Excellent Potential of Geometric Brownian Motion (GBM) as a Random Process Model for Level of Drowsiness Signals

We show that Geometric Brownian Motion (GBM) appears to be an excellent choice of random process model to describe mathematically the real-life signals that represent the evolution with time of the level of drowsiness (LoD) of an individual, such as a driver. We collected data from thirty (30) healthy participants, who each underwent three tests (either driving in a simulator or performing Psychomotor Vigilance Tests) at successive levels of sleep deprivation. During each test, the LoD was produced by a photooculography (POG) based device designed and built by our team. We so obtained a total of 90 LoD signals. For each, we applied statistical methods to determine whether a GBM was a valid model for it. All 90 signals passed statistical tests of normality and independency, meaning that each can be modeled by GBM, thereby showing the excellent potential of GBM as a random process model for LoD signals. This finding could lead to the development of a number of innovative means for predicting the evolution of the LoD and the occurrence of related events beyond the present moment. The resulting technology should help reduce the number of accidents due to drowsy driving.