Real-time sleep spindle detection using adaptive Kalman filtering and innovation variance

Sleep spindles are transient sigma-band oscillations occurring mainly during NREM Stage N2 and are associated with thalamocortical synchronisation and memory consolidation. Manual spindle scoring remains the clinical gold standard, yet it is labour-intensive and subject to inter-scorer variability. Many automated detectors depend on extensive preprocessing, handcrafted features, or black-box learning models, which may limit interpretability and real-time feasibility.We present an interpretable and computationally efficient spindle-detection framework based on adaptive Kalman filtering (AKF) and innovation variance. First, a proof-of-concept AKF models a single 30 s N2 epoch as a second-order kinematic state-space system and uses the time-varying innovation variance as a direct marker of local nonstationarity. Spindles are detected by a minimal thresholding rule applied to innovation variance, without band-pass filtering, envelope extraction, or time-frequency decomposition. On the pilot epoch, the AKF identifies two spindle events consistent with expert visual annotation, whereas a sigma-band Hilbert-envelope detector and a Martin-type RMS detector capture only a short, high-amplitude segment of the second spindle.Second, we generalise the approach to nine full-night recordings and introduce an AKF-Balanced (AB) detector. AB combines sigma-band filtering with AKF estimation in a three-state (amplitude-velocity-acceleration) model and delineates events using energy-like criteria and innovation-based morphological validation. Compared with two RMS-based detectors, a wavelet/Gabor-like detector, and the innovation-only AKF, AB yields physiologically plausible spindle densities and realistic duration statistics while maintaining a balanced overlap profile against a conservative RMS reference. Overall, model-based adaptive Kalman filtering with innovation variance provides a transparent, real-time-compatible alternative for sleep spindle detection.