Localization Requirements for Autonomous Vehicles

Tyler G. R. Reid; Sarah E. Houts; Robert Cammarata; Graham Mills; Siddharth Agarwal; Ankit Vora; Gaurav Pandey

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Localization Requirements for Autonomous Vehicles

Tyler G. R. Reid, Sarah E. Houts, Robert Cammarata, Graham Mills, Siddharth Agarwal, Ankit Vora, Gaurav Pandey

arXiv:1906.01061v1Jun 3, 2019cs.ROeess.SPeess.SY

TL;DR

Autonomous vehicles need precise, reliable localization to support safe operation across weather, traffic, and road settings. The paper derives requirements from safety-integrity targets and vehicle-road geometry, obtaining stringent freeway and local-street bounds. It also identifies system-level and deployment constraints that limit current implementations.

Problem
Autonomous vehicles require precise position and orientation knowledge in all weather and traffic conditions for safe operation.
Method
The paper derives localization requirements by combining integrity-risk allocation with vehicle dimensions and road-geometry constraints.
Results
Freeway passenger vehicles require lateral, longitudinal, and vertical error bounds of 0.57 m, 1.40 m, and 1.30 m, respectively, with 1.50 deg attitude bounds in each direction.
Takeaways & Limitations
The requirements provide a baseline for autonomous-vehicle localization systems, with local-street geometry imposing more stringent bounds than freeway operation.
Takeaways & Limitations
The requirements concern knowledge of mapped roads and lanes, while additional operational constraints will continue to evolve.

Abstract

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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%).

I. INTRODUCTION

The paper frames autonomous-vehicle localization as a safety-critical problem requiring lane-level position knowledge and reliability beyond existing driving-assistance requirements. It derives system requirements by combining integrity targets with vehicle and road geometry.

Motivation: Decimeter-level positioning is required on highways, while local and residential streets demand near-centimeter-level accuracy to ensure the vehicle remains within its lane.The requirements separate horizontal error into lateral and longitudinal components and also include vertical road-level identification.
Scope: Level 3+ autonomous operation is the paper’s focus, because it requires the accuracy needed for active vehicle control.Some results may also apply to level 2 systems.
Approach: The requirements are derived by allocating integrity risk from a target safety level and defining positioning bounds from lane widths, road curvature, vehicle dimensions, and related geometry.The analysis uses methods developed in civil aviation and focuses on US road and passenger-vehicle standards.
Localization concepts: Protection levels estimate maximum possible instantaneous position error, while alert limits are geometry-driven bounds chosen to guarantee lane containment.The paper represents lateral, longitudinal, and vertical protection levels as a box around the vehicle.
Localization concepts: Accuracy, integrity, and availability describe complementary aspects of safety-critical localization performance.Accuracy captures typical 95th-percentile performance, integrity concerns errors exceeding protection levels, and availability measures how often protection levels remain within alert limits.
Practical challenge: No single localization technology currently satisfies safe-operation requirements across all weather, road, and traffic scenarios.The research platform therefore combines LiDAR, radar, cameras, GNSS, and an IMU, while production faces sensor-cost, compute, storage, and infrastructure trade-offs.

II. INTEGRITY

The paper derives autonomous-vehicle integrity requirements from a target road-safety improvement, historical crash data, and system-level risk allocation. It assigns localization a stringent failure-risk target because localization feeds other virtual-driver subsystems.

Safety target: 100× improvement in road safety sets TLS = 2×10^-10 fatal crashes per vehicle mile.This target matches the 2010–2015 commercial-aviation fatality rate after conservatively converting fatalities to fatal crashes.
Data limitation: The fatal-crash-to-incident estimate is conservative and may be accurate only within an order of magnitude for most driving scenarios.Underreporting of property-damage-only and injury crashes limits confidence in the automotive crash data.
Risk allocation: Pvds = Pveh = 10^-8 failures/mile results from allocating equal integrity risk to the virtual driver and vehicle systems.The allocation is derived from the target safety level and the fatal-crash-to-incident ratio.
Historical evidence: Vehicle system failure rates are estimated at nearly 10^-8 failures/mile from crash reports, NHTSA causation estimates, and vehicle miles traveled.The authors state that uncertainty in these inputs still places current vehicle systems near the proposed order of magnitude.
Subsystem allocation: Localization requires lower failure probability because its output feeds planning and other virtual-driver elements.The virtual driver includes perception, localization, planning, and control, with localization supplying input to planning.
Integrity requirement: 10^-8 failures/hour is the allowable integrity risk for the localization system as a whole.The paper relates this target to ASIL D and approximately 5.73σ under a Gaussian interpretation.

III. HORIZONTAL REQUIREMENTS

Horizontal localization requirements are derived from vehicle dimensions and road geometry to keep the vehicle within its lane. Lateral and longitudinal alert limits trade off differently across freeways and local streets.

III. HORIZONTAL REQUIREMENTS: Vehicle dimensions and road geometry determine the lateral and longitudinal alert limits needed to keep the vehicle within its lane.The analysis uses vehicle width and length together with lane width and curvature.
III. HORIZONTAL REQUIREMENTS: Freeway and local-road trade-offs are evaluated using lane widths, minimum curvature, and passenger-vehicle dimension limits.Freeway analysis uses 3.6-meter lanes and 150-meter minimum curvature; local-road cases include 3.0- or 3.3-meter lanes and sharper curves.
III. HORIZONTAL REQUIREMENTS: Freeway curvature is generally minimal, allowing a larger longitudinal error before lateral requirements become overly constrained.The lateral and longitudinal error budget remains coupled through road curvature and width.
III. HORIZONTAL REQUIREMENTS: 1.5 meters is the freeway longitudinal alert-limit design value, yielding a 0.72-meter lateral alert limit for passenger vehicle dimensions.The longitudinal limit is constrained by vehicle operation, including on/off-ramp finding and collaborative V2X operation.
III. HORIZONTAL REQUIREMENTS: 0.33 meters is the balanced lateral and longitudinal alert limit for the largest passenger vehicles negotiating limiting local-street turns.The local-road analysis considers narrow roads and sharp curvature, making both directions more stringent.

IV. VERTICAL REQUIREMENTS

Vertical localization must determine which road level a vehicle occupies, especially at multi-level interchanges. The analysis uses vertical clearance standards and treats the resulting vertical alert limit as vehicle independent.

IV. VERTICAL REQUIREMENTS: Vertical position must be known more precisely than ± half the clearance to avoid ambiguity between road levels on multi-decked interchanges.The Phoenix ‘Mini Stack’ illustrates the multi-level-road problem.
IV. VERTICAL REQUIREMENTS: The vertical alert limit is vehicle independent because it is used only to determine the road level.This differs from horizontal requirements, which keep a vehicle of specified dimensions within lane bounds.
IV. VERTICAL REQUIREMENTS: The vertical analysis assumes that highly automated vehicles have a map to help resolve position.The paper distinguishes this mapped setting from interim V2X applications that may lack maps.
IV. VERTICAL REQUIREMENTS: Map-free V2X vertical requirements depend on trajectory estimation for collision-path assessment, a more complex analysis outside this paper’s scope.Elevation error can make a grade-separated interaction appear to be an at-grade crossing with collision potential.

V. ORIENTATION REQUIREMENTS

Position and attitude errors combine to inflate the effective protection level around the vehicle. The analysis maps roll, pitch, and heading errors into an inflated three-dimensional protection box.

V. ORIENTATION REQUIREMENTS: Position protection levels combine lateral, longitudinal, and vertical errors, while attitude is represented by roll, pitch, and heading.The combined model accounts for both positioning and orientation error sources.
V. ORIENTATION REQUIREMENTS: Heading errors rotate position errors and enlarge the effective uncertainty area around the vehicle.This combined effect is illustrated by the lateral and longitudinal protection-level geometry.
V. ORIENTATION REQUIREMENTS: The inflated protection box is obtained by applying an Euler rotation sequence to the vehicle’s position-protection dimensions.The original box dimensions are transformed into inflated dimensions representing combined position and orientation protection levels.
V. ORIENTATION REQUIREMENTS: Small-angle approximations simplify the worst-case orientation-error bounds by taking cos(δ·) → 1 and sin(δ·) → δ·.The approximation applies because roll, pitch, and heading errors are required to be much smaller than one radian.
V. ORIENTATION REQUIREMENTS: VPL = δvert + (δlat + wv/2) δθ + (δlon + lv/2) δφ expresses vertical protection-level inflation from position and orientation errors.The expression follows from combining the transformed protection box with the position and orientation error definitions.
V. ORIENTATION REQUIREMENTS: Protection-level inflation grows with attitude error, and allocating position versus orientation error is a design choice.The scaling is evaluated using freeway alert limits and passenger-vehicle design limits.

VI. UPDATE FREQUENCY

Localization update frequency must account for vehicle speed and road geometry because longer intervals increase the distance traveled between updates. The paper therefore links sampling rates to protection-level budgets for highways and local streets.

VI. UPDATE FREQUENCY: At 130 km/h, 10 Hz produces 3.6 meters between updates, equal to the width of a freeway lane.At 100 km/h, 10 Hz produces 2.7-meter spacing, comparable to some local-street lane widths.
VI. UPDATE FREQUENCY: 200 Hz produces 0.17-meter update spacing at 130 km/h, keeping sampling uncertainty to a small fraction of the 1.5-meter highway protection level.The paper identifies 200 Hz as an appropriate system-level update rate at highway speeds.
VI. UPDATE FREQUENCY: 100 Hz or greater appears appropriate for both highway and local-street operation.At 15 km/h on local streets, one tenth of the 0.33-meter alert limit corresponds to approximately 125 Hz.
VI. UPDATE FREQUENCY: Update rate can be throttled at lower speeds to save compute and power and increase range.The required rate depends on speed rather than being fixed across all driving conditions.

VII. LOCALIZATION REQUIREMENTS DESIGN

The design allocates localization position and attitude errors so protection levels remain within alert limits, using vehicle dimensions and road geometry across road types. Freeways permit larger longitudinal errors, while tighter local-road geometry demands more stringent lateral, longitudinal, and orientation performance.

Design process: Protection levels must remain ≤ alert limits to ensure knowledge that the vehicle stays within its lane and on the appropriate road level.The equations combine position and orientation errors while satisfying alert-limit constraints derived from road geometry and vehicle dimensions.
Design process: Lateral, longitudinal, and vertical alert limits are allocated jointly because road curvature couples lateral positioning to longitudinal error.Freeway curvature is minimal, allowing a larger longitudinal error before lateral requirements become overly constrained.
Freeway requirements: 1.5 degrees of orientation error contributes 0.15 meters for freeway passenger vehicles, yielding a 0.57-meter lateral positioning error limit.The calculation assumes a 5.8-meter limiting vehicle length and a 0.72-meter freeway lateral alert limit.
Local-road requirements: 0.5 degrees of orientation error contributes 0.05 meters on local streets, leaving a 0.29-meter allowable lateral position error.Local streets have a 0.33-meter lateral alert limit and require nearly a threefold improvement over freeway design numbers.
Freeway requirements: 0.20 meters at 95% accuracy and 0.57 meters at 99.999999% define the desired freeway lateral error distribution.The distribution assumes Gaussian lateral positioning errors for passenger vehicle dimension limits.
Local-road requirements: Local-road operation requires lateral and longitudinal accuracies around 0.1 meters at 95%, with pointing requirements of 0.17 degrees.Freeway longitudinal and vertical requirements are more forgiving, around 0.4 meters at 95%, with 0.5-degree pointing requirements.

VIII. CONCLUSION

The paper establishes system-level localization requirements from safety integrity, road geometry, and vehicle dimensions. It reports stringent freeway and local-road bounds, while noting that certification, map uncertainty, and evolving operational constraints remain important boundaries.

Conclusion: Passenger vehicles on freeways require a 0.57 m lateral bound, 1.40 m longitudinal bound, 1.30 m vertical bound, and 1.50 deg attitude bound.The corresponding 95% accuracies are 0.20 m, 0.48 m, 0.43 m, and 0.51 deg, respectively.
Conclusion: Local streets require 0.29 m lateral and longitudinal error bounds with a 0.50 deg orientation requirement.The corresponding 95% requirements are 0.10 m for position and 0.17 deg for orientation.
Scope and certification: The requirements apply to a multi-component localization system rather than one particular localization method or technology.The system must meet both 95% accuracy and safety integrity requirements in intended weather and traffic conditions.
Map reference: Map-relative and global localization uncertainties must be related explicitly through vehicle, map, and global-frame uncertainty.The paper identifies WGS-84 as an example global reference and distinguishes σmap, σrelative, and σglobal.
Scope and future requirements: The presented bounds are a baseline based on limiting road geometry, while additional operational constraints may evolve and detailed maps may enable on-the-fly resource adjustment.Achieving the requirements remains challenging for sensors, algorithms, and multimodal sensor fusion.