# Spectral Pre-Filtering for Context-Adaptive Sensor Fusion: A Four-Role FFT-GDCB Integration for High-Stakes Decision Systems

arXiv: https://arxiv.org/abs/2608.22023 · HTML: https://mlsanity.com/paper/2608.22023/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 34 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Builds on (most cited first, 3 of 3)

- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Personalized HeartSteps: A Reinforcement Learning Algorithm for Optimizing Physical Activity](https://mlsanity.com/paper/1909.03539/) (2019)
- [Human-in-the-Loop Contextual Bandits for Short-Term Rental Dynamic Pricing: Structural Equivalence of Historical Warm-Up and Approval-Gated Live Learning](https://mlsanity.com/paper/2606.02595/) (2026)

## Abstract (arXiv)

Context-adaptive Kalman filters calibrate their noise covariance matrices Q and R from innovation residuals via online regression. When the underlying sensor or signal carries periodic structure -- mechanical LiDAR rotation harmonics, engine vibration, ground multipath, weekly and annual demand cycles, dosing-interval rhythms, weekly media-buying cadence -- the regression input is contaminated and the fitted covariance models structural modes rather than genuine state uncertainty. We introduce a four-role FFT pre-filter that solves this problem at O(Nlog N) cost and serves three additional roles "for free": (i) it whitens coloured noise before the Kalman update, restoring the optimality assumption; (ii) it cleans innovations before covariance regression, preventing periodic contamination of hatR and hatQ; (iii) it generates spectral context features that enrich the downstream bandit's regime-selection state; (iv) it deseasonalises the input feature vector before any supervised regression that produces a sensitivity coefficient (beta, dose offset, bid modifier). We position the algorithm inside the Gated Decoupled Compositional Bandits (GDCB) family, where it acts as a preprocessing layer for the supervised scaler. The single O(Nlog N) FFT call thereby serves four downstream consumers, fits in <0.1% of the sensor-fusion or pricing-pipeline compute budget, and is a drop-in addition with no changes to the Kalman filter, bandit, or runtime composition operator. We summarise empirical validation across six independent domains (rocket descent, autonomous-vehicle tracking, short-term rental pricing, clinical drug dosing, airline fare distribution, and ad-operations bid calibration), all returning a PROVES verdict under a pre-registered evaluation protocol.