Optimal experiment design for modeling and estimation of intra-cortical neuronal activity from EEG recordings : a Kalman filtering approach

Abstract

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advent of the nonlinear Cubature Kalman Filter (CKF) allows for stable parametric estimation in inherently nonlinear systems driven by random inputs of Gaussian nature. Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. As with any estimation technique, the solution accuracy remains dependent on the quality of the input-output data sets over finite recording horizon. To improve accuracy, an Adaptive Design Optimization (ADO) can be employed for intelligently choosing inputs whose corresponding outputs are maximally informative about unknown parameters and-or hidden states. In this dissertation, we address improving model fitting (states and parameters estimation) and model assessment (model selection) procedures in a Kalman-based framework and by integrating techniques from Adaptive Design Optimization (ADO). We proposed efficient identification algorithms that select in single experimental trials those system inputs that cause the output trajectory to be maximally informative about the nonlinear system model parameters. We demonstrated the performance of these algorithms in several simulated scenarios that are derived from benchmark nonlinear problems (Double-well and Van der Pol oscillators), as well as from nonlinear stochastic neuronal models of electric potential generation (conductance-based neuronal models and the Jansen model) and metabolic activity signals (hemodynamic model). Such algorithms include OID-SCKF algorithm which is an adaptive approach for joint input design and parametric identification of nonlinear system models. When compared to estimation with Kalman filter with inputs being randomly selected, th