Improvement Brought by Adding Integer Resolution of GLONASS Ambiguities

In order to fully benefit from the precision of GLONASS carrier phase measurements, GLONASS ambiguities have to be estimated as integers. It involves 2 steps: calibrating GLONASS biases during a static data collection in a clear-sky environment and performing the correct processing of GLONASS ambiguities in the software in order to isolate them as integers. The first step is described

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in 4.2.7.1, while the second step is described in 4.2.7.4. In this section, GLONASS carrier phase measurements were corrected from GLONASS inter-channel biases and GPS/GLONASS combined integer ambiguity resolution is performed. Although the receiver has been completely powered off between the 2 data collection, the same inter-channel bias correction value of 0.47 cm for 2 adjacent frequencies is used for both data sets.

6.5.1

Position Error on Data Set 1

The first data set was reprocessed using the proposed weighting scheme, the cycle slip resolution module, the multipath exclusion module activated and adding GLONASS ambiguities in the integer estimation step. The improvement is significant, as seen on Figure 6.29 and Figure 6.30.

Figure 6.29 Position error in downtown Toulouse (data set 1). Black asterisk represents epochs when ambiguity vector is validated

and fixed as integer

Figure 6.30 Position error on Toulouse’s beltway (data set 1). Black asterisk represents epochs when ambiguity vector is validated and fixed as integer

The number of epochs with fixed ambiguities has been improved in both environments. The number of wrong fixes in downtown Toulouse is also greatly reduced. The fixing statistics are presented in Table 6.15.

Table 6.15 Statistics of GPS+GLONASS ambiguity validation in beltway and downtown environment, for data set 1.

Toulouse beltway

Downtown Toulouse Number of epoch with at least 5

GPS+GLONASS ambiguities 81.8 % 64.0%

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

test of at least 3 61.8% 17.0%

Comparing with Table 6.2, it can be seen that on the beltway the number of epoch with at least 5 ambiguities grows from 70.8% to 81.8% whereas the final fixing rate grows from 45.9% to 61.8%

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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compared to the previous experience. It shows that the improvement in the ambiguity fixing success rate is not only due to the larger number of epochs with the minimum number of carrier phase measurements required, but also to the improved effectiveness of the LAMBDA method and the ratio test in finding and validating the correct integer vector due to a better geometry. However, ambiguity are still fixed less than one fifth of the time in urban environment despite 64% availability of the minimum number of ambiguities required. Indeed, the float solution is not accurate enough because of code multipath and weak satellite geometry, which makes the ratio test fail.

6.5.2

Position Error on Data Set 2

In the second data set, the improvement brought by adding GLONASS ambiguities in the integer ambiguity estimation step is also very clear, as seen on Figure 6.31 and Figure 6.32.

Figure 6.31 Position error in downtown Toulouse (data set 2). Black asterisk represents epochs when ambiguity vector is validated

and fixed as integer

Figure 6.32 Position error on Toulouse’s beltway (data set 2). Black asterisk represents epochs when ambiguity vector is validated and fixed as integer

The number of epoch with fixed ambiguities grows from 22.8% to 39.7% on the beltway, as seen on Table 6.17. Similarly to the first data set, the number of wrong fix has been greatly reduced on the beltway to 0.1%. In urban environment, the number of wrong fixes still represents more than 11% of the total fixes. However, considering the small number of total number of fixes, wrong integer fixing does not greatly affect horizontal position error.

However, the fixing rate of the second data set in the beltway is still significantly lower than for the first data set, probably due to a worst placement of the antenna as explained in 6.2.2.

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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Table 6.16 Statistics of GPS+GLONASS ambiguity validation in beltway and downtown environment, for data set 2.

Toulouse beltway

Downtown Toulouse Number of epoch with at least 5

GPS+GLONASS ambiguities 81.2 % 52.3%

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

test of at least 3 43.5% 8.1%

6.5.3

Conclusion on the Impact of GPS+GLONASS Integer

Ambiguity Resolution

The addition of GLONASS ambiguities was shown to bring benefit, as it both improves the geometry of the integer estimation problem and the availability of the integer estimation algorithm. Results are summarized in Table 6.17.

Table 6.17 Performance summary of the baseline solution improved by GLONASS code inter-channel bias correction, the proposed observation weighting scheme, the cycle slip resolution module, the multipath exclusion

module and the addition of GLONASS ambiguities in the integer estimation step, with the 2 studied data sets

Horizontal Position Error

68th percentile 95th percentile 99th percentile _{Fix rate Wrong Fix rate}

Data Set 1 1.08 meters 2.91 meters 3.86 meters 32.7% 0.8%

urban 1.60 meters 3.44 meters 4.09 meters 17.0% 2.2%

Beltway 0.14 meters 0.89 meters 1.33 meters 61.8% 0.2%

Data Set 2 0.96 meters 3.13 meters 5.41 meters 21.4% 2.7%

urban 1.52 meters 3.48 meters 6.47 meters 8.1% 11.0%

beltway 0.22 meters 0.66 meters 0.94 meters 43.5% 0.1%

The proposed calibration method was found to be efficient in removing most part of the carrier phase inter-channel bias, allowing successful and reliable GLONASS integer ambiguity fixing. Fix rate has increased in all environments due to improved geometry, while wrong fix rate has decreased. In particular, only 0.2% and 0.1% of the ambiguity fixes on the beltway are wrongly fixed for data set 1 and 2 respectively. Horizontal position error 95th _{percentile remains stable in urban environment, but}

benefits from the increased fix rate on the beltway. This result is more particularly visible with the 68th

percentile. Indeed, 68% of the estimated positions are within 14 cm and 22 centimeters of the reference trajectory on the beltway respectively for both data sets, and within 1.60 meters and 1.52 meters of the reference trajectory respectively in urban data set 1 and 2. Therefore, calibrating GLONASS interchannel biases and estimating GLONASS integer ambiguities together with GPS was found to provide a very significant performance leap in term of position accuracy.