MAPS AND FLOOR PLANS ENHANCED 3D MOVEMENT MODEL FOR PEDESTRIAN NAVIGATION

Abstract

A model that realistically imitates real pedestrian movement can be used for numerous applications such as infrastructure design, evacuation planning, architecture, robot-human interaction or navigation. Within the scope of this paper, the purpose of such models is to quantitatively represent both the stochastic and deterministic nature of 3D pedestrian movement in order to generate a movement model for sequential Bayesian filtering techniques, such as particle-filtering. The prediction stage of sequential Bayesian positioning estimators depends entirely on the movement model to determine the probability density function of the pedestrian’s location and motion at each time step. A movement model that accurately represents the pedestrian’s motion ensures that measurement data used for positioning is consistent with how a normal pedestrian might move. Furthermore, the model has to be efficiently implemented to that it can be employed in realizations such as Particle Filters. We note that the model does not need to predict the motion of a single pedestrian accurately in any singular experiment; but it needs to correctly model the expected motion in a probabilistic sense. In this paper, a three-dimensional movement model that is suitable for pedestrian navigation will be illustrated. Specifically, the knowledge of maps and floor-plans is used in our movement model and the performance gain on the overall positioning will be investigated. A combination of three-dimensional movement models will be used to model the pedestrian motion. The constituents are a three dimensional Stochastic Behavioral Movement Model and a three dimensional Targeted Movement Model. Some specific constraints are applied on the pedestrian movement while moving on stairs to have a realistic stairs movement. 3D Stochastic Behavioral Movement Model: Human movement is parameterized by physical parameters such as speed, direction and as a result the position. Building layouts are obviously amongst the main parameters that affect the movement of the pedestrian. In order to add the third dimension, the model of [KKRA08] was extended to be able to predict the elevation of the pedestrian at each time step. A linear speed function is used for modeling the elevation. This vertical speed is designed to be a function of time, steepness of the stairs and "activeness" of the pedestrian. Accordingly, the probability distribution of the distance moved in the Z-direction can be calculated. The direction of vertical movement could also be modeled, but in order to have a more realistic movement in the stairs area, the direction is predicted using a targeted movement model described below. Outside the stairs area, the elevation is assumed to be constant. 3D Target Driven Movement Model: To represent target driven human motion, a so-called "diffusion movement" model [KKRA08] is applied. It is derived from "gas diffusion" in space studied in thermodynamics and is a standard solution for path finding of robots [ScA93]: The idea is to have a source continuously effusing gas that disperses in free space and which gets absorbed by walls and other obstacles. A path towards this source is computed by following the steepest gradient, starting at the current position. To model the stochastic nature of a human´s motion, the destination points are chosen randomly, and a Markov process models the fact that the destination may change. In order to add the third dimension, the set of destinations can be distributed over all the floors. The stairs area is projected into a 2D area that can be included in the respective floor plan of each floor. Accordingly, the diffusion matrix calculation can be started at any of the floors. The diffusion matrix at the stairs area of the destination floor is calculated for the stairs going up and down and then copied to the stairs areas of the respective neighboring floors. The diffusion matrix is then calculated from the stairs area to the rest of the respective