Kalman filtering to reduce measurement noise of sample entropy: An electroencephalographic study

In the analysis of electroencephalography (EEG), entropy can be used to quantify the rate of generation of new information. Entropy has long been known to suffer from variance that arises from its calculation. From a sensor's perspective, calculation of entropy from a period of EEG recording can be treated as physical measurement, which suffers from measurement noise. We showed the feasibility of using Kalman filtering to reduce the variance of entropy for simulated signals as well as real-world EEG recordings. In addition, we also manifested that Kalman filtering was less time-consuming than moving average, and had better performance than moving average and exponentially weighted moving average. In conclusion, we have treated entropy as a physical measure and successfully applied the conventional Kalman filtering with fixed hyperparameters. Kalman filtering is expected to be used to reduce measurement noise when continuous entropy estimation (for example anaesthesia monitoring) is essential with high accuracy and low time-consumption.