Lane-Keeping Safety and Time Correlation of Navigation Errors

Abstract

Recent work has constructed alert limits for autonomous vehicle lane-keeping applications, where safety criteria were based on the sensor readings of the navigation system. One limitation of this prior work is that measurement errors were compared directly to lane and vehicle geometry, with the assumption that measurement errors would map directly to errors in vehicle position or attitude. In fact, measurement errors pass through a dynamic system that includes many processes that transform the error, including natural processes that correlate sensor measurements over time and closed-loop vehicle dynamics. These processes reshape error distributions, such that the true position and heading error distributions induced by sensor noise have different forms than the original measurement error distributions. This paper explores these effects when the measurement error is time correlated. To this end, we abstract the dynamic system using a unicycle model of vehicle dynamics, a representative controller, and a first-order Gauss-Markov process to represent measurement correlation. Implementing this model in a Monte Carlo simulation, we investigate the case of a vehicle moving on a curved road when the time constant for measurement correlation is moderately long (10 seconds). Simulations show that the effects of heading-measurement error are mitigated by the dynamic system. Meanwhile, the two-dimensional position error distribution rotates relative to the road, an effect which makes position errors more difficult to bound.