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

• URL: http://arxiv.org/abs/2608.22023v1
• Date: Sat, 22 Aug 2026 15:57:25 GMT
• Title: Spectral Pre-Filtering for Context-Adaptive Sensor Fusion: A Four-Role FFT-GDCB Integration for High-Stakes Decision Systems
• Abstract summary: Context-adaptive Kalman filters calibrate their noise covariance matrices Q and R from innovation residuals via online regression.<n>We introduce a four-role FFT pre-filter that solves this problem at $O(Nlog N)$ cost and serves three additional roles "for free"<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $O(N\log N)$ 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 $\hat{R}$ and $\hat{Q}$; (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 $O(N\log N)$ 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.

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