A Two-Level Stochastic Model for the Lateral Movement of Vehicles Within Their Lane Under Homogeneous Traffic Conditions

TL;DR

This work addresses the need for submicroscopic lateral-position modeling to validate autonomous driving under homogeneous traffic. It presents a two-level stochastic framework that decomposes lateral movement into a coarse Markov-based component κ and a fine noise-driven component φ, with x(i) = κ(i) + φ(i), calibrated on real German highway data. Evaluations show good agreement with real trajectories across multiple tours, while delivering extreme computational efficiency (≈$1.8\times 10^{4}$ evaluations in 0.36 s, ≈10000× real time), enabling hardware-in-the-loop and batch simulations. The approach offers a foundation for driver-specific and scenario-based validation, with clear paths to incorporate environmental and traffic interactions via Hidden Markov extensions and coupling to physical dynamics.

Abstract

The lateral position of vehicles within their lane is a decisive factor for the range of vision of vehicle sensors. This, in turn, is crucial for a vehicle's ability to perceive its environment and gain a high situational awareness by processing the collected information. When aiming for increasing levels of vehicle autonomy, this situational awareness becomes more and more important. Thus, when validating an autonomous driving function the representativeness of the submicroscopic behavior such as the lateral offset has to be ensured. With simulations being an essential part of the validation of autonomous driving functions, models describing these phenomena are required. Possible applications are the enhancement of microscopic traffic simulations and the maneuver-based approach for scenario-based testing. This paper presents a two-level stochastic approach to model the lateral movement of vehicles within their lane during road-following maneuvers under homogeneous traffic conditions. A Markov model generates the coarse lateral offset profile. It is superposed with a noise model for the fine movements. Both models are set up using real-world data. The evaluation of the model shows promising qualitative and quantitative results, the potential for enhancements and extreme low computation times (10000 times faster than real time).

Figures (12)

• Figure 1: Effect of lateral offset between vehicles on same lane on the forward perception range for LiDAR (Valeo Scala Gen. 2, DBSCAN-based detection ester1996density) and camera (Mask R-CNN / MS COCO he2017mask). The ego lane perception range varies between 30.0 m and 110.0 m (LiDAR) and $\approx$ 200.0 m (camera), motivating the goal to realistically represent this effect in virtual validation.
• Figure 2: Lateral offset for different velocity ranges and lanes.
• Figure 3: Illustration of the model setup (in blue, left side) and its inversion, the model usage (in green, right side). The $*$ operator stands for a convolution of the lateral offset profile with a Gaussian kernel. Elements in purple illustrate how the real data are used for calibrating the two stochastic models.
• Figure 4: Illustration of the effect of convolving the coarse lateral offset profile generated by the Markov model with a kernel $g_s$, $s = 0.6~s$ on the final artificial trajectories: clearly visible steps that are not observable in the real lateral offset profiles vanish.
• Figure 5: Capping of fine movement signal to avoid deviations due to peaks.