# Localization Requirements for Autonomous Vehicles

## TL;DR

This paper derives precise localization accuracy requirements for autonomous vehicles based on safety, geometry, and road standards, ensuring safe operation across various conditions and environments.

## Contribution

It provides a first-principles framework for defining localization error bounds and safety levels specific to autonomous vehicle operation.

## Key findings

- Lateral error bound of 0.57 m for freeway vehicles
- Longitudinal error bound of 1.40 m for freeway vehicles
- More stringent error bounds on local streets

## Abstract

Autonomous vehicles require precise knowledge of their position and orientation in all weather and traffic conditions for path planning, perception, control, and general safe operation. Here we derive these requirements for autonomous vehicles based on first principles. We begin with the safety integrity level, defining the allowable probability of failure per hour of operation based on desired improvements on road safety today. This draws comparisons with the localization integrity levels required in aviation and rail where similar numbers are derived at 10^-8 probability of failure per hour of operation. We then define the geometry of the problem, where the aim is to maintain knowledge that the vehicle is within its lane and to determine what road level it is on. Longitudinal, lateral, and vertical localization error bounds (alert limits) and 95% accuracy requirements are derived based on US road geometry standards (lane width, curvature, and vertical clearance) and allowable vehicle dimensions. For passenger vehicles operating on freeway roads, the result is a required lateral error bound of 0.57 m (0.20 m, 95%), a longitudinal bound of 1.40 m (0.48 m, 95%), a vertical bound of 1.30 m (0.43 m, 95%), and an attitude bound in each direction of 1.50 deg (0.51 deg, 95%). On local streets, the road geometry makes requirements more stringent where lateral and longitudinal error bounds of 0.29 m (0.10 m, 95%) are needed with an orientation requirement of 0.50 deg (0.17 deg, 95%).