Defining Pseudorange Integrity - Overbounding

Abstract

One of the most critical requirements for aviation applications is integrity. For Category I precision approach, the International Civil Aviation Organization (ICAO) has defined an integrity requirement of 10-7 per approach on the probability that the system fails in a way that causes misleading information. Since the performance of GNSS can vary dramatically depending on satellite geometry, mathematical bounds on the position error have been defined to evaluate this requirement for a particular approach. These bounds are the horizontal and vertical protection levels (HPL and VPL, respectively), and are defined in RTCA and ICAO documents. The protection level equations are constructed on the assumption that the individual error components (pseudorange errors) are exactly characterized by a zero- mean Normal distribution, whose variance is known. Unfortunately, this assumption has not been validated. In fact, testing has indicated that there can be small residual means and the tails of the error distribution are not necessarily characterized by a Normal distribution. In order to generalize the integrity requirements for individual pseudorange error components, these effects must be accommodated. This paper proves that the assumption for a zero-mean, Normal error distribution can be replaced by a requirement that the error distribution is symmetric, unimodal, and whose cumulative distribution function (cdf) is bounded by a Normal error distribution (overbounded for errors less than the mean, underbounded for errors greater than the mean). This result is extended to accommodate non-zero means, which can be accounted for by inflating the variance of the assumed Normal error model. Three methods of inflating this variance are described.