Parameter estimation for macroscopic pedestrian dynamics models from microscopic data

TL;DR

This paper presents a novel framework for estimating parameters in macroscopic pedestrian flow models using microscopic trajectory data, combining stochastic differential equations and PDEs, with methods validated under various conditions.

Contribution

It introduces a new approach integrating stochastic and PDE models for parameter estimation from individual trajectories, including optimization and Bayesian methods, and analyzes their performance.

Findings

Effective parameter estimation from microscopic data demonstrated.

Methods perform well across different flow and geometry conditions.

Framework enhances understanding of pedestrian dynamics modeling.

Abstract

In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -- microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in- and outflow conditions, for varying numbers of individual trajectories and for differing channel geometries.