Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation
Abstract
:1. Introduction
2. Methodologies
2.1. Maximum Correntropy Criterion
2.2. Extended Kalman Filter
2.3. Maximum Correntropy Extended Kalman Filter
2.4. Maximum Correntropy Criterion-Based Extended Kalman Filter with Nonlinear Regression
- (1)
- Let us first consider a kernel bandwidth , and with small positive value for the error tolerance. Then initialize , ;
- (2)
- Then predict, ,
- (3)
- Updating,If thenOtherwise
- (4)
- Iteration loop: Calculation of using the following steps:
- i.
- ii.
- iii.
- iv.
- v.
- vi.
- vii.
- viii.
- (5)
- If then go to step 6; otherwise, set , and go back to step 4.
- (6)
- Then, set , and go back to step 2.
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Filters | East (m) | North (m) | Altitude (m) |
---|---|---|---|
EKF [29] | 28.5627 | 21.7379 | 40.5981 |
MCCEKF-BC [31] | 19.3647 | 16.6939 | 25.4365 |
MCCEKF-DS [34] | 16.5144 | 15.4960 | 24.1786 |
MCCEKF-GL [32] | 16.5886 | 15.6737 | 24.4489 |
MCCEKF-NR [Present] | 16.4092 | 15.3790 | 24.0792 |
Mixture-LRMCCEKF [Present] | 16.4124 | 15.3989 | 24.1061 |
Filters | East (m) | North (m) | Altitude (m) |
---|---|---|---|
EKF [29] | 1.0496 × 104 | 2.8975 × 103 | 7.4510 × 103 |
MCCEKF-BC [31] | 1.1562 × 103 | 752.3388 | 1.1221 × 103 |
MCCEKF-DS [34] | 603.6376 | 469.2932 | 904.7247 |
MCCEKF-GL [32] | 597.2612 | 493.8688 | 929.5508 |
NRMCCEKF [Present] | 603.4894 | 469.0979 | 904.6238 |
Mixture-LRMCCEKF [Present] | 603.5379 | 469.1823 | 904.6829 |
Filters | East (m) | North (m) | Altitude (m) |
---|---|---|---|
EKF [29] | −4.4477 | 2.0030 | −7.7829 |
MCCEKF-BC [31] | −3.5017 | −0.4887 | −8.6859 |
MCCEKF-DS [34] | −1.9928 | 0.3381 | −7.2658 |
MCCEKF-GL [32] | −2.0206 | 0.3320 | −7.3809 |
MCCEKF-NR [Present] | −1.8926 | 0.2726 | −7.1856 |
Mixture-LRMCCEKF [Present] | −2.0108 | 0.2862 | −7.2701 |
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Biswal, A.; Jwo, D.-J. Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation. Appl. Sci. 2024, 14, 7657. https://doi.org/10.3390/app14177657
Biswal A, Jwo D-J. Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation. Applied Sciences. 2024; 14(17):7657. https://doi.org/10.3390/app14177657
Chicago/Turabian StyleBiswal, Amita, and Dah-Jing Jwo. 2024. "Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation" Applied Sciences 14, no. 17: 7657. https://doi.org/10.3390/app14177657