Failure Detection and Exclusion via Range Consensus (2008)

With 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).