Adaptive input design for nonlinear Kalman-based estimation of neuronal activity models

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. 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. The paper considers the challenging problem of modeling cortical activity in multiple interconnected areas based on electrical potential recordings. The model parameters (connectivity strengths) and the hidden states (neuronal activity) are estimated in a neuronal model of multiple interconnected cortical areas for which the inter-area connection strengths are unknown. These parameters (connectivity strength) along with hidden states (neuronal activity) were estimated in a Kalman-based framework based on (a) simulated local field potential observations and (b) designed external stimulation inputs using ADO method. Importantly, when compared to random inputs, it is demonstrated that the simulated optimized inputs lead to faster convergence and more accurate estimates of the unknown model parameters.