Toward personalized human-in-the-loop training: Real-time estimation of individual motor learning dynamics using the dual-rate model

Previous studies have shown that the dual-rate model, a stochastic framework comprising a multi-state slow-learning, slow-forgetting process and a single-state fast-learning, fast-forgetting process, can predict motor outputs in paradigms including spontaneous recovery and anterograde interference. However, existing methods for estimating the model's states and parameters, including the Expectation Maximization algorithm, operate offline and require the entire behavioural dataset. Furthermore, prior work has typically used average group performance, neglecting individual differences in learning and forgetting rates. Here, we have developed online system identification approaches using Joint Extended Kalman Filter (JEKF) and Moving Horizon Estimation (MHE) to estimate dual-rate model states and parameters in real-time while accounting for individual learning differences. We also introduced adaptive versions that dynamically adjust sensitivity based on motor output noise. For validation, we first used Monte Carlo simulations to demonstrate the accuracy and robustness of these frameworks across varying learning profiles, training schedules, and initial conditions. We then conducted a visuomotor adaptation experiment comprising well-established schedules: block, alternating, and random schedules. Our results confirm that JEKF and MHE can effectively obtain personalized models in real-time, achieving average parameter estimation errors below 11 % across all parameters and simulations. Notably, both methods captured how learning and forgetting rates evolved with task transitions and scheduling changes, trends that offline methods missed. Overall, JEKF is efficient for predictable schedules (e.g., block), whereas MHE, though more than two times slower due to its optimization, provides more reliable estimates in unpredictable environments, achieving up to 26 % lower parameter estimation errors and demonstrating no significant degradation under poor initialization. These findings highlight the potential of the proposed frameworks for real-time, personalized motor learning modelling and online decision-making.