Sigma-mean monitoring for the local area augmentation of GPS

The local area augmentation system (LAAS) is a ground-based differential GPS system being developed to support aircraft precision approach and landing navigation with guaranteed integrity. To quantitatively appraise navigation integrity, an aircraft computes vertical and lateral protection levels using the standard deviation of pseudo-range correction errors, σ_{pr_gnd}, broadcast by the LAAS ground facility (LGF). Thus, one significant integrity risk is that the true standard deviation (sigma) of the pseudo-range correction error distribution may grow to exceed the broadcast correction error sigma or that the true mean of the correction error distribution becomes excessive during LAAS operation. This event may occur due to unexpected anomalies of GPS measurements. To insure that the true error distribution is bounded by a zero-mean Gaussian distribution with the broadcast sigma value, real-time sigma and mean monitoring is necessary. Both direct estimation and cumulative sum (CUSUM) methods are useful to detect violations with acceptable residual integrity risk. For sigma monitoring, the estimation method more rapidly detects small violations of σ_{pr_gnd} but the fast initial response (FIR) CUSUM variant more promptly detects significant violations that would pose a larger threat to user integrity. For the purposes of mean monitoring, the FIR CUSUM variant is superior to the estimation method in detecting any mean violations. The results demonstrate that real-time protection is achievable against all sizes of sigma/mean failures that can threaten navigation integrity.