Sigma overbound for aircraft landing in presence of day-to-day multipath correlation

Purpose The purpose of this work is to obtain an overbounded broadcast sigma from actual (non-Gaussian) correction error distribution under the stringent navigation integrity requirements for aircraft precision approach and landing. Design/methodology/approach Approach is statistically to overbound satellite pseudorange correction error distribution with the use of numerical solution of Fisher-Z transformation. Inflation factors for overbounding broadcast sigma are extracted from Fisher-Z transformation based on measured correlation and counted independent identically distributed (iid) sample sizes of true empirical data. Findings New overbounded broadcast sigma values for eight long-pass satellites were obtained based on measured actual empirical data and ensured integrity risk at 10−8 probability level. Proposed methodology successfully overbounds ground reflection multipath-type systematic and temporal errors sources. Originality/value This paper introduced a new method of accounting for ground reflection multipath for local area augmentation system/ground-based augmentation system navigation integrity. The method is also applicable to statistically overbound any other serially correlated temporal variation in measured data if both correlation values and finite iid sample sizes are known.

High-Integrity GPS/INS Integrated Navigation with Error Detection and Application to LAAS

A dynamic state realization for tightly coupling Global Positioning System (GPS) measurements with an Inertial Navigation System (INS) is described. The realization, based on the direct fusion of GPS and INS systems through Kalman filter state dynamics, explicitly accounts for temporal and spatial decorrelation of GPS measurement errors (such as tropospheric, ionospheric, and multipath errors) through state augmentation, thereby ensuring Kalman filter integrity under fault-free error conditions. Predicted system performance for a Local Area Augmentation System (LAAS) aircraft precision approach application is evaluated using covariance analysis and validated with flight data.Built-in fault detection mechanisms based on the Kalman filter innovations are also evaluated to help provide integrity under certain fault conditions. It is shown that an algorithm based on the integral of Kalman filter innovations outperforms other existing GPS fault detection methods in the detection of slowly developing ranging errors, such as those caused by ionospheric and tropospheric anomalies.

A Method of Over Bounding Ground Based Augmentation System (GBAS) Heavy Tail Error Distributions

The purpose of this paper is to describe a statistical method for modelling and accounting for the heavy tail fault-free error distributions that have been encountered in the Local Area Augmentation System (LAAS), the FAA's version of a ground-based augmentation system (GBAS) for GPS. The method uses the Normal Inverse Gaussian (NIG) family of distributions to describe a heaviest tail distribution, and to select a suitable NIG family member as a model distribution based upon a statistical observability criterion applied to the FAA's LAAS prototype error data. Since the independent sample size of the data is limited to several thousand and the tail probability of interest is of the order of 10−9, there is a chance of mismodelling. A position domain monitor (PDM) is shown to provide significant mitigation of mismodelling, even for the heaviest tail that could be encountered, if it can meet certain stringent accuracy and threshold requirements. Aside from its application to GBAS, this paper should be of general interest because it describes a different approach to navigation error modelling and introduces the application of the NIG distribution to navigation error analysis.