How compare Waymo turning trajectories statistically

Problem

You have aerial-drone data that records the 2D turning trajectories of vehicles passing through multiple intersections. Each trajectory corresponds to one vehicle executing a turn (e.g., left or right) within an intersection.

Some trajectories are from Waymo autonomous vehicles, and the rest are from other vehicles (human-driven and/or other fleets). You want to quantify whether Waymo’s turning behavior differs from the population of all other vehicles.

Data (assume)

Each observed turn is a trajectory with timestamps:

• 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) Optionally derived signals (from smoothing/finite differences):
• speed v(t) , heading θ(t) , curvature κ(t) , acceleration a(t)

Tasks

1. Define a statistical approach to test/quantify whether Waymo trajectories differ from other vehicles.
   • What trajectory representation / 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.