Gaussian Bounding for Multivariate Distributions with an Application to GNSS Integrity

We describe a Gaussian overbounding concept for multivariate distributions. This overbounding concept results in a practical criterion to determine whether a given multivariate Gaussian overbounds a multivariate distribution. The sufficiency of this criterion is demonstrated mathematically. As an example, we show how this concept can be used to determine temporal error models for GNSS clock and ephemeris errors.