In this section, we first give initial illustrations of performance of float RTK integrated with INS, followed by IAR results.
With the presence of precise INS information, inertial predictions of position states and Doppler-derived clock delay rate are utilized as additional observables inside the CS-DR scheme. Therefore, only the rural Data set 1 will be used herein for tests. With the urban Data set 2, a positioning performance with 3 sigma values at a level of 5 meters is definitely not precise enough to provide extra references to CS repair.
Instead of a big inflation on CS-deteriorated ambiguitiesβ covariance, it will be more of interest if a proper value, for example the corresponding covariance calculated inside the CS LS filter, can be used.
Conserving the same CS-DR parameters as in Section 5.2.3, i.e. the triplet (πΌ1, πΌ2, πππ ) = (π. πππ, π, ππ) and a minimum of 5 satellites required for CS-free declaration, the positioning results with ambiguities inflated by calculated covariance values are plotted in Figure 7-3. The 95 percentile of
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horizontal positioning errors is 1.89 meters, larger than 1.39 meters of the case when only float RTK-GNSS is involved. The number of epochs having more than 5 CS-free satellites is herein 824 in Figure 7-4, and the number of epochs having CS detected is 648 in Figure 7-5. Remind that in the float RTK-GNSS case (Figure 5-34), the numbers were 862 the number of epochs holding CS-free satellites and 734, the number of epochs having CS detected. Herein, a cleaner CS condition is reflected and there is no sign of fatal miss-detections of big CSs.
By comparing the positioning errors, quite similar curves are observed in both Figure 7-3 and Figure 5-36, except for the interval from epoch 450 to epoch 480. Only during this temporal section a remarkable deterioration is found. According to the Figure 7-4, the algorithm constantly declares all satellites CS-deteriorated during epochs 450 to 480. Instead of occasionally modifying the positioning results in the case only-GNSS, herein the integration system choses to stick with the biased but tolerable-to-INS solution, until the continuous convergence of GNSS ambiguities reclaims.
Figure 7-3. On the left: Horizontal Float RTK/INS position difference between estimated trajectory and the reference trajectory (Data set 1) with ambiguity covariance inflation by corresponding CS covariance. On the right: Portion of Figure 5-36, case only βGNSS.
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Figure 7-4. Number of satellites declared CS-free in each epoch (Data set 1, minimum number of 5 is required). CS-DR scheme takes the values (πΌ1, πΌ2, πππ ) = (0.003, 0, 10).
Figure 7-5. Number of satellites declared CS-deteriorated in each epoch (Data set 1). CS-DR scheme takes the values (πΌ1, πΌ2, πππ ) = (0.003, 0, 10). On the left: minimum number of 5 satellites is required for CS-free declaration. On the right: no requirement on minimum number of satellites for CS-free declaration.
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Figure 7-6. Number of satellites declared CS-free in each epoch (Data set 1). CS-DR scheme takes the values (πΌ1, πΌ2, πππ ) = (0.003, 0, 10).
Figure 7-7. Horizontal Float RTK/INS position difference between estimated trajectory and the reference trajectory (Data set 1) with ambiguity covariance inflation by corresponding CS covariance.
Minimum number of 5 is not required for CS-free declaration.
With the consideration of the additional 4 (i.e., 3 position states and the clock-delay rate) measurements, the minimum number of 5 satellites for declaring CS-free is no longer required. In this way, the number of epochs holding CS-free satellites arises from 824 to 918, as indicated in Figure 7-6. By comparing the 2 plots in in Figure 7-5, another 20 CS-affecting epochs (648-628) are released. The 95 percentile of horizontal positioning errors is 1.32 meters, a performance comparable to 1.39 meters of the only-GNSS case. The relation between temporal positioning errors and their corresponding 3-sigma plots is showed in Figure 7-7. Compared with the Figure 7-3, along with the increased presence of CS-free satellites, much smoother positioning performance and 3-sigma envelopes are reflected in Figure 7-7.
Besides, the positioning bias during epochs 450 and 480 is perfectly controlled.
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Same as in previous Section 5.2.4, the performance of the Partial-IAR (Partial-Integer Ambiguity Resolution) methodology with associated parameters such as the threshold for the probability of success fixing ππ,0 = 99.5%, an empirical ratio threshold of 2 and a minimum number of 5 DD ambiguities to enter IAR, will be presented. First of all, the value of ππ calculated based on the best 5 satellites having the lowest uncertainty is studied in Figure 7-8. The percentage of holding a ππ greater than ππ,0 is herein 19.05%. The value was 12.8% in Section 5.2.4. As expected, continuous estimation of ambiguities provides a better anticipation of success fixing.
Figure 7-8. The probability of success Ps calculated based on the 5 ambiguities having the lowest uncertainty (Data set 1)
Figure 7-9. Horizontal performance of the IAR solution using the proposed Partial-IAR as the ambiguity validation method (Data set 1)
Table 7-1. Performance summary of the IAR results processing the Data set 1 using a modified Partial-IAR validation scheme.
Horizontal Positioning Error (in meter)
Data Set 1 68th
Percentile 95th
Percentile 98th
Percentile Fix Rate Wrong Fix Rate
GNSS IAR 0.74 1.80 2.52 5.6% 16.7%
GNSS/INS IAR 0.74 1.26 1.75 4.8% 9.3%
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The horizontal positioning results are provided in Figure 7-9. With the positioning statistics of the GNSS case, new GNSS/INS performance indicators are summarized in Table 7-1. Smaller horizontal positioning error percentiles are obtained in the case GNSS/INS. A 95th percentile of 1.26 meter is comparable with the previous float GNSS/INS case. Still a comparably low fix rate of 4.8% is obtained.
The fixing zone is mainly located between epoch 500 and 600, where a constantly big value of ππ is guaranteed. Nevertheless, the wrong fix rate is much lower 9.3%, in comparison with 16.7% of the GNSS case.
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