No. 915

Title:

GARCH-control of covariance in dynamical estimation of  inverse solutions

Author(s):

Galka, Andreas (ISM);
Yamashita, Okito (ISM);
Ozaki, Tohru (ISM)

Key words:

Inverse problem; spatiotemporal Kalman Filter; GARCH; stochastic differential equation.

Abstract:

The problem of estimation of unobserved states of high-dimensional dynamical systems poses an inverse problem, which can be solved by Kalman Filtering; in order to provide the model of the dynamics with more flexibility with respect to space and time, we suggest to combine the concept of GARCH-control of covariance, well-known in econometrics, with Kalman Filtering. We formulate this algorithm for spatiotemporal systems governed by stochastic diffusion equations and present a numerical simulation designed to imitate the situation of the generation of electroencephalographic recordings from the human cortex.