GPS World, September 2016

Unfortunately the raw dual frequency geometry free combination is affected by ionospheric delay To mitigate the ionospheric smooth trend a fourth order time difference is computed Still the result suffers from rapid variations of ionospheric delay When four frequencies are available six dual frequency combinations can be computed One is sufficient to detect the presence of simultaneous cycle slips of the same magnitude The choice will again depend on the ratio between combination precision and the smallest effect of simultaneous one cycle slips On the one hand differencing the combination results affects precision On the other hand the cycle slip thus the smallest effect to detect will be amplified by high order differencing The best ratio is obtained with a fourth order difference see TABLE 3 even if a smooth variation due to the ionosphere is already removed in the second degree differencing see FIGURE 1 Even if one combination is sufficient our approach will use two of them to double check their outputs E1 E5a and E1 E5a b since they offer the best ratios Detection Method To detect a discontinuity due to a cycle slip in the testing quantity it is necessary to establish detection thresholds Thresholds are one of the key parameters in cycleslip detection since they lead to the decision on the presence of a cycle slip or not If the threshold is too restrictive some real slips can be missed a false negative On the other hand if it is not restrictive enough discontinuities that do not match with a cycle slip could be abusively detected a false positive It is important to notice as our study highlights that there is no perfect threshold that suits all the needs and constraints The choice must be made considering the positioning application at hand Threshold values given in this article are representative and were empirically determined to be optimal with respect to our goal of cycle slip detection under high ionospheric activity Results and further discussions about different thresholds can be found in the first authors thesis see Further Reading Cycle slips will affect the raw Simsky combination by a shift in the mean combination value whereas the time differenced one will be affected by a spike Detection Using Simsky Combination Cycle slip detection on the triple frequency Simsky combination is performed in two cascading steps see FIGURE 2 The first one uses a time differenced combination to detect potential cycle slips using a 20 observation sized forward and backward moving average window in which the mean and standard deviation statistical parameters are computed The current epoch is compared to the previous ones to detect a spike which could correspond to a cycle slip Two types of Carriers used Simsky combination precision σ S meters Smallest impact meters E1 E5a E5b 00024 E1 0024 E1 E5a E5a b 00018 E1 0012 E1 E5b E5a b 00019 E1 0012 E5a E5b E5a b 00028 E5a 0255 TABLE 2 Simsky combinations thresholds are used statistical or relative and absolute As shown in FIGURE 3 using a statistical threshold allows us to adapt detection to the inertia of statistical parameters Assuming the noise on the observations here the Simsky combination results follows a normal distribution a confidence interval of 3 sigma around the mean includes 95 percent of the observations Given the ratio of the two Simsky combinations used computed earlier the success rate reaches 100 percent for both combinations which means any ICS and SCS DM slips on data will be detected for sure no false negatives Nevertheless false positives may occur because 5 percent of the data is statistically outside the 3 sigma bounds To reduce this rate an absolute threshold is also applied SEPTEMBER 2016 WWW GPSWORLD COM GPS WORLD 53