Real-Time Detection and Correction of Abnormal Errors in GNSS Observations on Smartphones
Abstract
:1. Introduction
2. Methods
2.1. Analysis of Abnormal Errors in Smartphone Pseudorange/Carrier Measurements
2.1.1. Analysis of Abnormal Errors in Land Pseudorange/Carrier Measurements
2.1.2. Analysis of Abnormal Errors in Water Pseudorange/Carrier Measurements
2.2. Design of Detection and Repair Solutions
2.2.1. Establishment of State Equations
2.2.2. Establishment of Observation Equations
2.2.3. Abnormal Detection Solution Computation
2.2.4. Abnormal Repair Solution Computation
- Equation establishment: The smartphone observation values are used to compute epoch-to-epoch differences, resulting in single-differenced observation values. These are used to establish the observation equations. The state vector includes the satellite-to-ground distance, rate of change, and acceleration, forming the system state equation;
- Anomaly detection computation: After determining the initial values and variances of the system state, Kalman filtering is employed to predict the satellite-to-ground distance. Differences between predicted values and pseudorange and carrier observation values for each epoch are calculated alongside their standard deviations. The standard deviation multiplied by two serves as the threshold to ascertain whether the differences exceed acceptable limits;
- Anomaly repair computation: Based on the anomalies identified in the second step, three scenarios are considered. First, if no abnormalities are detected in the epoch, the original observation values are directly output without any alterations. Second, if abnormalities are present in some observations within the epoch, normal observations are used to establish observation equations for subsequent Kalman filtering. The resultant filtered values replace the abnormal observations to rectify errors. Third, if all observations within the epoch exhibit abnormalities, predicted values replace the observations to rectify errors.
3. Results
3.1. Experimental Description
3.2. Performance Analysis of Detection and Repair Methods
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Receiver Models | GNSS Chipset Model | Tracked Satellite Systems | Supported Signal Frequencies |
---|---|---|---|
Zhonghaida iRTK2 | NovAtel OEM719 (2016) | GPS/GLONASS/Galileo/BDS/QZSS/WAAS/MSAS/EAGAN | GPS (L1 C/A, L2C, L5) GLONASS (G1, G2) Galileo (E1, E5a, E5b) BDS (B1I, B1C, B2a) |
Xiaomi Mi 8 | Broadcom BCM47755 (2018) | GPS/GLONASS/Galileo/BDS/QZSS | GPS (L1 C/A, L5) GLONASS (G1) Galileo (E1, E5a) BDS (B1I) |
Huawei Mate 40 Pro | Kirin 9000 integrated GNSS chipset (2020) | GPS/GLONASS/Galileo/BDS/QZSS/NavIC | GPS (L1 C/A, L5) GLONASS (G1) Galileo (E1, E5a) BDS (B1I, B1C, B2a, B2b) |
Pseudorange Standard Deviation | Carrier Standard Deviation | ||||||
---|---|---|---|---|---|---|---|
Total Observation Epochs | Epochs with Abnormal Errors | Proportion | Total Observation Epochs | Epochs with Abnormal Errors | Proportion | ||
Mi8 | GPS L1 | 4048 | 31 | 0.76% | 4032 | 57 | 1.41% |
BDS B1 | 4077 | 164 | 4.02% | 3983 | 2 | 0.05% | |
Galileo E1 | 4075 | 55 | 1.34% | 3997 | 11 | 0.28% | |
GLONASS G1 | 4080 | 0 | 0.00% | 3865 | 82 | 2.12% | |
Mate40 Pro | GPS L1 | 3596 | 0 | 0.00% | 3596 | 118 | 3.28% |
BDS B1 | 4027 | 45 | 1.12% | 4027 | 27 | 0.67% | |
Galileo E1 | 3838 | 297 | 7.74% | 3796 | 203 | 5.34% | |
GLONASS G1 | 2740 | 189 | 6.90% | / | / | / |
Pseudorange Standard Deviation | Carrier Standard Deviation | ||||||
---|---|---|---|---|---|---|---|
Total Observation Epochs | Epochs with Abnormal Errors | Proportion | Total Observation Epochs | Epochs with Abnormal Errors | Proportion | ||
Mi8 | GPS L1 | 2023 | 877 | 43.35% | 1561 | 612 | 39.21% |
GPS L5 | 2052 | 22 | 1.02% | 1360 | 494 | 36.32% | |
BDS B1I | 3013 | 221 | 7.33% | 1657 | 328 | 19.79% | |
Mate40 Pro | GPS L1 | 2629 | 1021 | 38.84% | 1463 | 710 | 48.53% |
GPS L5 | 2603 | 892 | 34.27% | 1610 | 432 | 26.83% | |
BDS B1I | 2811 | 412 | 14.66% | 1645 | 128 | 7.78% | |
BDS B1C | 2826 | 388 | 13.73% | 1071 | 31 | 2.89% |
Pseudorange Standard Deviation (m) | Carrier Standard Deviation (m) | ||||||
---|---|---|---|---|---|---|---|
Repair Method | Satellite Number | Before Repair | After Repair | Improvement | Before Repair | After Repair | Improvement |
The proposed method | G02 | 34.157 | 17.679 | 48.29% | 39.345 | 17.529 | 55.41% |
G09 | 46.742 | 35.352 | 24.36% | 59.036 | 36.221 | 38.65% | |
G12 | 27.321 | 25.894 | 5.22% | 53.159 | 32.644 | 38.59% | |
C01 | 54.792 | 20.581 | 62.52% | 13.742 | 13.506 | 1.72% | |
C04 | 39.235 | 30.231 | 22.94% | 15.285 | 15.161 | 0.81% | |
C15 | 64.238 | 27.346 | 57.46% | 37.761 | 33.288 | 11.85% | |
E11 | 365.829 | 58.164 | 46.78% | 198.465 | 56.124 | 44.83% | |
R05 | 168.432 | 50.387 | 46.19% | 130.762 | 53.124 | 45.03% | |
The State-Based method | G02 | 34.157 | 18.972 | 44.46% | 39.345 | 18.918 | 51.95% |
G09 | 46.742 | 35.944 | 23.12% | 59.036 | 38.023 | 35.60% | |
G12 | 27.321 | 26.035 | 4.74% | 53.159 | 34.285 | 35.52% | |
C01 | 54.792 | 22.263 | 59.38% | 13.742 | 13.522 | 1.58% | |
C04 | 39.235 | 30.996 | 21.02% | 15.285 | 15.176 | 0.76% | |
C15 | 64.238 | 29.672 | 53.81% | 37.761 | 33.724 | 10.69% | |
E11 | 365.829 | 209.547 | 42.72% | 198.465 | 115.937 | 41.59% | |
R05 | 168.432 | 98.272 | 41.66% | 130.762 | 77.329 | 40.87% |
Pseudorange Standard Deviation (m) | Carrier Standard Deviation (m) | ||||||
---|---|---|---|---|---|---|---|
Repair Method | Satellite Number | Before Repair | After Repair | Improvement | Before Repair | After Repair | Improvement |
The proposed method | G02 | 50.353 | 50.353 | 0.00% | 95.392 | 50.756 | 46.82% |
G09 | 47.742 | 31.263 | 34.55% | 91.254 | 41.865 | 54.13% | |
G12 | 87.323 | 45.401 | 48.02% | 75.564 | 37.554 | 50.29% | |
C01 | 92.090 | 50.205 | 45.50% | 91.351 | 49.866 | 45.42% | |
C04 | 107.340 | 52.412 | 51.17% | 38.311 | 37.782 | 1.38% | |
C15 | 91.234 | 40.413 | 55.72% | 122.306 | 57.247 | 53.20% | |
E11 | 397.812 | 59.214 | 40.92% | 223.487 | 56.217 | 38.89% | |
R05 | 154.892 | 47.238 | 33.98% | 117.348 | 50.174 | 34.27% | |
The State-Based method | G02 | 50.353 | 50.353 | 0.00% | 95.392 | 56.173 | 41.12% |
G09 | 47.742 | 33.041 | 30.79% | 91.254 | 47.548 | 47.90% | |
G12 | 87.323 | 50.615 | 42.05% | 75.564 | 42.456 | 43.82% | |
C01 | 92.090 | 54.885 | 40.41% | 91.351 | 54.814 | 40.00% | |
C04 | 107.340 | 59.363 | 44.70% | 38.311 | 37.842 | 1.22% | |
C15 | 91.234 | 46.372 | 49.18% | 122.306 | 64.938 | 46.91% | |
E11 | 397.812 | 255.614 | 35.75% | 223.487 | 145.312 | 34.98% | |
R05 | 154.892 | 108.626 | 29.88% | 117.348 | 81.523 | 30.53% |
Pseudorange Standard Deviation (m) | Carrier Standard Deviation (m) | ||||||
---|---|---|---|---|---|---|---|
Repair Method | Satellite Number | Before Repair | After Repair | Improvement | Before Repair | After Repair | Improvement |
The proposed method | G04 | 512.000 | 87.895 | 82.81% | 401.611 | 54.118 | 86.61% |
G05 | 173.341 | 51.287 | 70.42% | 240.025 | 40.598 | 83.08% | |
G17 | 266.932 | 37.281 | 86.04% | 192.669 | 78.266 | 59.34% | |
C07 | 106.402 | 44.599 | 58.11% | 169.804 | 61.962 | 63.52% | |
C12 | 537.453 | 81.235 | 84.87% | 141.295 | 37.969 | 73.11% | |
C22 | 311.510 | 67.359 | 78.39% | 186.350 | 60.866 | 67.38% | |
E17 | 450.187 | 64.239 | 72.34% | 320.876 | 59.783 | 68.91% | |
R22 | 251.476 | 52.831 | 61.27% | 183.945 | 53.928 | 61.89% | |
The State-Based method | G04 | 512.000 | 132.132 | 74.19% | 401.611 | 96.793 | 75.90% |
G05 | 173.341 | 83.811 | 51.65% | 240.025 | 86.085 | 64.14% | |
G17 | 266.932 | 95.970 | 64.05% | 192.669 | 93.054 | 51.70% | |
C07 | 106.402 | 61.515 | 42.19% | 169.804 | 93.117 | 45.17% | |
C12 | 537.453 | 216.217 | 59.77% | 141.295 | 59.116 | 58.17% | |
C22 | 311.510 | 130.773 | 58.02% | 186.350 | 83.764 | 55.05% | |
E17 | 405.872 | 187.154 | 58.43% | 320.876 | 133.573 | 58.37% | |
R22 | 487.234 | 136.869 | 45.58% | 183.945 | 99.119 | 46.12% |
Pseudorange Standard Deviation (m) | Carrier Standard Deviation (m) | ||||||
---|---|---|---|---|---|---|---|
Repair Method | Satellite Number | Before Repair | After Repair | Improvement | Before Repair | After Repair | Improvement |
The proposed method | G04 | 418.108 | 50.213 | 88.04% | 194.363 | 55.726 | 71.40% |
G05 | 511.642 | 70.885 | 86.11% | 377.612 | 59.233 | 84.29% | |
G17 | 488.341 | 49.631 | 89.84% | 162.391 | 61.727 | 61.99% | |
C07 | 131.039 | 59.004 | 55.00% | 103.877 | 49.199 | 52.61% | |
C12 | 179.353 | 41.962 | 76.65% | 131.754 | 54.878 | 58.36% | |
C22 | 611.274 | 39.741 | 93.47% | 209.375 | 80.168 | 61.72% | |
E17 | 450.187 | 64.239 | 72.34% | 320.876 | 59.783 | 68.91% | |
R22 | 251.476 | 52.831 | 61.27% | 183.945 | 53.928 | 61.89% | |
The State-Based method | G04 | 418.108 | 116.083 | 72.24% | 194.363 | 89.453 | 53.98% |
G05 | 511.642 | 160.752 | 68.58% | 377.612 | 165.104 | 56.28% | |
G17 | 488.341 | 100.521 | 79.42% | 162.391 | 79.816 | 50.85% | |
C07 | 131.039 | 78.654 | 39.98% | 103.877 | 63.817 | 38.57% | |
C12 | 179.353 | 75.106 | 58.13% | 131.754 | 65.093 | 50.60% | |
C22 | 611.274 | 134.967 | 77.92% | 209.375 | 116.212 | 44.50% | |
E17 | 450.187 | 199.693 | 55.64% | 320.876 | 137.872 | 57.03% | |
R11 | 251.476 | 116.422 | 53.70% | 183.945 | 86.707 | 52.87% |
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Mu, H.; Yu, X.; Aragon-Angel, A.; Wang, J.; Wu, Y. Real-Time Detection and Correction of Abnormal Errors in GNSS Observations on Smartphones. Remote Sens. 2024, 16, 3117. https://doi.org/10.3390/rs16173117
Mu H, Yu X, Aragon-Angel A, Wang J, Wu Y. Real-Time Detection and Correction of Abnormal Errors in GNSS Observations on Smartphones. Remote Sensing. 2024; 16(17):3117. https://doi.org/10.3390/rs16173117
Chicago/Turabian StyleMu, Hongbo, Xianwen Yu, Angela Aragon-Angel, Jiafu Wang, and Yanze Wu. 2024. "Real-Time Detection and Correction of Abnormal Errors in GNSS Observations on Smartphones" Remote Sensing 16, no. 17: 3117. https://doi.org/10.3390/rs16173117