Experimental and Theoretical Results on the LAAS Sigma Overbound

The Local Area Augmentation System (LAAS) is the differential satellite navigation architecture standard for civil aircraft precision approach and landing. While the system promises great practical benefit, a number of key technical challenges have been encountered in the definition of the architecture. Perhaps chief among these has been the need to ensure compliance with stringent requirements for navigation integrity. In this context, this paper defines a practical way to describe and quantitatively establish LAAS correction error broadcast sigma for final integrity risk assessment at aircraft. The method involves a synthesized solution of both data-based analysis for gaussian (or nearly gaussian) error sources and a theoretical bound for non-gaussian error sources such as ground reflection multipath. In addition, this paper covers the largely unresolved issues (binning, etc.) concerning sigma quantification by direct use of data. INTRODUCTION Local Area Augmentation System (LAAS) integrity risk is quantified at the aircraft via the computation of Vertical and Lateral Protection Levels (termed VPL and LPL, respectively). The prescribed algorithms for the generation of these protection levels implicitly assume zero-mean, normally distributed fault-free error distributions for the broadcast pseudorange corrections. While the assumed error model may be consistent with the effects of thermal noise and diffuse multipath, it is understood that remaining errors such as ground reflection multipath and systematic reference receiver/antenna errors are not necessarily reliably modeled by zero-mean normal distributions. Therefore, to ensure that the computed values of VPL and LPL at the aircraft are meaningful and that integrity risk is properly managed, special care must be taken by the LAAS Ground Facility (LGF) in the establishment of the broadcast pseudorange correction error standard deviation ( gnd _ pr σ ). In this paper, we address major remaining unresolved issues concerning the establishment of gnd _ pr σ . These include the definition of a sufficient process by which empirical error data may be processed to ensure spatially stationarity of error, quantification and compensation for the effects of seasonal variation of error, and a methodology to account for potential nonGaussian error sources. For normally distributed errors such as receiver thermal noise and diffuse multipath, standard deviations can be estimated using experimental data alone. In this case, however, it is still necessary to account for the additional integrity risk incurred by statistical uncertainty (due to finite sample size) in the knowledge of reference receiver error standard deviation and error correlation between multiple reference receivers. In this regard, a detailed methodology has been developed for the definition of minimum acceptable inflation parameters for the sample standard deviation [1]. (The inflation parameters are functions of the number of samples available and the sample correlation coefficient.) However, in order for such an empirical process to be applied, it is first necessary to define a proper method to collect data into spatial bins prior to sigma estimation. While large bin sizes are desired to maximize sample size (to limit required inflation factors), bin size is ultimately constrained by the need for spatial stationarity of all data within the bin (i.e., all error data within a bin must have the same underlying distribution). The quantitative resolution of this critical tradeoff, which is conceptually illustrated in Figure-1, is a major subject of the work described in this paper. Size of Bins R eq ui re d In fla tio n Fa ct or o n σ p r gn d Sp at ia l V ar ia tio n of E rro r D is tri bu tio n W ith in B in