# Deep Robust Moving Horizon Estimation for Nonlinear Multi-Rate Systems

## TL;DR

This paper introduces a deep learning method to improve state estimation in complex, asynchronous systems using a robust moving horizon estimation approach.

## Contribution

The novelty lies in combining deep learning with MHE to handle model mismatch and enforce stability constraints in multi-rate nonlinear systems.

## Key findings

- A synchronization method transforms asynchronous systems into synchronous ones for estimation.
- A deep learning framework learns MHE weights while ensuring stability via barrier-function regularization.
- The proposed method is validated through a target tracking example.

## Abstract

In this paper, a moving horizon estimation (MHE)-based state estimation problem is studied for asynchronous multi-rate nonlinear systems. First, the asynchronous multi-rate system is transformed into a synchronous system at measurement sampling points through pseudo-measurement synchronization modeling. Secondly, a MHE strategy with a time-discounted quadratic objective is proposed. Under the detectability assumption, the exponential stability of the proposed MHE is established via the Lyapunov method, and the corresponding linear matrix inequality (LMI) constraints are derived. Moreover, to address the model mismatch after synchronization, a deep learning-based framework is proposed to approximate and learn the weighting parameters of the MHE. Then, barrier-function regularization is introduced to enforce the aforementioned LMI feasibility conditions, keeping the learned weights within the feasible region throughout training. Finally, the result is illustrated by a target tracking example.