How compare Waymo turning trajectories statistically

Problem

You have aerial-drone recordings that capture the 2D turning trajectories of vehicles passing through several intersections. Each trajectory is tied to one vehicle making a turn (such as a left or right turn) within an intersection. Some trajectories come from Waymo autonomous vehicles, and the rest come from other vehicles (human-driven and/or other fleets). The goal is to quantify whether Waymo’s turning behavior differs from the population made up of all other vehicles.

Data (assume)

Each observed turn is a timestamped trajectory containing:

• intersection_id
• vehicle_type (Waymo vs Other)
• turn_type (left/right/straight, if available)
• t (time)
• $x(t), y(t)$ (position in a local intersection coordinate frame) Optional derived signals (from smoothing/finite differences):
• speed $v(t)$, heading $\theta(t)$, curvature $\kappa(t)$, acceleration $a(t)$

Tasks

1. Specify a statistical approach for testing or quantifying whether Waymo trajectories differ from those of other vehicles.
   • What trajectory representation or features would you use?
   • What distributional assumptions, if any, would you make?
   • What hypothesis test or model would you use?
   • What effect size would you report?
2. Follow-up (traffic volume differs by intersection): Intersections have different traffic volumes and potentially different driving patterns.
   • How would you adjust your analysis so differences aren’t confounded by intersection-level factors (including traffic volume)?
   • What model or design would you use to compare Waymo vs Other fairly across intersections? State key assumptions, pitfalls, and how you’d validate them. Overview: This question evaluates statistical inference and trajectory-analysis skills, including representation of 2D turning paths, time-series feature extraction, and comparative modeling to detect behavioral differences between an autonomous fleet and other road users.