Position Error on Data Set 2

Similarly to 6.2.1, the addition of GLONASS code bias correction and then of both GLONASS code bias correction and proposed weighting scheme is tested on the second data set.

Position error obtained by simply correcting GLONASS code biases can be found on Figure 6.14 and Figure 6.15. 09:15 09:20 09:25 09:30 09:35 09:40 -10 -8 -6 -4 -2 0 2 4 6 8 10

Error in the estimated position (Downtown Toulouse)

Time of Day (hours:minutes)

m e te rs Up East North Fix mode 09:45 09:50 09:55 -10 -8 -6 -4 -2 0 2 4 6 8 10

Error in the estimated position (Toulouse's beltway)

Time of Day (hours:minutes)

m e te rs Up East North Fix mode

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Figure 6.14 Difference between estimated trajectory and reference trajectory in downtown Toulouse (data set 2). Black asterisk represents epochs when ambiguity vector is validated and

fixed as integer. Baseline configuration + GLONASS code bias correction

Figure 6.15 Difference between estimated trajectory and reference trajectory on Toulouse’s beltway (data set 2). Black asterisk represents epochs when ambiguity vector is validated and fixed as integer. Baseline configuration + GLONASS code bias correction

Once again, the improvement in terms of position accuracy is small. However, these biases correction improves both the fix rate and the estimated position variance performance, as seen on Table 6.3. The improvement brought by using the proposed weighting scheme is shown on Figure 6.24 and Figure 6.9.

Figure 6.16 Difference between estimated trajectory and reference trajectory in downtown Toulouse (data set 2). Black asterisk represents epochs when ambiguity vector is validated and

fixed as integer. Baseline configuration + GLONASS code bias correction + proposed weighting scheme

Figure 6.17 Difference between estimated trajectory and reference trajectory on Toulouse’s beltway (data set 2). Black asterisk represents epochs when ambiguity vector is validated and fixed as integer. Baseline configuration + GLONASS code bias correction + proposed weighting scheme

The adoption of the proposed weighting scheme has the effect of removing slowly, i.e. with variation over a few minutes, changing effects due to code multipath. The improvement in term of position accuracy is very clear.

However, despite the very high accuracy of the float solution on Toulouse’s beltway, the number of fixed ambiguities is very small compared to the first data set. In order to determine the reason of the poor ambiguity fixing rate, ambiguity validation statistics were collected and reported on Table 6.2 for

12:30 12:45 13:00 13:15 13:30 -10 -8 -6 -4 -2 0 2 4 6 8 10

Error in the estimated position (Downtown Toulouse)

Time of Day (hours:minutes)

m e te rs Up East North Fix mode 13:40 13:50 14:00 14:10 14:20 -10 -8 -6 -4 -2 0 2 4 6 8 10

Error in the estimated position (Toulouse's beltway)

Time of Day (hours:minutes)

m e te rs Up East North Fix mode 12:30 12:45 13:00 13:15 13:30 -10 -8 -6 -4 -2 0 2 4 6 8 10

Error in the estimated position (Downtown Toulouse)

Time of Day (hours:minutes)

m e te rs Up East North Fix mode 13:40 13:50 14:00 14:10 14:20 -10 -8 -6 -4 -2 0 2 4 6 8 10

Error in the estimated position (Toulouse's beltway)

Time of Day (hours:minutes)

m e te rs Up East North Fix mode

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both data sets. As explained in section 4.2.6, a GPS ambiguity vector is validated and fixed if it fulfills 2 conditions: it composed of at least 5 GPS ambiguities i.e. 6 GPS satellites visible, the ratio-test exceeds the value of 3. As explained in section 6.1.1, GLONASS ambiguities are kept as floats.

Table 6.2 Statistics of GPS ambiguity validation in beltway environment, for both data sets

data set 1 beltway

data set 2 beltway Number of epoch with at least 5

GPS ambiguities 70.8 % 67.7%

Number of epoch with at least 5 GPS ambiguities a ratio-test of at

least 3 50.2% 18.8%

As seen on Table 6.2, GPS carrier phase availability is similar in both data collections. However, ambiguity validation fails in the second data set due to the ratio-test. It indicates that the distance between the float ambiguity vector and the closest integer vector is too important. The poor success rate of the ratio-test can be due to both code multipath or carrier phase biases such as residual atmospheric delay or carrier phase multipath. However, considering the high accuracy of the position obtained on Figure 6.17, the most probable reason is carrier phase biases. The time of the day of the second data set is closer to the daily ionospheric peak and the baseline can exceed 10 km during several epochs. In these conditions, ionospheric differential biases can reach a few centimeters and jeopardize ambiguity resolution. The distribution of epochs with fixed ambiguity as a function of the baseline length with the 2 beltway data sets can be found on Figure 6.18 and Figure 6.19.

It can be seen that contrary to the first data set where ambiguities are more successfully fixed when the baseline length is short, the correlation between successful ambiguity resolution and baseline length seems less clear in the second data set, which tend to discard the hypothesis of a low fixing rate due to residual atmospheric delays.

Another explanation to the low ambiguity resolution success rate can be that the antenna was not placed on a large metallic ground plane in the second experiment whereas the antenna was magnetically sticked to the roof of the vehicle in the first data set, as explained in section 5.2.1. Therefore, elevation-dependent biases due to larger phase center position variation and carrier phase multipath coming from the roof of the vehicle might also be the cause of a lower fixing rate.

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Figure 6.18 Ambiguity resolution status (float or fixed) as a function of the baseline length on Toulouse beltway (data set

1).

Figure 6.19 Ambiguity resolution status (float or fixed) as a function of the baseline length on Toulouse beltway (data set 2).

6.2.3

Conclusion on the Baseline Solution Performance

Cumulative density function values of horizontal position error, fix rate and wrong fix rate are reported in Table 6.3 and

Table 6.4.

Table 6.3 Performance summary of the impact of adding GLONASS inter-channel bias correction with the 2 studied data sets

Horizontal Position Error

68th percentile 95th percentile 99th percentile Fix rate Wrong Fix rate Data Set 1 2.11 meters 4.73 meters 6.44 meters 9.1% 60.5% urban 2.30 meters 5.30 meters 6.58 meters 4.7% 98.9% Beltway 1.83 meters 2.90 meters 3.32 meters 17.2% 41.0% Data Set 2 1.65 meters 3.69 meters 6.37 meters 6.2% 52.7% urban 2.01 meters 4.36 meters 7.46 meters 3.0% 92.0% beltway 1.23 meters 2.03 meters 2.24 meters 11.5% 35.4%

09:45 09:50 09:55 0 2000 4000 6000 8000 10000 12000

Time of Day (hours:minutes)

B a s e lin e l e n g th ( m e te rs ) Data set 1 Fix Mode Float Mode 13:40 13:50 14:00 14:10 14:20 0 2000 4000 6000 8000 10000 12000

Time of Day (hours:minutes)

B a s e lin e l e n g th ( m e te rs ) Data set 2 Fix Mode Float Mode

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Table 6.4 Performance summary of the the impact of adding GLONASS inter-channel bias correction and the proposed observation weighting scheme with the 2 studied data sets

Horizontal Position Error

68th percentile 95th percentile 99th percentile Fix rate Wrong Fix rate Data Set 1 0.92 meters 3.46 meters 4.47 meters 20.3% 12.2% urban 1.36 meters 3.87 meters 4.87 meters 5.8% 51.8% Beltway 0.31 meters 0.80 meters 1.19 meters 47.1% 3.3% Data Set 2 1.17 meters 3.75 meters 6.74 meters 9.7% 30.4% urban 1.68 meters 4.47 meters 7.54 meters 4.2% 82.6% beltway 0.58 meters 0.97 meters 1.25 meters 18.8% 11.0% The correction of GLONASS inter-channel biases using table-based calibration was shown to make the ambiguity resolution more successful and reliable by removing systematic biases and improving the position accuracy especially in difficult environment. Contrary to the baseline solution, a difference could be seen between both environments in term of fix rate when GLONASS code biases are corrected. Sub-meter accuracy is obtained 95% of the time on the beltway, in both environments. Secondly, it was shown that an observation covariance matrix reflecting the actual quality of measurements is beneficial to the accuracy of the estimated position. In the case of a low-cost receiver, a weighting scheme depending on the environment seems to better fit the discrepancy that exists in measurements quality between clear-sky environment and urban environment. An environment- dependent weighting scheme is then recommended.