GPS World, January 2014

INNOVATION Algorithms Methods Introduced Calculated 0 100 200 300 400 500 600 1000 500 ï 0 Cycles 0 100 200 300 400 500 600 08 06 04 02 0 Epochs FIGURE 9 Introduced and calculated cycle slips upper plot and detection error lower plot Few cycle slips case reference satellite with PRN 22 bias and general drift trends which need some elaboration In fact the bias error can be the result of more than one cause The low cost inertial sensors always have bias in their characteristics which plays a major role in this The drift is further affecting relatively lower elevation angle satellites which can also be attributed to more than one reason Indeed one reason for choosing this specific trajectory which was conducted in 2011 was to test the algorithm with severe ionospheric conditions as the year 2011 was close to a solar maximum a period of peak solar activity in the approximately 11 year sunspot cycle Moreover the time of the test was in the afternoon which has the maximum ionospheric effects during the day Thus most part of the drift trend must be coming from ionospheric effects as the rover is moving away from the base receiver during this portion of the trajectory Furthermore satellite geometry could contribute to this error component Most of the sudden jumps coincide with or follow sharp vehicle turns and rapid tilts Table 2 shows the averaged RMS and standard deviation std DD carrier phase estimation error for the sample satellite pairs We introduced cycle slips at different rates or intensities and different sizes to simulate real life scenarios Fortunately cycle slips are usually big as mentioned earlier and this was corroborated by our observations from real trajectory data Therefore it is more important to detect and correct for Introduced Calculated 0 100 200 300 400 500 600 1000 500 ï 0 Cycles 0 100 200 300 400 500 600 4 2 0 ï ï FIGURE 10 Introduced and calculated cycle slips upper plot and detection error lower plot Moderate cycle slips case reference satellite with PRN 22 bigger slips in general Introducing and Detecting Cycle Slips To test the robustness of the algorithm we started with an adequate cycle slip size Cycle slips of size 10 1000 cycles were introduced with different intensities These intensities are categorized as few 1 slip per 100 epochs moderate 10 slips per 100 epochs and severe 100 slips per 100 epochs This was applied for all DD carrier phase measurement sets simultaneously The threshold was set to 19267 average of RMS error for all satellite pairs cycles Four metrics were used to describe the results Mean square error MSE accuracy the detected cycle slip size with respect to the introduced size True detection TD ratio and Mis detection MD ratio Due to space constraints and the similarity between results for different satellites we only show results for the reference satellite with PRN 22 FIGURES 9 12 show introduced versus calculated cycle slips along with the corresponding detection error for sample satellites in the different scenarios TABLES 3 5 summarize these results All introduced cycle slips were successfully detected in all of the few moderate and severe cases with very high accuracy A slight change in the accuracy increasing with higher intensity among the different scenarios shows that detection accuracy is not affected by cycle slip intensity Higher mis detection ratios for smaller cycle slip intensity comes from bigger error margins than Epochs Satellite pair RMS cycles Std cycles Ref PRN 9 115 085 Ref PRN 14 145 138 Ref PRN 18 358 247 Ref PRN 22 093 087 Ref PRN 27 249 186 Average 193 149 TABLE 2 Estimation error for DD carrier phases in cycles Satellite pair Accuracy TD MD MSE cycles Ref PRN 9 9972 100 9375 014 Ref PRN 14 9985 100 9603 008 Ref PRN 15 9914 100 9861 156 Ref PRN 22 9990 100 9107 002 Ref PRN 27 9940 100 9816 066 Average 9960 100 9550 049 TABLE 3 Few slips 1 slip per 100 epochs Satellite pair Accuracy TD MD MSE cycles Ref PRN 9 9983 100 5833 0127 Ref PRN 14 9989 100 6855 0194 Ref PRN 15 9951 100 8659 1237 Ref PRN 22 9992 100 4845 0082 Ref PRN 27 9965 100 8287 0600 Average 9976 100 6859 0448 TABLE 4 Moderate slips 10 slips per 100 epochs the threshold for several satellite pairs However this is not affecting the overall accuracy strongly as all mis detected slips are of comparably very small sizes MD ratio is zero in the intensive cycle slip case as all epochs contain slips is an indicator of performance compromise with slip intensity It is less likely to have very small cycle GPS World January 2014 www gpsworld com 68