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

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 floor. The stairs diffusion matrix of the next upper or lower stairs is calculated using the values of the current floor and so on. Paths to the destinations are found in the same 2D manner but continuing to the upper or lower floors until the destination is reached. Combined Model: If the pedestrian is outside the stairs area a top-level Markov process is used to determine whether to use the stochastic behavioral or the diffusion model; therefore, the model switches between motion that is more goal oriented or stochastic. The destination point for the diffusion model is kept until the destination is reached or until the top-level Markov process determines that the stochastic behavioral movement model is again used. When applying the diffusion model the path is computed in two steps: the direction is chosen to follow the gradient of the gas diffusion towards the target while the speed of the pedestrian is predicted with the stochastic behavioral movement model. If the pedestrian enters the stairs area then the three dimensional Stochastic Movement Model will be used to predict distances moved in X, Y, Z directions. These distances are passed to the Targeted Movement Model to be combined with the paths and obtain the new positions. Maps and Floor-Plans: The effect of the advance knowledge of specific maps and floor-plans will be tested in an already available distributed simulation and demonstration system for mobility, and location estimation. The system allows us to integrate several types of sensors, Bayesian Filters, movement models, maps and floor plans. We will discuss quantitative performance improvements that our 3D movement model allows when combined with maps and floor-plans in the overall estimation process in pedestrian indoor/outdoor navigation applications.