Composite Gaussian Function Modeling of Mobility Prediction Accuracy for Wireless Users

Mobility entropy is proposed to measure the predictability of human movements, based on which the upper and lower bound of prediction accuracy is deduced, but corresponding mathematical expressions of prediction accuracy keep yet open. In this work, the prediction accuracy in terms of the mobility entropy is modelled from the empirical results on a large-scale call detail record(CDR) data set using 2-order Markov chain prediction model. The probability density distribution of accuracy in terms of the quantified entropy interval is fitted with Gaussian distribution and its mean and standard deviation are estimated. After observing that the parameters vary with increasing entropy, the mean can be modelled as a linear function, while the standard deviation can be modelled as a Gaussian function. So, the probability density function of accuracy for given entropy can be expressed by composite Gaussian function. The insights from our work are the first step to model the correlation between prediction accuracy and predictability entropy, thus shed light on further work in this direction.