State estimation in high dimensional space is a big challenge problem. Commonly, we use Lie group to implement 6DoF state estimation in 3D space. However, how does the brain implement path integration in 3D space based on neural dynamics?

Low et al. 2018 developed a novel unsupervised learning algorithm incorporating temporal dynamics, in order to characterize population activity as a trajectory on a nonlinear manifold — a space of possible network states. The manifold’s structure captures correlations between neurons and temporal relationships between states, constraints arising from underlying network architecture and inputs. The manifold structure of population activity is well-suited for organizing information to support memory, planning, and reinforcement learning. 

The model may give us some inspirations for implementing state estimation in high dimensional space based on neural dynamics.

For further info, please read the paper Low et al. 2018

Low, Ryan J., Sam Lewallen, Dmitriy Aronov, Rhino Nevers, and David W. Tank. “Probing variability in a cognitive map using manifold inference from neural dynamics.” bioRxiv(2018): 418939.