A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields—Part I: Fundamental Principles and Implementation Aspects

A fundamental drawback of synthetic mobility models is that the spatial configuration of the path is determined by the temporal features of the mobile station (MS), such as its speed. This is, however, not true in reality. This first part of our paper establishes a new approach for generating fully spatial random trajectory (mobility) models to which different speed scenarios can be applied. We employ the new approach to the proposal of a highly flexible trajectory model based on the primitives (integrals) of Brownian fields (BFs). We construct a drifted partial random bridge from a given starting point to a random terminating point in the 2D plane. If the bridge is partially established, a target zone with a predefined radius and center can be reached via random paths. If the bridge is fully established, a certain destination point can be achieved by means of random bridges. For the broken bridge, completely random terminating points are obtained. The smoothness of the path can be controlled by the primitives of the employed BF. The implementation aspects of the path model in simulation environments are discussed. In wireless communications, the model can be used for tracking (estimating) the location of the MS, performance analysis of mobile ad hoc networks, and channel modeling under non-stationary conditions.