Learning-based Moving Horizon Estimation through Differentiable Convex Optimization Layers

TL;DR

This paper introduces a differentiable convex optimization layer-based moving horizon estimation method for constrained linear systems with uncertain parameters, enabling online parameter tuning and improved state estimation accuracy.

Contribution

It presents a novel MHE framework using differentiable convex layers to estimate states and tune unknown parameters online in systems with constraints and uncertainties.

Findings

Effective online parameter tuning via stochastic gradient descent.

Enhanced state estimation accuracy with physical constraints.

Successful application to temperature estimation in manufacturing machines.

Abstract

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.