# Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica

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## Abstract

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## 1. Introduction

## 2. Precise Orbit Positioning Processing Approach

#### 2.1. Global Navigation Satellite System Observation Model

#### 2.2. Ambiguity Fixing

#### 2.3. Ambiguity Fixing of BeiDouObservations

## 3. Validation with Data from International GNSS Service

#### 3.1. Data Description

#### 3.2. Performance of Ambiguity Fixing

#### 3.3. Performance of Positioning

## 4. Result of a Real Flight Experiment

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The RMS values of IF code residuals of PPP and POP solutions. For each system, the code residuals of all involved satellites are lumped together to calculate the RMS values. The Beidou code observations before and after corrected with the satellite-induced code bias are shown in the right two subplots.

**Figure 2.**The distribution of global multi-GNSS network used in this study. The colors represent the tracked GNSS systems on a station, GPS in blue, GLONASS in green, Galileo in red and Beidou in black.

**Figure 3.**The distribution of GLONASS stations selected for integer ambiguity fixing. The red diamonds denote the SEPT POLARX5 receivers, the blue dots denote the TRIMBLE NETR9 receivers, the yellow squares denote the JAVAD TRE_G3TH DELTA receivers and the green triangles denote the LEICA GR25 receivers. The firmware versions for different types of receivers are ignored in this study.

**Figure 4.**The fixing percentages of PPP and POP AR with 14 days of single-, dual- and four-system observations. By doing a chi-squared distribution test with a 0.05 level of significance, it is shown that the p-value that indicates the significance-level for the differences between PPP and POP calculated with GLONASS, Galileo, BDS, GR, GE, GC and GREC observations is 0.062, 0.078, 0.0030, 0.25, 0.09, 0.0036 and 0.019, respectively, with respect to GPS. We can see there are significant differences between the PPP and POP results with BDS, GC, and GREC observations.

**Figure 5.**The single-, dual- and four-system PPP (upper half) and POP (lower half) float and fixed solutions with respect to the IGS nominal position for station CAS1 on 1 January 2018. We can see better performance of POP than PPP with BDS involved solutions.

**Figure 6.**The average RMS values of kinematic PPP and POP solutions after converged for stations CAS1, DAV1, OHI3 and MCM4 with different types of observations in the east, north and up components. For each day, the RMS values are calculated for each type of solutions, i.e., the PPP float with GPS observations in the east component, with reference to the IGS nominal position. Then the average RMS values are obtained over 14 days.

**Figure 7.**The trajectory of this flight with the latitude shown on the radius and the longitude on the arc. FD83 is the reference station.

**Figure 8.**The time series of baseline length of the three antennas derived from DD, PPP and POP approaches. Both the float as well as fixed solutions are shown for PPP and POP. For clarity, the DD, PPP float, PPP fixed and POP float results are shifted by 0.2, 0.4, 0.6 and 0.8 m, respectively.

**Figure 9.**The satellite visibility tracked by the reference station FD83 (blue) and the rover AIR2 (red). Only 10 satellites are shown here. Receivers losing track of the satellites may introduce biases in the DD solutions.

**Figure 10.**The number of DD observations used in the processing for the three baselines. During 20:00–21:00, the number is 6 and is not beneficial for the calculation of DD solutions.

**Figure 11.**Statistics of the distances between the three antennas derived from the five types of solutions. It is seen that the POP fixed solutions generate the best baseline results.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, M.; Xu, T.; Flechtner, F.; Förste, C.; Lu, B.; He, K.
Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica. *Remote Sens.* **2019**, *11*, 992.
https://doi.org/10.3390/rs11080992

**AMA Style**

Li M, Xu T, Flechtner F, Förste C, Lu B, He K.
Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica. *Remote Sensing*. 2019; 11(8):992.
https://doi.org/10.3390/rs11080992

**Chicago/Turabian Style**

Li, Min, Tianhe Xu, Frank Flechtner, Christoph Förste, Biao Lu, and Kaifei He.
2019. "Improving the Performance of Multi-GNSS (Global Navigation Satellite System) Ambiguity Fixing for Airborne Kinematic Positioning over Antarctica" *Remote Sensing* 11, no. 8: 992.
https://doi.org/10.3390/rs11080992