# Data-driven derivation of macroscopisc fundamental diagram from floating car trajectories

## TL;DR

This paper introduces a GPS-based method to accurately estimate traffic flow patterns using vehicle data, improving urban traffic management.

## Contribution

A novel GPS-based methodology for MFD estimation using floating car data, overcoming limitations of fixed detectors and penetration rate assumptions.

## Key findings

- Unary cubic curves achieved optimal MFD fitting with R2 up to 0.9157.
- The HMM-CRF algorithm reduced position error by 29% and intersection mismatch by 40%.
- Queue length estimation accuracy reached RMSE 22.8m and MAPE 18.5%.

## Abstract

This study proposes a novel GPS-based methodology for Macroscopic Fundamental Diagram (MFD) estimation to overcome limitations of fixed detectors and inaccurate penetration rate assumptions. The approach dynamically identifies stop-line positions using spatiotemporal floating car data, calculates maximum queue lengths per signal cycle by combining floating car positions with estimated arriving vehicle lengths, and establishes a speed-based nonlinear model to determine queuing vehicle counts. A dynamic scaling coefficient derived from maximum queue lengths enables assumption-free estimation of total regional vehicles when applied to the floating car population. Validation using Chengdu data demonstrates significant improvements: unary cubic curves achieve optimal fitting for MFD relationships (R2 up to 0.9157); the HMM-CRF hybrid map-matching algorithm reduces average position error by 29% and intersection mismatch rate by approximately 40%; simulation results show queue length estimation accuracy of RMSE 22.8m and MAPE 18.5%, while MFD estimation error for maximum network flow drops from −17.5% to −3.5%, representing an 80% relative accuracy improvement. The proposed methodology provides robust technical support for urban road network assessment and management by enabling high-precision acquisition of MFDs from floating car data, effectively addressing critical challenges in macroscopic traffic modeling and monitoring. This advancement presents potential value for perimeter control applications and other MFD-based traffic management strategies.