Task-Supervised and Cost-Aware Koopman–Kalman Filtering for Recognition under Missing Observations

Learning from partially observed sensor streams requires representations that preserve task-relevant information without reconstructing every missing measurement. Temporal predictions can compensate for incomplete observations, yet unreliable priors may also distort informative current measurements. We propose Task-Supervised and Cost-Aware Koopman–Kalman Filtering (TSCA-KKF), a unified framework for recognition under missing observations and sensing budgets. TSCA-KKF learns a task-supervised latent representation with approximately linear Koopman dynamics and recursively combines temporal predictions with current measurement states through a measurement-anchored update. A bounded, adaptive prior-use coefficient accounts for observation incompleteness, prior confidence, and innovation magnitude, thereby limiting prior intervention when measurements are sufficiently informative or strongly disagree with the prediction. We further couple the estimator with a budgeted observation policy that balances predicted task utility, update value, sensing cost, and sensor redundancy. Theoretically, we establish deterministic bounds on prior-induced representation displacement, derive finite-time estimation-error bounds, and characterize recursive stability under an explicit contraction condition. Experiments on four wearable activity-recognition benchmarks demonstrate favorable recognition–cost tradeoffs under incomplete sensing. On three incomplete-observation benchmarks, TSCA-KKF improves macro-F1 by 1.6–2.4 percentage points over the evaluated mask-aware routing baselines while using lower mean sensing cost. In a strong-observation regime, it preserves recognition performance where fixed prior fusion causes substantial degradation. These results demonstrate that task-supervised latent dynamics, controlled prior intervention, and cost-aware sensing provide a principled approach to recognition from incomplete sequential observations.