One of the key approaches to monitor the integrity of Global Satellite Navigation Systems (GNSS) is receiver autonomous integrity monitoring (RAIM). Existing RAIM algorithms utilise two tests in the position domain (for RAIM availability) and measurement domain (for failure detection). This paper proposes an alternative RAIM algorithm, which is based entirely in the measurement domain. This algorithm can be used for sensitivity analyses to support performance specification and system design. It can also be used during actual flight operations where the trigger is the phase of flight and its required navigation performance (RNP) parameters. This is made possible by computationally efficient calculation of the chi-squared parameters. The algorithm reverts to the current approach if the phase of flight is unknown. Simulation results for non-precision approach (NPA) have been used to demonstrate the effectiveness of the proposed algorithm.

A measurement domain receiver autonomous integrity monitoring algorithm

Systems, methods and devices for improving the accuracy of GNSS data are provided Specifically, embodiments of the invention can advantageously use sensor input to improve the accuracy of position fixes The use of physical 5 sensors in navigation systems is deemed particularly advantageous, especially where altitude data derived from the pressure sensor is calibrated with and/or blended with GNSS altitude data

GNSS positioning using pressure sensors

With the increasing automation of measurement, adjustment, outlier detection and the consequential use of the results for real-time applications, reliable methods to detect and mitigate an outlier are required. However, it is frequently advised that the outlier test should not be used as a means to automatically reject an outlier. One of the reasons for this is that the outlier detection test at times can identify a wrong measurement. To address this issue, this paper proposes a new outlier separability test to confirm that the identified outlier, by the outlier test, can be confidently rejected as the outlier. In addition, the Minimally Separable Bias and the separability multiplying factor are also obtained for the proposed outlier separability test. With the initial comparisons between the proposed method with the reapplication of the global model test method and multiple hypothesis method, the advantages of the new outlier separability test are demonstrated.

New Outlier Separability Test and Its Application in GNSS Positioning

In the next ten years the number of pseudorange sources and their quality is expected to increase dramatically: The United States is going to add two new civil frequencies (L5 and L2C) in the modernized GPS, and the European Union is planning to launch Galileo, which is planned to be fully operative before 2015, also with multiple frequencies. By combining two frequencies, users will be able to remove the ionospheric delay which is currently the largest error, thus reducing nominal error bounds by more than 50%. This reduction in nominal error bounds together with the large number of satellites is not only going to increase the accuracy of the positioning, but more importantly, it is going to increase the robustness against satellite failures (or other range errors), even without augmentation (e.g., Inertial Reference Unit (IRU), baro-altimeter). Preliminary studies suggest that, using Receiver Autonomous Integrity Monitoring (RAIM), it might be possible to provide a 50m Vertical Alert Limit (VAL) worldwide, with a bound on the maximum error, even in the event of one satellite failure, one constellation failure or a multiple satellite failure. The purpose of this work is to investigate which VALs could be achieved with RAIM under conservative failure assumptions. This paper also summarizes previous work concerning RAIM algorithms and compares their results against a common standard. First, in light of the experience with the Wide Area Augmentation System (WAAS), a threat space for a dual frequency Galileo-GPS constellation is defined. This threat space is necessary in order to achieve a low VAL, as it does not suffice to assume single failures only. Second, RAIM methodologies adapted to the threat space are compared, and the most practical one was found to be a multiple hypothesis approach. Finally, the performance results of the chosen RAIM scheme with a Galileo-GPS dual frequency constellation are presented. It was found that an unaided Galileo-GPS constellation yielded Vertical Protection Level (VPL) values under 20m for the combined dual system. This optimistic conclusion indicates that it will likely be possible to provide vertical guidance to aircraft without the need for any additional augmentation when the future GPS and Galileo constellations are operational. INTRODUCTION This work aims to evaluate the performance of an unaided Galileo-GPS constellation from a vertical integrity standpoint (e.g. for aviation precision approach). A multitude of algorithms or methods were proposed for RAIM over time, both for GPS alone and more recently for combined Galileo-GPS constellations. However, the presented results were hard to compare between the different papers due to the lack of a standardized threat model and also the different assumptions made by each author. This paper seeks instead to establish a Satellite Failure Threat Space that is general enough to allow testing different algorithms and assumptions against a standard model. To accommodate the different assumptions existing in the literature, parametric studies are conducted on factors external to the integrity monitor, such as the satellite failure probability and the expected User Range Accuracy (URA). Three of the existing algorithms, called Least Squares (LS), Maximum Solution Separation and Multiple Hypothesis Solution Separation (MHSS) were implemented as part of the current study. The resulting VPL values from using these different algorithms are then compared and the origin of the inherent differences is discussed. The most practical algorithm for use with the dual constellation will be adopted. Based on the final results with this algorithm, a conclusion is drawn on the capabilities of the unaided combined constellation and direction for future work is laid out. The current work evaluates what is the maximal threat space against which it is possible to offer protection, and does not involve Fault Detection and Elimination (FDE). SATELLITE FAILURE THREAT SPACE The threat space is a consistent and complete set of assumptions about the environment in which a RAIM algorithm is applied. A standardized threat space can be regarded as a general test case against which each individual algorithm may be applied. It has to be universal enough such that it can constitute a frame in which to apply the particular set of assumptions of each particular algorithm, and it should include all considered threats. The threat space is in fact the sample space of all failure modes, including the “no failure” case or nominal conditions. A failure mode is the outcome of each of the ION NTM 2006, 18-20 January 2006, Monterey, CA 1 navigation beacons (i.e. satellites or space vehicles (SVs)) being in a “healthy” or “failed” binary state, with a certain probability. Nominal conditions contain the expected modes of behavior from the satellites, propagation medium, and user receiver with its surrounding environment. Under these conditions, the users achieve their expected level of performance. The failed state is an anomalous condition that can threaten the accuracy and integrity of the system when undetected, and the continuity and availability when it is detected. Such failures should be infrequent and short in duration. The threat model places limits on the extent and behaviors of fault modes. The threat space needs to be all-inclusive, such that all feared events are taken into account, including events introduced by the algorithm itself. Each method can be different with respect to its vulnerability to various fault modes. For the purposes of this study, dual frequency full GPS and Galileo constellations will be assumed. Therefore, ionospheric threats will not be considered (In future studies, second order TEC delays and scintillation will be investigated). The clock and ephemeris errors are assumed to be normally distributed N(0, σURA) under nominal, healthy satellite conditions. The troposphere model will match the one in the WAAS MOPS and is assumed to be bounded by the confidence level provided in [7]. Receiver noise and multipath are also bounded by the provided iono-free sigma term. Note that, like GBAS and SBAS, receiver failure and excessive multipath terms are not explicitly put into the threat space. However, RAIM offers some protection against such fault modes where no ground augmentation can. Previous literature seems to be much in agreement on a theoretical way to describe errors at the user. For that reason, the latest model in [4] was considered appropriate. The position error variance for satellite i is described there by: σi 2 = σURA 2 + σi,tropo 2 + σi,iono-free 2 + σL1L5 . Multiple independent faults will be considered in the combined constellation. This algorithm can be expanded to handle different probabilities of multiple failures, but the independent fault model was adopted in light of possible satellite clock failures as main threat sources. Additionally, separate constellation failure modes will be considered for the case where correlated faults exist across either the GPS or Galileo constellations but not both. Furthermore, a particular user can only receive information from a subset of the SVs, specifically the ones at an elevation above a predefined mask angle. Thus, it is practical to consider only the satellites in view from the location of each specific user. The a priori probability of satellite failure will be discussed and an analysis will be conducted for the relevant number of failures. The satellite failure is defined here as the behavior of a SV when its corresponding range error cannot be overbounded with a Gaussian N(0, σURA). This seems to be a more natural way to describe a failure for this algorithm. Although it is a good binary discriminator, the customary method of setting a failure threshold for pseudorange error does not help identify systematic errors when they are just below the threshold. The practicality of detecting failures according to this new definition needs nonetheless some further scrutiny in future studies. The total error budget for providing Hazardous Misleading Information (HMI) is strictly limited for the case of aviation precision approaches, such that the maximum allowable integrity risk is 10/approach. This budget needs to be divided between all the possible failure modes, and the resulting VPL will be very sensitive on the allocation of this integrity budget. Normally, in applying any RAIM algorithm, multiple failures are neglected, for modes which are less likely than a certain threshold. The reason why certain improbable failure modes need to be neglected is that the entire threat space is extremely large and impractical to compute. Therefore, it is imperative to limit the computation of the position error only to the most dangerous events from an integrity point-of-view. In the same time, one can afford to conservatively assume the worst case scenario (i.e. failure generating HMI) for the remaining threats, as they have a small enough probabilistic impact on the total error or the total integrity anyway.

Galileo-GPS RAIM for Vertical Guidance

A new approach based on the moving average (MA) is proposed to perform satellite failure detection and exclusion (FDE). By taking the average of the last few sums of the squares of the GPS range residual errors, the MA filter is applied to speed up failure detection. The detection threshold cannot be obtained directly because the cumulative distribution of a random process with an MA filter is unknown. Therefore, the Markov chain approach is applied to resolve the threshold. In addition, variations in the number of visible satellites may cause problems in data fusion. The probability integral transformation (PIT) method is adopted to overcome this. After a satellite failure is detected, the multivariate MA filter is used to reduce the incorrect exclusion rate (IER) by taking the average of the last few parity vectors. Simulation results show that, in comparison with the conventional least-squares-residuals method, the MA filter demonstrates higher performance in detecting small failures and a similar level of performance in detecting large failures. Moreover, simulation results also verify that the proposed method has lower IER than the conventional parity space method.

GPS fault detection and exclusion using moving average filters

Working Group 5 of RTCA Special Committee (SC )-159 has spent the past several years working on the problem of GPS fault detection and exclusion (FDE) for a primary-means navigation system that can support oceanic en route through nonprecision approach modes of flight. The results of this working group's activities have been incorporated into RTCA/DO-229, Minimum Operational Performance Standards (MOPS) for GPS/WAAS Airborne Equipment, and will also serve as a baseline for the GPS/GLONASS and GPS/INS MOPS. The purpose of this paper is to provide a history of the development of the FDE requirements, algorithms, and test procedures, as well as a summary of the main issues addressed by the GPS Integrity (FDE) Working Group.

Martin Beckmann

Papers

Summary of RTCA SC-159 GPS Integrity Working Group activities

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