Robust estimation of event-related potentials via particle filter

In clinical examinations and brain-computer interface (BCI) research, a short electroencephalogram (EEG) measurement time is ideal. The use of event-related potentials (ERPs) relies on both estimation accuracy and processing time. We tested a particle filter that uses a large number of particles to construct a probability distribution.

We constructed a simple model for recording EEG comprising three components: ERPs approximated via a trend model, background waves constructed via an autoregressive model, and noise. We evaluated the performance of the particle filter based on mean squared error (MSE), P300 peak amplitude, and latency. We then compared our filter with the Kalman filter and a conventional simple averaging method. To confirm the efficacy of the filter, we used it to estimate ERP elicited by a P300 BCI speller.

A 400-particle filter produced the best MSE. We found that the merit of the filter increased when the original waveform already had a low signal-to-noise ratio (SNR) (i.e., the power ratio between ERP and background EEG). We calculated the amount of averaging necessary after applying a particle filter that produced a result equivalent to that associated with conventional averaging, and determined that the particle filter yielded a maximum 42.8% reduction in measurement time. The particle filter performed better than both the Kalman filter and conventional averaging for a low SNR in terms of both MSE and P300 peak amplitude and latency. For EEG data produced by the P300 speller, we were able to use our filter to obtain ERP waveforms that were stable compared with averages produced by a conventional averaging method, irrespective of the amount of averaging.

We confirmed that particle filters are efficacious in reducing the measurement time required during simulations with a low SNR. Additionally, particle filters can perform robust ERP estimation for EEG data produced via a P300 speller.