An adaptive unknown input approach to brain wave EEG estimation. (January 2023) - Griffith, Tristan D.; Gehlot, Vinod P.; Balas, Mark J.; Hubbard, James E.
Abstract: Objective: Real time, high fidelity estimation and reconstruction of brain wave dynamics is complicated by the nonstationary and nonlinear effects of electroencephalography (EEG) measures. This work aims to introduce a novel state space architecture, which continuously updates a linear brain wave model and estimates the exogenous input to the brain wave system. This continuous update is adaptive, because the estimator continuously monitors its own performance and can modify its own parameters by a closed loop action. This highly nonlinear estimator should reconstruct the EEG measure in real time for analysis and diagnostic information. Methods: The development of this adaptive unknown input estimator focuses on treating the known phenomena of brain waves. The adaptive law accounts for nonlinearities in the EEG measure while the input estimator simultaneously accounts for the exogenous input to the system. The estimator is further robust to general process uncertainty in the plant dynamics. Results: The stability of the adaptive unknown input estimator for EEG measures is shown. This estimator is shown to outperform standard linear models, such as Kalman filtering techniques especially at points where the EEG measure changes sharply. Conclusion: This adaptive unknown input estimator reconstructs unmodeled EEG data in real time by accounting for the nonlinear brain wave dynamics. Because the adaptive law updates a linear model over time, much of the interpretability and intuition of linear state space modeling is preserved. Highlights: Adaptive state estimators are proposed for the identification of EEG dynamics. The resultant estimator architecture updates a time varying state space model. The estimator outperforms traditional estimators when the EEG dynamics are nonlinear. The architecture treats nonlinear dynamics and uncertainty in the EEG dynamics.