We study pedestrian dynamics using Kalman filtering methods. Kalman filters apply the Bayesian approach to a time series and incorporate the uncertainty in both the measurement and the mathematical model to create a better state estimate of a system, and are commonly used to reduce error in state estimates for applications ranging from radar systems to GPS.
Our goal is to combine a Kalman filter and the Kuhn-Munkres algorithm to not only predict the locations of the pedestrians but also reconstruct their walking path trajectories. We first worked on the linear system of stochastic differential equations to model undisturbed pedestrian dynamics, which is motivated by the work from Corbetta et al. The model uses Langevin equations to describe the Brownian motion-like perturbations in pedestrian trajectories. We utilize the data collected over one year from the Eindhoven University of Technology MetaForum building. While our measurement data are recorded with relatively high frequency and low noise, we also investigate the effect of reduced data quality by downsampling our data set.
In the next step, we extend our study to a pedestrian model similar to the social force model described by Helbing et al. which includes pedestrian avoidance behavior on a second data set, the Eindhoven train station. The data set contains pedestrian data for different crowd densities and includes more interactions among pedestrians.
We find that using a Kalman filter improved results for both data sets, especially for connecting trajectories when more pedestrians are present. Using the pedestrian model with avoidance versus without avoidance showed no improvement.
|Commitee:||Chaderjian, Bruce, Kim, Eun Heui|
|School:||California State University, Long Beach|
|Department:||Mathematics and Statistics|
|School Location:||United States -- California|
|Source:||MAI 58/05M(E), Masters Abstracts International|
|Keywords:||Kalman filter, Pedestrian tracking, Stochastic differential equation|
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