Online identification of Time-Varying Pilot Dynamics Using a Recursive Sliding-Window Fourier Coefficient Method

Abstract

Online identification of time-varying pilot control behavior is essential for understanding human adaptation and enabling adaptive human-machine systems. This study presents a recursive sliding-window Fourier Coefficient Method (rFCM) for online estimation of pilot dynamics in a single-axis compensatory tracking task. The rFCM was evaluated using Monte Carlo simulations under both time-invariant and time-varying conditions. For time-invariant cases (C1-C2: single- and double-integrator dynamics), increasing the observation window length (T_win) from 5.12 to 10.24 s significantly improved identification performance, reducing normalized root-mean-square error (NRMSE) by up to 63.7%, lowering skipped windows by factors of five (C1) and ten (C2), and increasing variance-accounted-for (VAF) by 10-15%. Further increases yielded smaller improvements, thus, an observation window length of T_win = 10.24 s provided the best trade-off between estimation accuracy and stability for the adopted settings within the rFCM framework. For time-varying conditions (C3-C6), recursive regularization reduced estimation variability while preserving responsiveness. A memory strength of λ=0.10 achieved a favorable balance between noise robustness and adaptability. The adaptive prior reduced the relative variance of the pilot gain K_p, and lead time constant τ_L by 56.2% and 55.4%, respectively. While stable estimates were obtained for the effective time delay τ_e, neuromuscular frequency ω_nm and damping ratio ζ_nm, rapid parameter changes induced transient mean relative bias peaks of approximately 50% for K_p and 20% for K_pdot = K_p · τ_L. Overall, rFCM provides a robust framework for online frequency-domain identification and tracking of gradual changes in pilot control behavior.