50,391 research outputs found
Failure Detection and Exclusion via Range Consensus
No full textWith the rise of enhanced GNSS services over the next decade (i.e. the modernized GPS, Galileo, GLONASS, and Compass constellations), the number of ranging sources (satellites) available for a positioning will significantly increase to more than double the current value. One can no longer assume that the probability of failure for more than one satellite within a certain timeframe is negligible. To ensure that satellite failures are detected at the receiver is of high importance for the integrity of the satellite navigation system. With a large number of satellites, it will be possible to reduce multipath effects by excluding satellites with a pseudorange bias above a certain threshold. The scope of this work is the development of an algorithm that is capable of detecting and identifying all such satellites with a bias higher than a given threshold.
The Multiple Hypothesis Solution Separation (MHSS) RAIM Algorithm (Ene, 2007; Pervan, et al., 1998) is one of the existing approaches to identify faulty satellites by calculating the Vertical Protection Level (VPL) for subsets of the constellation that omit one or more satellites. With the aid of the subset showing the best (or minimum) VPL, one can expect to detect satellite faults if both the ranging error and its influence on the position solution are significant enough. At the same time, there are geometries and range error distributions where a different satellite, other than the faulty one, can be excluded to minimize the VPL. Nevertheless, with multiple constellations present, one might want to exclude the failed satellite, even if this does not always result in the minimum VPL value, as long as the protection level stays below the Vertical Alert Limit (VAL).
The Range Consensus (RANCO) algorithm, which is developed in this work, calculates a position solution based on four satellites and compares this estimate with the pseudoranges of all the satellites that did not contribute to this solution. The residuals of this comparison are then used as a measure of statistical consensus. The satellites that have a higher estimated range error than a certain threshold are identified as outliers, as their range measurements disagree with the expected pseudoranges by a significant amount given the position estimate. All subsets of four satellites that have an acceptable geometric conditioning with respect to orthogonality will be considered. Hence, the chances are very high that a subset of four satellites that is consistent with all the other “healthy” satellites will be found. The subset with the most inliers is consequently utilized for identification of the outliers in the combined constellation.
This approach allows one to identify as many outliers as the number of satellites in view minus four satellites for the estimation, and minus at least one additional satellite, that confirms this estimation. As long as more than four plus at least one satellites in view are consistent with respect to the pseudoranges, one can reliably exclude the ones that have a bias higher than the threshold. This approach is similar to the Random Sample Consensus Algorithm (RANSAC), which is applied for computer vision tasks (Fischler, et al., 1981), as well as previous Range Comparison RAIM algorithms (Lee, 1986). The minimum necessary bias in the pseudorange that allows RANCO to separate between outliers and inliers is smaller than six times the variance of the expected error. However, it can be made even smaller with a second variant of the algorithm proposed in this work, called Suggestion Range Consensus (S-RANCO). In S-RANCO, the number of times when a satellite is not an inlier of a set of four different satellites is computed. This approach allows the identification of a possibly faulty satellite even when only lower ranging biases are introduced as an effect of the fault.
The batch of satellite subsets to be examined is preselected by a very fast algorithm that considers the alignment of the normal vectors between the receiver and the satellite (first 3 columns of the geometry matrix). Concerning the computational complexity, only 4 by 4 matrices are being inverted as part of both algorithms. With the reliable detection and identification of multiple satellites producing very low ranging biases, the resulting information will also be very useful for existing RAIM Fault Detection and Elimination (FDE) algorithms (Ene, et al., 2007; Walter, et al., 1995)
Sigma Overbounding using a Position Domain Method for the Local Area Augmentaion of GPS
No full textThe local area augmentation system (LAAS) is a differential GPS navigation system being developed to support aircraft precision approach and landing navigation with guaranteed integrity and availability. While the system promises to support Category I operations, significant technical challenges are encountered in supporting Category 11 and III operations. The primary concern has been the need to guarantee compliance with stringent requirements for navigation availability. This paper describes how a position domain method (PDM) may be used to improve system availability by reducing the inflation factor for standard deviations of pseudo-range correction errors. Used in combination with the current range domain method (RDM), a 30% reduction in the inflation factor is achieved with the same safety standard. LAAS prototype testing verifies the utility of the PDM to enhance Category IVIII user availability.
High-Integrity Local-Area Differential GNSS Architectures Optimized to Support Unmanned Aerial Vehicles (UAVs)
No full textSigma-mean monitoring for the local area augmentation of GPS
No full textThe 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. sigma(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 sigma(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.The constructive comments and advice regarding this work provided by many other people in the Stanford GPS research group are greatly appreciated
Assessment of Nominal Ionosphere Spatial Decorrelation for LAAS
No full textThe 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 evaluate navigation integrity, an aircraft computes vertical and lateral protection levels as position-error bounds using integrity parameters broadcast by a nearby LAAS Ground Facility (LGF). These parameters include a standard deviation of ionosphere spatial decorrelation because the range errors introduced by the ionosphere vary between LGF receivers and LAAS users. Thus, it is necessary to estimate typical ionosphere gradients for nominal days and to determine an appropriate upper bound to sufficiently cover the differential error due to the ionosphere spatial decorrelation. In this paper, both Station-Pair and Time-Step methods are used to assess the standard deviation of vertical (or zenith) ionosphere gradients ( vig ó ). The Station-Pair method compares the simultaneous zenith delays from two different reference stations to a single satellite and observes the difference in delay across the known ionosphere pierce point (IPP) separation. Because most of these IPP separations are larger than 100 km, the Time-Step method is also used to better understand ionosphere gradients at LAAS-applicable distance scales (10 – 40 km). The Time-Step method compares the ionospheric delay of a single line-of-sight (LOS) at one epoch with the delay for the same LOS at the other epoch a short time (seconds or minutes) later. This method has the advantage of removing inter-frequency bias (IFB) calibration errors on different satellites and receivers while possibly introducing an estimation error due to temporal ionosphere gradients. This paper shows results from analyzing the post-processed ionosphere database for the Wide Area Augmentation System (WAAS), known as “supertruth”, as well as JPL post-processed data from the Continuously Operating Reference Stations (CORS) database. CORS data is adequate for the Station-Pair method because of the relatively dense CORS receiver network. However, WAAS data is of higher quality since each reference station has three high-quality receivers that aid in removing measurement outliers and reducing noise. The results of this study demonstrate that typical values of vig ó are on the order of 1 – 3 mm/km for non-stormy ionosphere conditions. As a result, a broadcast vig ó of 4 mm/km is conservative enough to bound ionosphere spatial decorrelation for nominal days with margin for more active days and for non-Gaussian tail behavior. Future work will attempt to better resolve the details of nominal ionosphere behavior over short distances as well as determine if the broadcast “bounding value” of vig ó can be reduced prior to LAAS commissioning
Targeted Ephemeris Decorrelation Parameter Inflation for Improved LAAS Availability During Severe Ionosphere Anomalies
No full textThe Local Area Augmentation System (LAAS) is a ground-based differential GNSS system designed to provide precision approach for aircraft landing at a LAASequipped airport. While most anomalies affecting the system can be mitigated in the range domain, positiondomain geometry screening is essential to mitigate threats from anomalous ionosphere spatial gradients. These can potentially cause large range-domain errors before detection by the LAAS Ground Facility (LGF). Existing algorithms for position-domain screening inflate the sigma values (óvig and ópr_gnd) broadcast by the LAAS Ground Facility (LGF). This ensures that subset satellite geometries (i.e. subsets of a set of approved GPS satellites for which the LGF broadcasts valid corrections) for which unacceptable errors can result are made unavailable to the user. These unsafe subsets are found by comparing the resulting Maximum Ionosphere-Induced Error in Vertical (MIEV) with maximum “safe” navigation system error (NSE) values derived from Obstacle Clearance Surface (OCS) applicable to CAT I precision approaches. Recent analyses of past ionosphere spatial gradients observed over the Conterminous United States (CONUS) resulted in very high maximum gradients for both low and high-elevation satellites. The new ionosphere anomaly “threat model” for LAAS CAT I specifies a maximum spatial gradient of 375 mm/km for low-elevation satellites (below 15o) while high-elevation (above 65o) satellites can experience gradients as high as 425 mm/km. Uniform inflation of the broadcast sigmas for all approved satellites results in a significant drop in system availability under the new threat model. To minimize this decline, this paper proposes a new algorithm to implement position-domain screening by inflating satellite-specific, targeted ephemeris decorrelation parameters (called “P-values”) and ópr_gnd values. Availability is assessed for ten major airports in the USA. Under normal conditions, 100% availability is achieved for eight airports, while availability for the two remaining airports exceeds 99%. Targeted inflation consistently results in better system availability compared to strategies that inflate all satellites by the same amount, such as the óvig approach.This work was funded by the affiliated members of the
Stanford Center for Position, Navigation, and Time
(SCPNT) and the FAA Satellite Navigation LAAS
Program Office. Their support is greatly appreciated.
However, the opinions expressed within this paper are
solely those of the authors
CUSUM-Based Real-Time Risk Metrics for Augmented GPS and GNSS
No full textSigma monitoring is a key component of the real-time integrity verification capability demonstrated by the Stanford University Local Area Augmentation System (LAAS) Ground Facility prototype known as the Integrity Monitor Testbed (IMT). The IMT has both sigma estimation and sigma Cumulative Sum (CUSUM) algorithms to detect small and large sigma violations, respectively. When combined with a prior probability distribution for the sigma parameter being monitored and the use of Bayes' rule, the CUSUM can provide a real-time posterior distribution of sigma based on the current CUSUM state. This paper presents the methodology for this "Bayesian CUSUM" technique and shows how it could be used to enhance integrity monitoring while better preserving continuity and availability.The authors would like to thank Ming Luo (Stanford), Todd Walter (Stanford), Boris Pervan (IIT), Ron Braff and Curt Shively (MITRE/CAASD), Ted Urda (FAA AND-710), Barbara Clark (FAA AIR-130), Victor
Wullschleger and John Warburton (FAA ACT-360), Navin Mathur (AMTI), and Frank Van Graas (Ohio University) for their help during this research. The advice and interest of many other people in the Stanford GPS research group is appreciated, as is funding support from the FAA LAAS Program Office (AND-710). The opinions discussed here are those of the authors and do not necessarily represent those of the FAA or other affiliated agencies
LAAS Position Domain Monitor Analysis and Failure-Test Verification
No full textThe Local Area Augmentation System (LAAS) is a ground-based differential GPS system being developed to support aircraft precision approach and landing navigation with guaranteed accuracy, integrity and continuity. Stanford University has designed, implemented and tested a LAAS Ground Facility (LGF) prototype, known as the Integrity Monitor Testbed (IMT). It is used to insure that the LGF meets its requirements for navigation integrity and continuity for Category I precision approach and to support future research for Category II/III operations. With support from the U.S Federal Aviation Administration (FAA), Stanford University has developed the Position Domain Monitor (PDM) algorithms and has implemented them in post-processing software on the IMT prototype platform. This paper describes in detail the PDM procedures and their roles in improving the LGF to meet integrity, availability and continuity requirements. The results of the most recent nominal and failure tests demonstrate that as an addition to the LGF architecture, PDM can provide the extra integrity in the event that the broadcast standard deviation of correction error ( pr_gnd) is violated Further the addition of the PDM adds support to improve high availability.The constructive comments and advice regarding this work provided by many other people in the Stanford GPS research group are greatly appreciated. The authors
gratefully acknowledge the Federal Aviation
Administration Satellite Navigation LAAS Program Office (AND-710) for supporting this research. The opinions discussed here are those of the authors and do not necessarily represent those of the FAA or other
affiliated agencies
Long Term Monitoring of Ionospheric Anomalies to Support the Local Area Augmentation System
No full textExtremely large ionospheric gradients can pose a potential integrity threat to the users of Local Area Augmentation System (LAAS), and thus the development of an ionospheric anomaly threat model is essential for system design and operation. This paper presents a methodology for long-term ionosphere monitoring which will be used to build an ionosphere threat model, evaluate its validity over the life cycle of system, continuously monitor ionospheric anomalies, and update the threat model when necessary. The procedure automatically processes data collected from external sources and networks and estimates ionospheric gradients at regular intervals. If extremely large gradients hazardous to LAAS users are identified, manual validation is triggered. This paper also investigates a simplified truth processing method to create precise ionospheric delay estimates in near real-time, which is the core of long-term ionosphere monitoring. The performance of the method is examined using data from the 20 November 2003 storm and the 31 October 2003 storm. It demonstrates the effectiveness of simplified truth processing within long-term ionosphere monitoring. From the case studies, the automated procedure successfully identified the two worst ionospheric gradients observed and validated to date
Assessment of ionosphere spatial decorrelation for global positioning system-based aircraft landing systems
No full textGround-based augmentations of the global positioning system demand guaranteed integrity to support aircraft precision approach and landing navigation. To quantitatively evaluate navigation integrity, an aircraft computes vertical and lateral protection levels as position-error bounds using the standard deviation of ionosphere spatial decorrelation. Thus, it is necessary to estimate typical ionospheric gradients for nominal days and to determine an appropriate upper bound to sufficiently cover the differential error due to the ionosphere spatial decorrelation. Both station-pair and time-step methods are used to assess the standard deviation of vertical (or zenith) ionospheric gradients (sigma(vig)). The station-pair method compares the simultaneous zenith delays from two different reference stations to a single satellite and observes the difference in delay across the known ionosphere pierce point separation. Because these ionosphere pierce point separations limit the observability of the station-pair method, the time-step method is also used to better understand ionospheric gradients at short distance scales (10-40 km). The time-step method compares the ionospheric delay of a single line of sight at one epoch with the delay for the same line of sight at another epoch a short time (a few to tens of minutes) later. This method has the advantage of removing interfrequency bias calibration errors on different satellites and receivers while possibly introducing an estimation error due to temporal ionospheric gradients. The results of this study demonstrate that typical values of sigma(vig) are on the order of 1-3 mm/,km for nonstormy ionospheric conditions. As a result, sigma(vig) of 4 mm/ k m is conservative enough to bound ionosphere spatial decorrelation for nominal days and still leave enough margin for more active days and for non-Gaussian tail behavior.Funding support from the Federal Aviation Administration (FAA)Satellite Navigation Program Office is acknowledged. The authors
would like to thank Todd Walter, Jason Rife, Ming Luo, and Juan Blanch of Stanford, Boris Pervan and Livio Gratton of the Illinois
Institute of Technology (IIT), and John Warburton of the FAA Technical Center for their help during this research. We also would like to express special thanks to Attila Komjathy at the Jet Propulsion
Laboratory (JPL) for providing us with data and comments. The advice and interest of many other people in the Stanford Global
Positioning System (GPS) research group are appreciated
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