Failure Detection and Exclusion via Range Consensus

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)

Astronautic Communication for Telepresence Applications

Numerous applications of telerobotics and telepresence are believed to have great potential to reliably and securely perform tasks in environments that are dangerous or inaccessible for human beings. Especially in the case of space flight missions certain operations cannot yet be automated but necessarily involve human interactions. In such cases, the communication between an operator at a ground station and a remote manipulator in space is critical for success. In this work, a novel simulator that allows for thoroughly analyzing the effects of wireless communication paths in diverse telepresence scenarios at low implementation complexity is developed and presented. The effects that significantly impact reliability and performance of data transmission are investigated; also new strategies for improving the overall system quality are proposed. The exemplary communication path between the DLR ground station in Weilheim and the International Space Station (ISS) is in the focus of our work

Enhancements of the Range Consensus Algorithm (RANCO)

In anticipation of the future GNSS constellations becoming operational, it will no longer be possible to assume that the probability of failure for more than one satellite within a certain timeframe is negligible. Further, it is questionable whether it is always reasonable to compute a position estimate based on all satellites in view, rather than selecting the “best” subset. The Range Consensus (RANCO) algorithm is not only capable of detecting multiple satellite failures at a time, but it also allows the determination of good estimates of the current ranging biases. RANCO calculates position solutions based on subsets of four satellites and compares this estimate with the pseudoranges of all the satellites not contributing to this solution. The residuals of this estimate are then used as a measure of statistical consensus. The scope of this work is the optimization of the performance of RANCO by restricting it to the detection of a certain number of failed satellites at a time and by finding an optimal subset selection process for this constraint. Furthermore, the computation of the subset quality was reconsidered and significantly improved by the use of the Weighted Dilution of Precision (WDOP). In this paper, the physical model for determining the threshold for the separation between correct and faulty satellite signals has been extended. The RANCO algorithm was also verified with respect to its capability of detecting and identifying satellites with a bias higher than a given threshold. Throughout the paper those satellites are defined to fail. The abilities of RANCO, to exclude multiple simultaneous ranging faults and low biases, paves the way for safety critical applications by combining receiver autonomous algorithms with the integrity channel information from future GNSS systems

A probabilistic assessment on the Range Consensus (RANCO) RAIM Algorithm

The Range Consensus Algorithm (RANCO) is a new RAIM method capable of detecting multiple satellite failures at reasonable computational effort. RANCO was first introduced at ENC 2008 [1]. Enhancements of the RANCO algorithm have been presented at the ION GNSS 2008 [2]. Up to now, optimal parameters with respect to the overall performance denoted by the probability of missed detection have only been found by means of simulation. The following work presents an analytical assessment of the detection probabilities in RANCO, making it possible to denote integrity parameters such as missed detection probability (PMD) and false alarm probability (PFA). The analysis done in this paper allows a proof of the algorithm’s ability to correctly detect multiple failed satellites, and a comparison against other existing RAIM algorithms well established in the integrity community and SoL applications. RANCO bases its decision about a satellite failure on multiple pseudorange comparisons referring to different satellite reference subsets (RS) of 4 SVs each. These subsets return a position solution without a pseudorange residual, thus no a-priori knowledge about the correctness of the RS can be assumed at this point. In the first step, a fault free RS is assumed, which leads to a reference position solution with an uncertainty derived from the estimated Gaussian noise on the 4 individual measurements. The range comparison between the satellite under test (SUT) and the reference subset contains both the error coming from the position projected into the line of sight (LOS) and the measurement error of the SUT itself, including a potential bias. Given the previously assumed probability of a fault free RS, the decision with respect to a bias detection on the SUT can now be performed using hypothesis testing based on the combined estimated noise variances from both the position solution mapped into the LOS, and the SUT measurement. For this step of the algorithm, detection probabilities can be determined both for the assumption that the RS contains a faulty satellite, and that it consists only of unbiased measurements from healthy satellites. The protected bias (Minimum Detectable Bias, MDB) for each satellite can therefore be given iteratively, first for the fault free assumption, and then for the assumption of a faulty RS. Given the above considerations, a probability of missed detection for the overall decision on failed satellites, as well as the probability of false alarm, can be given. Similar to classic RAIM [3], the detection rates depend on the decision thresholds which can be adjusted according to fixed requirements. With assignable detection rates, the thresholds and thus the detectable biases for each satellite test can be projected into the position domain which gives a bound on the position error. Multiple failed satellites pose the danger of unobservable biases also for RANCO, and this threat has to be considered separately. However, the nature of RANCO, which analyzes satellites multiple times with different references, minimizes this threat. [1] G. Schroth, A. Ene, J. Blanch, T. Walter, and P. Enge, “Failure Detection and Exclusion via Range Consensus,” in Proceedings of the ENC GNSS Conference, 2008. [Online]. Available: http://elib.dlr.de/54263/ [2] G. Schroth, M. Rippl, A. Ene, J. Blanch, B. Belabbas, T. Walter, P. Enge, and M. Meurer, “Enhancements of the Range Consensus Algorithm (RANCO),” in Proceedings of the ION GNSS Conference, 2008