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

Kurzfassung

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.