Symmetric overbounding of correlated errors

In aviation navigation systems such as the Ground-Based and Space-Based Augmentation Systems (GBAS and SBAS) for GPS, it is critical for users to compute a conservative navigation error bound during precision approach and landing. This paper describes a method for overbounding outputs of linear systems (i.e., conservatively describing their error distributions). Whereas earlier overbounding methods apply only to sets of independent samples, the methods developed in this paper handle samples drawn from correlated time series, so long as those samples have a probability distribution which a linear mapping can make spherically symmetric. Conservative error bounds constructed with these methods are useful in modeling the worst-case performance of filters under a wide range of environmental conditions. An example illustrates how symmetric bounding could enable aircraft to apply user-customized filtering to differential GPS corrections in GBAS or SBAS.