Neural Moving Horizon Estimation: A Systematic Literature Review
Bibliographic record
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. To address this gap, this systematic review screened 1164 records and ultimately included 22 primary studies, following the preferred reporting items for systematic reviews and meta-analyses (PRISMA) protocol. This paper (1) explains the fundamental principles of NMHEs, (2) explores three major NMHE architectures, (3) analyzes the types of NNs used, such as multi-layer perceptrons (MLPs), long short-term memory networks (LSTMs), radial basis function networks (RBFs), and fuzzy neural networks, (4) reviews real-time implementability—including reported execution times ranging from 1.6 μs to 11.28 s on different computing hardware—and (5) identifies common limitations and future research directions. The findings show that NMHEs can be realized in three principal ways: model learning, cost function learning, and approximating the real-time optimization in moving horizon estimation. Cost function learning offers flexibility in capturing task-specific estimation goals, while model learning and optimization approximation approaches tend to improve estimation accuracy and computational speed, respectively.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.075 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.006 | 0.008 |
| Bibliometrics | 0.008 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".