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The Theory
behind the parsing filtering method hinges on the assumption that instantaneous heart rate does not have discontinuities, i.e., that the heart does not skip beats and that the heart rate does not change quickly. Given this assumption, it is feasible to implement a predictive algorithm that can guess where the next likely heartbeat would be and then assign a heartbeat given time points where the ECG has a large value and has a second derivative above a certain threshold. Unfortunately, since it seemed quite unlikely that we would be able to characterize the heart rate of the ECG we are dealing with according to a mathematical distribution, we simply used a rolling average or pseudo-mean in order to determine the prediction characteristics. This is in line with statistical estimation in which the blind estimator, which assumes no knowledge about future events, is simply the mean of previous heart rate values. Although the parsing filtering method is not well grounded in the Hilbert-space classification scheme taught in class, it does serve as a standard of comparison, since the medical literature that discusses heartbeat detection and heart rate variability seems to refer most often to a parsing method as a means of detecting heart beats. It is true that this parsing filtering method can be classified as algorithmic detection, and though algorithmic detection is currently an active topic of research (note that Lydia Kavraki of Rice University researches robotics navigation and object detection), this project was not large enough in scope to involve such a level of investigation.
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