research: next-generation estimation theory for FusionCore (cross-industry ideas)

[manankharwar]

Overview

This tracks five independent research directions that would move FusionCore from state-of-the-art for a ROS package to genuinely novel in the estimation theory literature. Each draws from a different industry where the underlying math has been proven at scale.

The common thread: the UKF innovation sequence is an underutilized signal. Every technique below extracts more information from it than the current implementation does.

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Sub-issues

• feat: conformal prediction for distribution-free sensor gating #50 Conformal prediction for distribution-free sensor gating (from ML theory: DeepMind, Stanford, MIT)
• feat: symplectic integration for the UKF predict step #51 Symplectic integration for the UKF predict step (from orbital mechanics: NASA trajectory computation)
• feat: information geometry and Riemannian UKF for optimal sigma point placement #52 Information geometry and Riemannian UKF (from quantum information and differential geometry)
• feat: transformer attention for dynamic sensor weighting #53 Transformer attention for dynamic sensor weighting (from LLMs and deep learning)
• feat: HMM regime detection for principled context-aware noise switching #54 HMM regime detection for context-aware noise switching (from quantitative finance and genomics)

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Implementation priority

Issue	Complexity	Impact	Suggested order
#51 Symplectic integration	Trivial (10 lines)	Eliminates systematic drift	1
#54 HMM regime detection	Medium	Unifies ZUPT, coast, adaptive noise	2
#50 Conformal prediction	Medium	Distribution-free gating guarantee	3
#53 Transformer attention	Medium (needs training data)	Proactive sensor weighting	4
#52 Information geometry	Hard	Theoretically optimal estimates	5

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The bigger picture

Symplectic integration is the free lunch: trivial to implement, airtight justification from orbital mechanics, zero prior art in ROS.

Conformal prediction is the paper: it connects FusionCore to the hottest area of statistics right now and the distribution-free guarantee is a story no other navigation package can tell.

HMM regime detection is the unifying architecture: it makes ZUPT, coast mode, adaptive noise, and slip detection one coherent probabilistic system instead of four separate threshold-based hacks.

Transformer attention and information geometry are the long-term technical moat: they require more investment but produce capabilities that would take any competitor years to replicate.