  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%).
