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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.
