The Unified Form of Code Biases and Positioning Performance Analysis in Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) Precise Point Positioning Using Real Triple-Frequency Data
Abstract
:1. Introduction
2. The Unified Forms of Code Biases
2.1. Basic Observation Equations
2.2. Inter Frequency Clock Bias
2.3. Inter System Clock Bias
3. Observation Models in Single or Multi-GNSS
3.1. Uncombined Observation Model with Triple-Frequency Multi-GNSS
3.2. Other Typical Observation Models
4. Analysis And Assessment
4.1. Experimental Strategy
4.1.1. Configuration Strategy
4.1.2. Availability of Multi-Frequency Models
4.2. Influence of Code Biases
4.2.1. Influence of IFB Bias
4.2.2. Influence of ISB Bias
4.2.3. Influence of Both IFB and ISB Biases
4.3. Results and Discussion of Single and Multi-GNSS PPP
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
BDS | BeiDou Navigation Satellite System |
CIF | conventional ionosphere-free model |
CIF2 | conventional ionosphere-free model with dual-frequency |
CIF2-BDS | conventional ionosphere-free model with dual-frequency BDS-only |
CIF2-C | conventional ionosphere-free model with dual-frequency BDS+GPS combination |
CIF2-GPS | conventional ionosphere-free model with dual-frequency GPS-only |
CIF3 | conventional ionosphere-free model with triple-frequency |
CIF3-BDS | conventional ionosphere-free model with triple-frequency BDS-only |
CIF3-C | conventional ionosphere-free model with triple-frequency BDS+GPS combination |
CORS | Continuously Operating Reference Stations |
CT | convergence time |
DCB | differential code bias |
DOY | day of year |
ECIF2-C | extended CIF2-C model |
FCB | fractional cycle bias |
GMF | Global Mapping Function |
GNSS | Global Navigation Satellite System |
GPS | Global Positioning System |
ICD | Interface Control Document |
IFB | inter-frequency clock bias |
ISB | inter-system clock bias |
ISC | inter-signal correction |
MGEX | Multi-GNSS Experiment |
M-W | Melbourne-Wubbena detecting |
PCO | Antenna Phase Center Offsets |
PCV | Antenna Phase Center Variations |
PPP | precise point positioning |
TGD | timing group delay |
UC | uncombined model |
UC2 | uncombined model with dual-frequency |
UC3 | uncombined model with triple-frequency |
UC3-BDS | uncombined model based with triple-frequency BDS-only |
UC3-C | uncombined model with triple-frequency BDS+GPS combination |
UPD | uncalibrated phase delay |
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Model | System | Observations | Parameters | Parameter Description |
---|---|---|---|---|
UC3 | Single | 6n | 4n+5+1 | X, Y, Z, , , IFB, n*(I,,,) |
Multi | 6n | 4n+5+m+1 | X, Y, Z, , , ISB, m*IFB, n*(I,,,) | |
CIF3 | Single | 2n | n+5 | X, Y, Z, , , n*N |
Multi | 2n | n+5+1 | X, Y, Z, , , ISB, n*N | |
UC2 | Single | 4n | 3n+5 | X, Y, Z, , , n*(I,,) |
Multi | 4n | 3n+5+1 | X, Y, Z, , , ISB, n*(I,,) | |
CIF2 | Single | 2n | n+5 | X, Y, Z, , , n*N |
Multi | 2n | n+5+1 | X, Y, Z, , , ISB, n*N |
Model | System | Signal Combination | (Cycle) | Noise (m) | |||
---|---|---|---|---|---|---|---|
CIF2 | GPS | , | 2.5457 | −1.5457 | 0 | 297.8 | 0.8934 |
, | 2.5457 | −1.5457 | 0 | 2.978 | 0.0089 | ||
BDS | , | 2.4872 | −1.4872 | 0 | 289.8 | 0.8694 | |
, | 2.4872 | −1.4872 | 0 | 2.898 | 0.0087 | ||
CIF3 | GPS | , , | 2.3269 | −0.3596 | −0.9673 | 254.5 | 0.7635 |
, , | 2.3269 | −0.3596 | −0.9673 | 2.545 | 0.0076 | ||
BDS | , , | 2.5664 | −1.2289 | −0.3375 | 286.5 | 0.8596 | |
, , | 2.5664 | −1.2289 | −0.3375 | 2.865 | 0.0086 |
Error Corrections | Setting |
---|---|
DCB | Multi-GNSS Experiment (MGEX) |
Cycle slip | Melbourne-Wubbena detecting (M-W) and Ionosphere Residuals |
Clock slip | Guo [33] |
Observation weighting | Witchayangkoon [34] and Helmert |
Earth rotation | Sagnac effect |
Relativistic effects | Xu and Xu [23] |
Troposphere | Random walk + Hopfield + Global Mapping Function (GMF) |
Antenna phase center | Antenna Phase Center Offsets (PCO)+Antenna Phase Center Variations (PCV) |
Phase windup | Corrected |
Earth tides correction | Solid/Pole tide |
Parameter | Setting |
---|---|
Rinex file | xxxx1000.18o |
Precise orbit product | gbm19962.sp3 |
Precise clock product | gbm19962.clk |
Pole shift/ut1-utc | gbm19962.erp |
Antenna phase center | igs14.atx |
Positioning mode | static |
Estimation algorithm | Standard Kalman Filter |
Reference coordinate | gbm19962.clk |
Sample rate | 30 s |
Elevation cutoff angle |
Model | CEDU | DARW | JFNG | KARR | KZN2 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | E | U | N | E | U | N | E | U | N | E | U | N | E | U | |
UC3-C | 16 | 23 | 108 | 14 | 47 | 84 | 27 | 34 | 45 | 15 | 64 | 35 | 24 | 19 | 35 |
CIF3-C | 15 | 19 | 97 | 17 | 50 | 81 | 26 | 34 | 42 | 16 | 70 | 33 | 13 | 24 | 37 |
ECIF2-C | 17 | 20 | 110 | 5 | 38 | 107 | 30 | 29 | 43 | 6 | 58 | 52 | 14 | 19 | 48 |
CIF2-C | 18 | 29 | 131 | 8 | 36 | 115 | 21 | 22 | 31 | 4 | 55 | 73 | 11 | 25 | 45 |
UC3-BDS | 33 | 18 | 108 | 18 | 29 | 164 | 13 | 55 | 165 | 23 | 29 | 64 | 29 | 53 | 147 |
CIF3-BDS | 33 | 17 | 119 | 21 | 33 | 162 | 11 | 48 | 115 | 23 | 28 | 74 | 26 | 56 | 151 |
CIF2-BDS | 33 | 17 | 119 | 19 | 34 | 159 | 11 | 48 | 115 | 23 | 28 | 74 | 25 | 56 | 149 |
CIF2-GPS | 18 | 33 | 139 | 8 | 41 | 136 | 20 | 18 | 24 | 4 | 54 | 84 | 11 | 24 | 49 |
Model | CEDU | DARW | JFNG | KARR | KZN2 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | E | U | N | E | U | N | E | U | N | E | U | N | E | U | |
UC3-C | 9 | 10 | 18 | 4 | 12 | 27 | 6 | 9 | 22 | 8 | 22 | 20 | 64 | 13 | 31 |
CIF3-C | 8 | 10 | 20 | 6 | 13 | 33 | 6 | 10 | 18 | 10 | 27 | 18 | 5 | 9 | 29 |
ECIF2-C | 6 | 8 | 24 | 4 | 16 | 26 | 12 | 15 | 31 | 5 | 17 | 27 | 7 | 16 | 37 |
CIF2-C | 5 | 9 | 36 | 3 | 9 | 23 | 8 | 7 | 20 | 4 | 10 | 33 | 7 | 8 | 34 |
UC3-BDS | 13 | 17 | 22 | 10 | 17 | 34 | 6 | 12 | 60 | 15 | 11 | 21 | 9 | 20 | 9 |
CIF3-BDS | 13 | 17 | 23 | 11 | 18 | 38 | 6 | 7 | 47 | 15 | 10 | 24 | 9 | 19 | 11 |
CIF2-BDS | 13 | 17 | 23 | 10 | 18 | 37 | 6 | 7 | 46 | 15 | 10 | 24 | 9 | 20 | 11 |
CIF2-GPS | 5 | 10 | 37 | 3 | 9 | 26 | 7 | 6 | 19 | 3 | 9 | 37 | 8 | 7 | 30 |
Model | Accuracy (N,E,U) (mm) | Precision (N,E,U) (mm) | Mean CT (s) | Median CT (s) |
---|---|---|---|---|
UC3-C | (19, 38, 61) | (7, 13, 24) | 46.6 | 40 |
CIF3-C | (18, 39, 58) | (7, 14, 23) | 54 | 55 |
ECIF2-C | (15, 33, 72) | (7, 14, 29) | 58.9 | 55.5 |
CIF2-C | (12, 33, 79) | (5, 8, 29) | 22.8 | 13.5 |
UC3-BDS | (23, 37, 130) | (11, 15, 29) | 163.8 | 179.25 |
CIF3-BDS | (23, 37, 124) | (10, 14, 28) | 190 | 196 |
CIF2-BDS | (22, 37, 123) | (22, 37, 123) | 191 | 197.5 |
CIF2-GPS | (12, 34, 86) | (5, 8, 30) | 16.4 | 15 |
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Liu, P.; Qin, H.; Cong, L. The Unified Form of Code Biases and Positioning Performance Analysis in Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) Precise Point Positioning Using Real Triple-Frequency Data. Sensors 2019, 19, 2469. https://doi.org/10.3390/s19112469
Liu P, Qin H, Cong L. The Unified Form of Code Biases and Positioning Performance Analysis in Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) Precise Point Positioning Using Real Triple-Frequency Data. Sensors. 2019; 19(11):2469. https://doi.org/10.3390/s19112469
Chicago/Turabian StyleLiu, Peng, Honglei Qin, and Li Cong. 2019. "The Unified Form of Code Biases and Positioning Performance Analysis in Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) Precise Point Positioning Using Real Triple-Frequency Data" Sensors 19, no. 11: 2469. https://doi.org/10.3390/s19112469
APA StyleLiu, P., Qin, H., & Cong, L. (2019). The Unified Form of Code Biases and Positioning Performance Analysis in Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) Precise Point Positioning Using Real Triple-Frequency Data. Sensors, 19(11), 2469. https://doi.org/10.3390/s19112469