By Domenico Campolo
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2005b). Then past and future realizations contain information of relevance to be used in the estimation procedure. Estimates for the states, that are optimal in the mean square sense, are given by Kalman filter and smoother algorithms. Of importance is the parametrization of the problem and the selection of an observation model for the measurements. , 2006) generic observation models were used based on time-shifted Gaussian smooth functions. Furthermore, data based observation models can also be used (Georgiadis, 2007).
The most obvious way to handle time variations between single-trial measurements is subaveraging of the measurements in groups. Sub-averaging could give optimal estimators if the EPs are assumed to be invariant within the sub-averaged groups. , 1991). g. , 2006). , 2005b). , 1989). , 2007; 2008). , 2005b). Then past and future realizations contain information of relevance to be used in the estimation procedure. Estimates for the states, that are optimal in the mean square sense, are given by Kalman filter and smoother algorithms.
Traditional analysis is based on averaged data often by forming extra grand averages of different populations. Thus, trial-to-trial variability and individual subject characteristics are largely ignored (Fell, 2007). Therefore, the study of isolated components retrieved by averages might be misleading, or at least it is a simplification of the reality. For example, habituation may occur and the responses could be different from the beginning to the end of the recording session. Furthermore, cognitive potentials exhibit rich latency and amplitude variability that traditional research based on averaging is not able to exploit for studying complex cognitive processes.