Markov Modulated Bi-variate Gaussian Processes for Mobility Modeling and Location Prediction

A general-purpose and useful mobility model must be able to describe complex movement dynamics, correlate movement dynamics with the nodes geographic position and be sufficiently generic to map the characteristics of the movement dynamics to general geographic regions. Moreover, it should also be possible to infer the mobility model parameters from empirical data and predict the location of any node based on known positions. Having the ability to model movement and predict future positioning of mobile nodes in complex environments can be very important to several operational and management tasks. Existing mobility modeling approaches are based on simple and limited models, specifically designed for particular application scenarios or requiring the complete knowledge of the mobility environment. These features make them unusable in complex scenarios with no (or partial) knowledge of the environment. This paper presents a discrete time Markov Modulated Bi-variate Gaussian Process that is able to characterize the position and mobility of any mobile node, assuming that the position within a generic sub-region can be described by a bi-variate Gaussian distribution and the transition between sub-regions can be described by an underlying (homogeneous) Markov chain. With this approach, it is possible to describe the mobile node movement within and between a set of geographic regions determined by the model itself and, due to the Markovian nature of the model, it is also possible to capture complex dynamics and calculate the future probabilistic position of a mobile node. The proposed approach can be applied to scenarios where the possible pathways are unknown or too complex to consider in a real model that must make a prediction in a very short time. The results obtained by applying the proposed model to real and publicly available data demonstrate the accuracy and utility of this approach: the model was able to efficiently describe the movement patterns of mobile nodes and predict their future position. Besides, the model has also revealed higher performances when compared to other modeling approaches.