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. INTRODUCTION Ground-Based and Space-Based Augmentation Systems (GBAS and SBAS) provide GPS users with high quality differential corrections that improve navigation accuracy. Depending on the configuration of the augmentation system, individual or networked reference stations make differential correction measurements and broadcast these to users through terrestrial VHF transmitters (in GBAS) or through a satellite link (in SBAS). In addition to differential corrections, GBAS and SBAS messages also contain integrity information: both in the form of alert messages, which warn of possible satellite failures, and in the form of error parameters, which enable construction of conservative navigation-error bounds. Aviation users performing precision approach and landing operations rely on this integrity information to ensure they meet the safety requirements imposed by civil aviation authorities. In practice, users must define confidence bounds which bracket all but the rarest errors, those occurring with a risk of less than 10 (or 10 for fully automated landing). The user computes this confidence bound on-the-fly and compares the bound to a maximum allowable error for which the aircraft can still land within its touchdown box. As long as its confidence bound does not