Estimating EEG Parameters in the Presence of Random Time Delays for Brain Computer Interfaces

The aim of this research work is to derive algorithm for estimating the signal amplitudes, frequencies and time delay while processing electroencephalogram (EEG) signals. This derived algorithm along with the estimated signals can be used in BCIs to get desired motion or end effects. To tackle this research problem we assume that the sequence of time delay uncertainties form a stationary sequence whose power spectral density depends upon unknown parameters. We directly evaluate the joint probability density function (PDF) of the discrete Fourier transform of their uncertainty sequence in terms of their power spectral density. Assuming these errors to follow a Gaussian law, parameter of the PDF is estimated by maximizing this joint PDF or likelihood functions. In this research work, we further choose an explicit form for the EEG signal as the sum of two sinusoidal with unknown amplitudes apart from the frequencies that is transformed by the delays having small uncertainties. The approximate likelihood function for the measured EEG signal is calculated. Additional white Gaussian noise is assumed to be present in the signal measurement. Simulation studies shows the MLE of the signal amplitude and frequencies when the time delay have random jitters with iid Gaussian law.

I. Introduction

An Electroencephalogram (EEG) is used for analysis of neuro (brain) signals so that abnormalities (if any) present in the brain can be detected. To obtain these signals electrode cap or number of electrodes in the form of small metallic discs are pasted on the scalp in some standard positions. Because of the potential change between two electrodes micro electrical charges are detected which shows some kind of activity in the brain cells. These electrical charges are very tiny, therefore, some kind of amplification is needed to analyze these EEG signals [1]–[2].