AI 中文总结
本研究针对传感器融合中周期性结构污染导致的卡尔曼滤波器协方差校准问题，提出FFT-GDCB四角色预滤波方案，在六个领域验证其性能且计算开销极低。
AI 中文摘要
上下文自适应卡尔曼滤波器通过在线回归从新息残差中校准其噪声协方差矩阵Q和R。当底层传感器或信号具有周期性结构时，如机械激光雷达旋转谐波、发动机振动、地面多路径、周度和年度需求周期、给药间隔节律、周度媒体采购节奏，回归输入会受到污染，拟合的协方差模型会表征结构模式而非真实状态不确定性。我们引入一种四角色FFT预滤波器，以O(N log N)的成本解决该问题，并额外提供三个“免费”角色：（i）在卡尔曼更新前对有色噪声进行白化，恢复最优性假设；（ii）在协方差回归前清理新息，防止周期性污染估计的R和Q；（iii）生成频谱上下文特征，丰富下游多臂老虎机的 regime 选择状态；（iv）在任何生成灵敏度系数（β、给药偏移量、出价调整因子）的有监督回归前对输入特征向量进行去季节化处理。我们将该算法置于门控解耦组合多臂老虎机（GDCB）家族中，作为有监督缩放器的预处理层。单次O(N log N)的FFT调用可为四个下游使用者提供服务，占用传感器融合或定价管道计算预算的<0.1%，且是即插即用的附加组件，无需更改卡尔曼滤波器、多臂老虎机或运行时组合算子。我们总结了在六个独立领域的经验验证结果，包括火箭下降、自动驾驶车辆跟踪、短期租赁定价、临床药物给药、航空公司票价分配和广告运营出价校准，所有领域在预注册评估协议下均返回PROVES判定。
英文摘要
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.
Comments15 pages, 3 figures, 3 tables
