate an MHE state estimator for systems with uncertain parameters. This formulation allows us to obtain the gradient of a squared and regularized output error, based on sensor measurements and state estimates, with respect to the current belief of the unknown system parameters. The parameters within the MHE problem can then be updated online using stochastic gradient descent (SGD) to improve the performance of the MHE. In a numerical example of estimating temperatures of a group of manufacturing machines, we show the performance of tuning the unknown system parameters and the benefits of integrating physical state constraints in the MHE formulation.