Approximations to composite GPS protection levels for aircraft precision approach and landing

Persistent pseudorange biases constitute a serious potential integrity problem for differential GPS systems used in aircraft precision approach and landing. Various approaches to solve this problem are documented in the literature, including composite protection levels (PLs) that incorporate an explicit bias term in their mathematical expressions. A statistical characterization for such a PL was previously presented in this journal. Modeling GPS error in the position domain as multivariate normal with nonzero mean resulted in the definition of vertical, horizontal, and radial composite PLs, termed VPLc, HPLc, and RPLc, respectively. In the present effort, approximations to these computationally intensive PLs are presented for possible use in real time. Two of these are shown to be over-bounding approximations to exact quantities VPLc and HPLc. An approximation to RPLc is also presented, as well as a method of quantitative evaluation for each of these composite PLs. Monte-Carlo simulations for a single GPS measurement epoch are then developed to illustrate the exact PLs and their approximations and demonstrate that the approximations to VPLc and HPLc over-bound the exact PLs. The approximation to RPLc is shown to be far simpler computationally than the exact PL, but demonstrating that the approximation is an over-bound is left to future research. This paper makes available to the reader both the methods and the Matlab simulation code needed to evaluate computationally efficient PL approximations. Thus, it fosters further research into the use of GPS in safety critical applications.