  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.
