GPS World, September 2016

Raw testing quantity Input file First order differenced testing quantity Relative threshold 1 Absolute threshold 1 0020 0015 0010 0005 0 0005 0010 0015 0020 equal to 04 times the smallest impact of a cycle slip on the combination see Table 2 If we can take Figure 3 as a suitable example of an extreme ionospheric disturbance leading to unusually high variability in combination results the absolute threshold will most of the time be far higher than the statistical one and will help to reduce the rate of wrong detections As an output of this first step a flag value is assigned to epochs with larger values than both thresholds and which are therefore potentially affected by cycle slips Once the locations of potential slips are achieved the second step consists in comparing the mean before and after potential cycle slips for the flagged epochs A second absolute threshold is applied equal to 08 times the smallest effect If another potential cycle slip is present in the detection window the size of the detection window will be reduced to avoid calculation of statistical parameters on partially shifted data The goal of the first step is to detect potential slips Therefore the priority is to avoid missing a real slip with low threshold values sometimes leading to false positive detection On the other hand the second step aims to separate the potential remaining false positives outlier spikes in the raw combination from the real cycle slip shifts on average The theoretical performance of this two step approach is 100 percent neither false positives nor false negatives should be encountered 54 GPS WORLD WWW GPSWORLD COM SEPTEMBER 2016 Detection Using Geometry Free Combination Since the fourth order differenced geometry free combination is affected by a residual ionospheric delay the previous procedure cannot be applied Like any time differenced testing quantity the slip will appear as a spike in the combination Therefore there is no way to distinguish cycle slips from outliers by a mean level comparison second step Consequently the detection method only consists of a forward and backward moving average window in which a 4 sigma confidence interval is compared to the current epoch combination value Indeed in this case we cannot afford to encounter false positives on 5 percent of epochs induced by the use of a 3 sigma threshold since no further step can be set up to eliminate remaining false positives The theoretical performances of the geometry free detection method are also expected to reach 100 percent Again neither false positives nor false negatives should be encountered Note that this calculation only takes ratios into account neglecting the fact that the geometry free combination is also sensitive to the variability of the ionosphere VALIDATION We have tested the quad frequency algorithm on 30 second quad frequency Galileo observations from stations GMSD in Nakatane Japan and NKLG in Libreville Gabon The GMSD observations were used to test algorithm robustness towards simulated particular cases whereas the NKLG data were used to assess algorithm behavior for cases met in the equatorial area Methodology Cycle slips were artificially inserted into the GMSD data simulating the following cycle slip scenarios ICS SCS DM and SCS SM The benefit of such a simulation approach is that the algorithm output can easily be compared to the already known solution Moreover these data had been used to determine whether the use of more carrier frequencies could increase cycle slip detection performance We analyzed a 50 day NKLG dataset covering observations from Jan 6 to Feb 1 and from June 24 to July 19 2014 This FIGURE 2 Detection method for the Simsky combination FIGURE 3 Statistical and absolute thresholds Absolute threshold 2 Potential cycle slip Cycle slip confirmed 2300 2400 2500 2600 2700 2800 Epoch Simsky E1 E5a E5b combination first difference meters Combination results Absolute threshold 04 x Statistical threshold 3 σ Carriers used Fourth order differenced geometry free combinations σ GF meters Smallest effect SCS SM 1 cycle meters E1 E5a 00136 01935 E1 E5b 00136 01740 E1 E5a b 00124 01836 E5a E5b 00091 00195 E5a E5a b 00072 00099 E5b E5a b 00072 00096 TABLE 3 Geometry free combinations