A Robust Adaptive Extended Kalman Filter Based on an Improved Measurement Noise Covariance Matrix for the Monitoring and Isolation of Abnormal Disturbances in GNSS/INS Vehicle Navigation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Steps of the Improved Robust Adaptive Factor Method
2.2. Classical GNSS/INS Loosely Coupled Integrated Procedure
2.3. Robust Adaptive Filtering Algorithm with Improved Measurement Noise Covariance Matrix
2.3.1. Construction of the Improved Measurement Noise Covariance Matrix
2.3.2. Robust Adaptive Filtering Construction
- Calculate the gain matrix: ;
- Calculate the state estimate at time k: ;
- Calculate the estimate error covariance matrix at time k: .
- Calculate the gain matrix: ;
- Calculate the state estimate at time k: ;
- Calculate the estimate error covariance matrix at time k: .
2.4. Datasets and Processing Strategies
3. Results
3.1. Experimental Results for the Measurement Noise Covariance Matrix
3.2. Vehicle Experimental Results
3.2.1. Vehicle Experimental 1 Results
- Regarding position error: In terms of the East–North–Up (ENU) position error, compared with EKF, the accuracy of RAKF increased by 27.03%, 77.92%, and 72.56%, respectively. Compared with AKF, the accuracy of RAKF improved by 2.84% and 10.85%, respectively. Compared with RKF, the accuracy of RAKF improved by 22.62%, 51.79%, and 54.19%, respectively. In the position average accuracy, compared with the three algorithms, the accuracy of RAKF improved by 72.43%, 2.54%, and 47.82%, respectively.
- Regarding velocity error: In terms of the East–North–Up (NEU) velocity error, compared with EKF, the accuracy of RAKF increased by 31.34%, 86.04%, and 26.44%, respectively. Compared with AKF, the accuracy of RAKF improved by 34.27% and 77.58%, respectively. Compared with RKF, the accuracy of RAKF improved by 29.57%, 79.91%, and 2.93%, respectively.
- Regarding attitude errors: In terms of the pitch–roll–heading–attitude error, compared with EKF, the accuracy of RAKF increased by 59.54%, 34.08%, and 35.85%, respectively. Compared with AKF, the accuracy of RAKF improved by 41.91%, 12.44%, and 32.79%, respectively. Compared with RKF, the accuracy of RAKF improved by 32.31%, 15.54%, and 19.86%, respectively.
3.2.2. The Comparison Results of the Single GPS System and GPS+GLONASS+BDS Three Systems
3.2.3. Vehicle Experiment 2 Results
- Regarding position error: In terms of the East–North–Up (ENU) position error, compared with EKF, the accuracy of RAKF increased by 0%, 66.28%, and 9.53%, respectively. Compared with AKF, the accuracy of RAKF improved by 5.34% and 64.86%, and 3.22%, respectively. Compared with RKF, the accuracy of RAKF improved by 8.24%, 44.23%, and 9.35%, respectively. In the position average accuracy, compared with the three algorithms, the accuracy of RAKF improved by 27.53%, 21.89%, and 15.63%, respectively.
- Regarding velocity error: In terms of the East–North–Up (ENU) velocity error, compared with EKF, the accuracy of RAKF increased by 19.81%, 29.67%, and 20.22%, respectively. Compared with AKF, the accuracy of RAKF improved by 16.16%, 27.82%, and 7.89%, respectively. Compared with RKF, the accuracy of RAKF improved by 14.87%, 16.16%, and 18.21%, respectively.
3.3. Add Different Disturbance Vehicle Experiment Results
3.3.1. Experimental Results of the First Group
- Regarding position error: When adding 1-s random disturbances ranging from 0 to 1 m, in terms of the East–North–Up (ENU) position error, compared with EKF, the accuracy of RAKF increased by 24.89%, 77.78%, and 68.79%, respectively. Compared to RKF, the accuracy of RAKF achieved improvements of 20.36%, 77.78%, and 68.79%, respectively. Figure 17a–c illustrates the comparison of position errors with 1-s disturbances ranging from 0 to 1 m. In this scenario, the RAKF algorithm outperformed RKF significantly. Compared to EKF and AKF, RAKF demonstrated comparable anti-interference capability but with slightly better performance and closer proximity to 0.
- Regarding velocity error: When adding 1-s random disturbances ranging from 0 to 1 m, in terms of the East–North–Up (ENU) velocity error, compared with EKF, the accuracy of RAKF improved by 31.20%, 86.04%, and 41.88%, respectively. Compared with AKF, the accuracy of RAKF improved by 34.13%, 77.58%, and 7.54%, respectively. Compared with RKF, the speed accuracy of RAKF improved by 29.43%, 79.91%, and 23.30%, respectively.
- Regarding attitude error: When adding 1-s random disturbances ranging from 0 to 1 m, in terms of the pitch, roll, heading, and attitude error, compared with EKF, the accuracy of RAKF improved by 59.38%, 30.15%, and 34.65%, respectively. Compared with AKF, the accuracy of RAKF improved by 14.18%, 7.21%, and 31.53%, respectively. Compared with RKF, the accuracy of RAKF improved by 32.06%, 10.50%, and 18.36%, respectively.
3.3.2. Experimental Results of the Second Group
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Measurement Factor (Q) | Description | 3D Accuracy (m) |
---|---|---|
1 | Fixed integer | 0.00–0.15 |
2 | Converged float or noise Fixed integer | 0.05–0.40 |
3 | Converging float | 0.2–1.0 |
4 | Converging float | 0.5–2.00 |
5 | DGPS | 1.00–5.00 |
6 | DGPS | 2.00–10.00 |
Gyroscopes | Accelerometers | |
---|---|---|
Bias | 0.25°/h | 0.025°/h |
Random noise | 0.04°/sqrt(h) | 0.03m/s/sqrt(h) |
Method | R |
---|---|
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 |
Mode | PE (m) | PN (m) | PU (m) | VE (m/s) | VN (m/s) | VU (m/s) | Pitch (°) | Roll (°) | Yaw (°) |
---|---|---|---|---|---|---|---|---|---|
EKF | 0.0703 | 0.2867 | 0.1833 | 0.0718 | 0.4025 | 0.0991 | 0.3230 | 0.2136 | 0.3824 |
1 | 0.0509 | 0.0632 | 0.0508 | 0.0482 | 0.0555 | 0.1001 | 0.1287 | 0.1404 | 0.2514 |
2 | 0.0514 | 0.0632 | 0.0542 | 0.0486 | 0.0558 | 0.0982 | 0.1301 | 0.1378 | 0.2453 |
3 | 0.0512 | 0.0631 | 0.0529 | 0.0484 | 0.0557 | 0.0729 | 0.1307 | 0.1408 | 0.2453 |
4 | 0.0513 | 0.0633 | 0.0503 | 0.0493 | 0.0562 | 0.0729 | 0.1307 | 0.1408 | 0.2409 |
5 | 0.0531 | 0.0639 | 0.0644 | 0.0497 | 0.0566 | 0.1052 | 0.1307 | 0.1377 | 0.2409 |
6 | 0.0520 | 0.0635 | 0.0607 | 0.0494 | 0.0563 | 0.0743 | 0.1295 | 0.1445 | 0.2406 |
7 | 0.0521 | 0.0638 | 0.0633 | 0.0495 | 0.0565 | 0.0793 | 0.1298 | 0.1419 | 0.2396 |
Improved (%) | 26.65% | 77.92% | 72.56% | 31.34% | 86.04% | 26.44% | 59.54% | 33.57% | 37.00% |
ERROR | EKF | AKF | RKF | RAKF | |
---|---|---|---|---|---|
Velocity (m/s) | Eastward | 0.0718 | 0.0750 | 0.0700 | 0.0493 |
Northward | 0.4025 | 0.2507 | 0.2797 | 0.0562 | |
Upward | 0.0991 | 0.0623 | 0.0751 | 0.0729 | |
Attitude (deg) | Pitch | 0.3230 | 0.2250 | 0.1931 | 0.1307 |
Roll | 0.2136 | 0.1608 | 0.1667 | 0.1408 | |
Heading | 0.3824 | 0.3650 | 0.3061 | 0.2453 | |
Position (m) | Eastward | 0.0703 | 0.0528 | 0.0663 | 0.0513 |
Northward | 0.2867 | 0.0710 | 0.1313 | 0.0633 | |
Upward | 0.1833 | 0.0428 | 0.1098 | 0.0503 | |
3D Accuracy(m) | 0.3475 | 0.0983 | 0.1836 | 0.0958 | |
improved accuracy (%) | 72.43% | 2.54% | 47.82% |
Eastward Error STD (m) | Northward Error STD (m) | Upward Error STD (m) | 3D Accuracy (m) | |
---|---|---|---|---|
Single GPS | 0.3059 | 0.5926 | 0.3148 | 0.7375 |
Three systems | 0.0521 | 0.0643 | 0.0510 | 0.0972 |
improved accuracy (%) | 82.97% | 89.15% | 83.80% | 86.82% |
ERROR | EKF | AKF | RKF | RAKF | |
---|---|---|---|---|---|
Velocity (m/s) | Eastward | 0.0207 | 0.0198 | 0.0195 | 0.0166 |
Northward | 0.0273 | 0.0266 | 0.0229 | 0.0192 | |
Upward | 0.0366 | 0.0292 | 0.0317 | 0.0357 | |
Attitude (deg) | Pitch | 0.0342 | 0.0335 | 0.0389 | 0.0333 |
Roll | 0.0339 | 0.0349 | 0.0307 | 0.0283 | |
Heading | 0.0803 | 0.0868 | 0.0921 | 0.0862 | |
Position (m) | Eastward | 0.1013 | 0.1067 | 0.1104 | 0.1010 |
Northward | 0.1978 | 0.1749 | 0.1196 | 0.0667 | |
Upward | 0.1962 | 0.1834 | 0.1958 | 0.1775 | |
3D Accuracy(m) | 0.2964 | 0.2750 | 0.2546 | 0.2148 | |
improved accuracy (%) | 27.53% | 21.89% | 15.63% |
Experimental | Add Perturbation Time/s | Add Perturbation Value/m | Disturbance Duration/s |
---|---|---|---|
Group 1 | 368963 | 0.1576 | 1 |
0.9706 | |||
0.9572 | |||
0.4854 | |||
0.8003 | |||
Group 2 | 369398 | 0.2721 | 1 |
369399 | 1.0997 | 1 | |
369400 | 1.1594 | 1 | |
369401 | 0.3380 | 1 | |
369402 | 0.2899 | 1 |
ERROR | EKF | AKF | RKF | RAKF | |
---|---|---|---|---|---|
Velocity (m/s) | Eastward | 0.0729 | 0.0478 | 0.0500 | 0.0486 |
Northward | 0.4126 | 0.0563 | 0.0570 | 0.0569 | |
Upward | 0.0993 | 0.1372 | 0.0766 | 0.0666 | |
Attitude (deg) | Pitch | 0.3373 | 0.1283 | 0.1830 | 0.1295 |
Roll | 0.2181 | 0.1372 | 0.1930 | 0.1483 | |
Heading | 0.3893 | 0.2304 | 0.3360 | 0.2359 | |
Position (m) | Eastward | 0.0709 | 0.0510 | 0.0567 | 0.0534 |
Northward | 0.2862 | 0.0626 | 0.0667 | 0.0635 | |
Upward | 0.1835 | 0.0517 | 0.0915 | 0.0701 | |
3D Accuracy(m) | 0.3473 | 0.0959 | 0.1266 | 0.1086 | |
improved accuracy (%) | 68.73% | - | 14.22% |
ERROR | EKF | AKF | RKF | RAKF | |
---|---|---|---|---|---|
Velocity (m/s) | Eastward | 0.0782 | 0.0478 | 0.0493 | 0.0486 |
Northward | 0.4575 | 0.0563 | 0.0565 | 0.0569 | |
Upward | 0.1251 | 0.1375 | 0.0712 | 0.0666 | |
Attitude (deg) | Pitch | 0.3858 | 0.1283 | 0.1387 | 0.1295 |
Roll | 0.2377 | 0.1386 | 0.1633 | 0.1483 | |
Heading | 0.4327 | 0.2304 | 0.3858 | 0.2359 | |
Position (m) | Eastward | 0.0889 | 0.0510 | 0.0553 | 0.0534 |
Northward | 0.4099 | 0.0626 | 0.0651 | 0.0635 | |
Upward | 0.2914 | 0.0654 | 0.0981 | 0.0701 | |
3D Accuracy(m) | 0.5107 | 0.1039 | 0.1301 | 0.1086 | |
improved accuracy (%) | 78.74% | - | 16.53% |
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Yin, Z.; Yang, J.; Ma, Y.; Wang, S.; Chai, D.; Cui, H. A Robust Adaptive Extended Kalman Filter Based on an Improved Measurement Noise Covariance Matrix for the Monitoring and Isolation of Abnormal Disturbances in GNSS/INS Vehicle Navigation. Remote Sens. 2023, 15, 4125. https://doi.org/10.3390/rs15174125
Yin Z, Yang J, Ma Y, Wang S, Chai D, Cui H. A Robust Adaptive Extended Kalman Filter Based on an Improved Measurement Noise Covariance Matrix for the Monitoring and Isolation of Abnormal Disturbances in GNSS/INS Vehicle Navigation. Remote Sensing. 2023; 15(17):4125. https://doi.org/10.3390/rs15174125
Chicago/Turabian StyleYin, Zhihui, Jichao Yang, Yue Ma, Shengli Wang, Dashuai Chai, and Haonan Cui. 2023. "A Robust Adaptive Extended Kalman Filter Based on an Improved Measurement Noise Covariance Matrix for the Monitoring and Isolation of Abnormal Disturbances in GNSS/INS Vehicle Navigation" Remote Sensing 15, no. 17: 4125. https://doi.org/10.3390/rs15174125
APA StyleYin, Z., Yang, J., Ma, Y., Wang, S., Chai, D., & Cui, H. (2023). A Robust Adaptive Extended Kalman Filter Based on an Improved Measurement Noise Covariance Matrix for the Monitoring and Isolation of Abnormal Disturbances in GNSS/INS Vehicle Navigation. Remote Sensing, 15(17), 4125. https://doi.org/10.3390/rs15174125