*Article* **Spatio-Temporal Synchronization of Cross Section Based Sensors for High Precision Microscopic TrafficData Reconstruction**

#### **Adrian Fazekas \* and Markus Oeser**

Institute for Highway Engineering, RWTH Aachen University, 52074 Aachen, Germany **\*** Correspondence: fazekas@isac.rwth-aachen.de

Received: 8 June 2019; Accepted: 17 July 2019; Published: 19 July 2019

**Abstract:** The next generation of Intelligent Transportation Systems (ITS) will strongly rely on a high level of detail and coverage in traffic data acquisition. Beyond aggregated traffic parameters like the flux, mean speed, and density used in macroscopic traffic analysis, a continuous location estimation of individual vehicles on a microscopic scale will be required. On the infrastructure side, several sensor techniques exist today that are able to record the data of individual vehicles at a cross-section, such as static radar detectors, laser scanners, or computer vision systems. In order to record the position data of individual vehicles over longer sections, the use of multiple sensors along the road with suitable synchronization and data fusion methods could be adopted. This paper presents appropriate methods considering realistic scale and accuracy conditions of the original data acquisition. Datasets consisting of a timestamp and a speed for each individual vehicle are used as input data. As a first step, a closed formulation for a sensor offset estimation algorithm with simultaneous vehicle registration is presented. Based on this initial step, the datasets are fused to reconstruct microscopic traffic data using quintic Beziér curves. With the derived trajectories, the dependency of the results on the accuracy of the individual sensors is thoroughly investigated. This method enhances the usability of common cross-section-based sensors by enabling the deriving of non-linear vehicle trajectories without the necessity of precise prior synchronization.

**Keywords:** sensor synchronization; microscopic traffic data; trajectory reconstruction; expectation maximization; vehicle matching
