A simple and robust K-factor computation method for GNSS integrity needs

Abstract

The aviation Minimum Operational Performance Standard defines the SBAS protection levels as the product of the estimated standard deviation of the positioning error and a scaling factor called K-factor. The K-factor depends on the time window of interest and on the correlation between errors in the time window. The K-factors defined in aviation are difficult to generalize to other specifications in other domains, such as rail and maritime applications. This article presents a simple formula to calculate the K-factor for any value of integrity risk and time interval. The resulting K-factor is shown to be mathematically rigorous under the hypothesis of Gaussian error distribution but without any assumption on the correlation structure of the successive position estimates. The Gaussian assumption can be relaxed and replaced by overbounding with a Gaussian distribution with a very good approximation. This formula can be used in any GNSS application where integrity is needed.