Neural Moving Horizon Estimation: A Systematic Literature Review

TL;DR

This systematic review surveys neural moving horizon estimation (NMHE), a hybrid approach that fuses neural networks with model-based moving horizon estimation to tackle nonlinear dynamics and model-uncertainty. It categorizes NMHE methods into three families: using NNs to learn more accurate system models, using NNs to adapt the MHE cost (e.g., weighting matrices), and using NNs to approximate the MHE pipeline for speed. The study synthesizes architectural choices (MLP, LSTM, ICNN, etc.), performance trends, and real-time hardware implementations, revealing that NMHE can deliver real-time, high-accuracy state estimation in complex domains such as rotorcraft, robotics, and process control, often with substantial hardware acceleration. It also identifies gaps, notably underexplored NN families (PINNs, transformers), stochastic formulations, and embedded hardware studies, and outlines concrete directions to improve robustness and practicality of NMHE in real-world systems.

Abstract

The neural moving horizon estimator (NMHE) is a relatively new and powerful state estimator that combines the strengths of neural networks (NNs) and model-based state estimation techniques. Various approaches exist for constructing NMHEs, each with its unique advantages and limitations. However, a comprehensive literature review that consolidates existing knowledge, outlines design guidelines and highlights future research directions is currently lacking. This systematic literature review synthesizes the existing knowledge on NMHE, addressing the above knowledge gap. The paper (1) explains the fundamental principles of NMHE, (2) explores different NMHE architectures, discussing the pros and cons of each, (3) investigates the NN architectures used in NMHE, providing insights for future designs, (4) examines the real-time implementability of current approaches, offering recommendations for practical applications, and (5) discusses the current limitations of NMHE approaches and outlines directions for future research. These insights can significantly improve the design and application of NMHE, which is critical for enhancing state estimation in complex systems.

Figures (7)

• Figure 1: Block diagram of MHE within a close-loop control system
• Figure 2: Illustration of moving horizon in MHE
• Figure 3: Overview of review methodology
• Figure 4: Distribution of studies by the year of publication
• Figure 5: Distribution of studies by their application areas