# Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees

arXiv: https://arxiv.org/abs/2101.10784 · HTML: https://mlsanity.com/paper/2101.10784/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2021.

## Built on by (most cited first, 6 of 6)

- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Robust Data-Driven Predictive Control using Reachability Analysis](https://mlsanity.com/paper/2103.14110/) (2021)
- [Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning](https://mlsanity.com/paper/2209.08073/) (2022)
- [Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics](https://mlsanity.com/paper/2111.04704/) (2021)
- [Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysis](https://mlsanity.com/paper/2609.27816/) (2026)

## Abstract (arXiv)

We propose a method to perform set-based state estimation of an unknown dynamical linear system using a data-driven set propagation function. Our method comes with set-containment guarantees, making it applicable to safety-critical systems. The method consists of two phases: (1) an offline learning phase where we collect noisy input-output data to determine a function to propagate the state-set ahead in time; and (2) an online estimation phase consisting of a time update and a measurement update. It is assumed that known finite sets bound measurement noise and disturbances, but we assume no knowledge of their statistical properties. These sets are described using zonotopes, allowing efficient propagation and intersection operations. We propose a new approach to compute a set of models consistent with the data and noise-bound, given input-output data in the offline phase. The set of models is utilized in replacing the unknown dynamics in the data-driven set propagation function in the online phase. Then, we propose two approaches to perform the measurement update. Simulations show that the proposed estimator yields state sets comparable in volume to the 3σ confidence bounds obtained by a Kalman filter approach, but with the addition of state set-containment guarantees. We observe that using constrained zonotopes yields smaller sets but with higher computational costs than unconstrained ones.