When Not to Normalize: Covariance Absorption in Variable-Rate Kalman Innovation Detection

Kalman innovation statistics are widely used to identify observations that are inconsistent with a tracker’s prediction. Under variable-rate reporting, however, the elapsed time between observations creates a two-sided detection problem. After a reporting gap, process-noise covariance grows rapidly. Normalized innovation squared (NIS) retains its nominal false-positive calibration but loses power against a fixed post-gap displacement. A fixed raw-innovation threshold exhibits the mirror-image failure, increasingly flagging nominal predictions as predictive uncertainty grows. Thus neither normalization nor its removal resolves variable-rate detection: elapsed time must be represented explicitly rather than absorbed into a single score. Controlled anomaly injections across six waterways serve as a mechanistic probe. Raw innovation reaches AUC 0.97 on the injected gap construction, while uncapped NIS reaches 0.65. Real-data validation exposes the boundary of that synthetic result. Five evaluated months of HawaiiCoast_GT contain 200 labeled track segments but only 37 anomalous vessel-months after repeated segments are resolved to the label’s natural unit. Month-stratified vessel-level AUCs for NIS, raw innovation, loiter, and a gap-only control range from 0.55 to 0.59 with overlapping uncertainty. No detector wins convincingly. The results show that synthetic kinematic separability does not transfer cleanly to incident-correlated data and that missingness itself is a necessary control. This record contains the author’s preprint. It has not undergone peer review and may differ from a subsequently accepted or published version.