A statistical characterization is presented of Global Positioning System (GPS) user range error as a normally distributed random variable with non-zero mean over the length of the aircraft precision approach operation, correlated from one GPS measurement epoch to another and from one satellite to another. This leads directly to modeling GPS error in the position domain as multivariate normal with non-zero mean. Based on this model, a vertical composite protection level VPL c and a horizontal composite protection level HPL c are each calculated as scalar values from a univariate normal distribution displaced from the origin by the worst-case position domain bias combination possible, given the maximum possible individual satellite bias magnitudes and the satellite geometry. A method is then presented by which exact values-that is, values accurate to a user-defined error tolerance and consistent with statistical assumptions-of VPL c and HPL c are obtained, and by which computationally efficient approximations may be evaluated. A statistical quadratic form under the multivariate normal distribution is used to derive a new class of protection levels based on the probability enclosed within a radius defined in two or more dimensions. A central Chi-square representation of this quadratic form is also presented and is incorporated into a six-step computational procedure for the two-dimensional composite radial protection level RPL c . This procedure is extended to the spherical protection level (SPL c ) and the ellipsoidal protection level (EPL c ).

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A modified Code Noise and Multipath (CNMP) algorithm is presented for dual‐frequency differential GPS precision approach and landing. Pseudorange noise and multipath are exchanged for reducible biases in both reference station and aircraft ranging measurements. The second frequency is used only to correct the code‐minus‐carrier observable. Corrected pseudorange measurements are combined using a single‐frequency carrier phase position domain smoothing (CPDS) algorithm. Flight test vertical and horizontal navigation system error is reduced from 0.80 m to 0.32 m and from 0.41 m to 0.33 m, respectively, as compared to Local Area Augmentation System single‐frequency processing. For six included 150‐s precision approaches, 95% error drops from 0.56 m to 0.26 m vertically and 0.28 m to 0.14 m horizontally. Composite protection levels (PLs) using CNMP‐derived quantities are much smaller than modified LAAS PLs. Mean PL values are reduced from 5.90 m to 2.60 m vertically and from 3.24 m to 1.38 m horizontally.

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 VPL c , HPL c , and RPL c , 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 VPL c and HPL c . An approximation to RPL c 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 VPL c and HPL c over-bound the exact PLs. The approximation to RPL c 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 Ò simulation code needed to evaluate computationally efficient PL approximations. Thus, it fosters further research into the use of GPS in safety critical applications.

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