Robust MPS-INS UKF Integration and SIR-Based Hyperparameter Estimation in a 3D Flight Environment
Abstract
:1. Introduction
2. Sensor Integration MPS/INS
2.1. Measurement Description and UKF Tightly Coupled Integration
2.2. Estimation of UKF Hyperparameters Using the SIR Process
Algorithm 1: PDF Calculation |
1: Compute the Probability Density Function (PDF) for measurement update in SIR-UKF: 2: Return the computed |
The terms are defined as follows:
|
Algorithm 2: SIR-UKF | ||||||
1: | for | do | ||||
2: | Distribute hyperparameter | |||||
3: | ||||||
4: | Start UT using distributed | |||||
5: | for | do | ||||
6: | ||||||
7: | Check the Measurement Synchronization (Sync) | |||||
8: | if | then | ||||
9: | ||||||
10: | else | |||||
11: | Calculate using Measurement and Observation model | |||||
12: | ||||||
13: | if | then | ||||
14: | ||||||
15: | end if | |||||
16: | end if | |||||
17: | end for | |||||
18: | Resampling and save hyperparameter | |||||
19: | Go back to | |||||
20: | end for |
3. Magnetic Vector Error Analysis During Flight
3.1. Experimental Environment
3.2. Experimental Details
3.2.1. Data with Rapidly Increasing Model Uncertainty
3.2.2. Data with Repeated Model Uncertainty
4. Navigation Results
4.1. Experiment Results
4.1.1. Results for Data with Rapidly Increasing Model Uncertainty (Set 1)
4.1.2. Results for Data with Repeated Model Uncertainty (Set 2)
4.2. Comparison of Navigation Solutions Between Conventional UKF and SUKF
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Set 1 | Navigation Method | Position RMSE [Centimeter] | Attitude RMSE [Deg] | ||||||
East | North | Up | 3D | Roll | Pitch | Yaw | 3D | ||
Sec 1 | MPS 3D LS | 5.43 | 4.63 | 6.55 | 9.69 | 2.00 | 2.17 | 1.49 | 3.30 |
LC EKF | 5.69 | 4.95 | 7.92 | 10.93 | 1.04 | 1.07 | 0.93 | 1.76 | |
LC UKF | 5.92 | 5.10 | 8.06 | 11.22 | 1.12 | 1.00 | 0.84 | 1.72 | |
TC EKF | 6.44 | 5.23 | 8.93 | 12.19 | 1.03 | 1.09 | 1.05 | 1.83 | |
TC UKF | 4.99 | 7.27 | 7.51 | 11.58 | 1.21 | 1.04 | 0.85 | 1.81 | |
Sec 2 | MPS 3D LS | 5.84 | 6.14 | 8.15 | 11.75 | 4.16 | 2.44 | 5.62 | 7.41 |
LC EKF | 6.25 | 6.35 | 9.65 | 13.14 | 1.86 | 1.16 | 5.37 | 5.80 | |
LC UKF | 6.43 | 6.58 | 9.81 | 13.45 | 1.73 | 1.11 | 4.85 | 5.27 | |
TC EKF | 4.83 | 6.15 | 12.19 | 14.48 | 1.88 | 1.28 | 2.50 | 3.38 | |
TC UKF | 5.46 | 5.95 | 10.05 | 12.90 | 2.15 | 1.76 | 1.29 | 3.07 | |
Sec 3 | MPS 3D LS | 5.28 | 7.89 | 6.42 | 11.46 | 2.11 | 2.25 | 2.12 | 3.74 |
LC EKF | 6.17 | 8.42 | 8.24 | 13.29 | 1.16 | 1.15 | 1.72 | 2.37 | |
LC UKF | 6.41 | 8.58 | 8.12 | 13.44 | 1.25 | 1.04 | 1.26 | 2.06 | |
TC EKF | 6.75 | 8.97 | 8.56 | 14.11 | 1.22 | 1.16 | 1.64 | 2.35 | |
TC UKF | 6.16 | 9.95 | 8.10 | 14.23 | 1.34 | 1.28 | 0.83 | 2.03 | |
Total | MPS 3D LS | 5.39 | 6.42 | 6.78 | 10.78 | 2.59 | 2.24 | 2.97 | 4.53 |
LC EKF | 5.95 | 6.81 | 8.33 | 12.30 | 1.31 | 1.11 | 2.68 | 3.78 | |
LC UKF | 6.17 | 6.97 | 8.38 | 12.53 | 1.35 | 1.03 | 2.34 | 2.90 | |
TC EKF | 6.23 | 7.13 | 9.43 | 13.36 | 1.32 | 1.15 | 1.65 | 2.41 | |
TC UKF | 5.55 | 8.21 | 8.21 | 12.87 | 1.51 | 1.31 | 0.93 | 2.20 |
Set 2 | Navigation Method | Position RMSE [Centimeter] | Attitude RMSE [Deg] | ||||||
---|---|---|---|---|---|---|---|---|---|
East | North | Up | 3D | Roll | Pitch | Yaw | 3D | ||
Sec 1 | MPS 3D LS | 4.68 | 6.59 | 7.81 | 11.24 | 1.96 | 1.88 | 1.92 | 3.33 |
LC EKF | 5.50 | 7.46 | 9.53 | 13.29 | 1.57 | 1.18 | 1.41 | 2.41 | |
LC UKF | 5.65 | 7.50 | 9.53 | 13.38 | 1.75 | 1.22 | 1.12 | 2.41 | |
TC EKF | 5.26 | 7.44 | 9.74 | 13.33 | 1.65 | 1.17 | 0.98 | 2.25 | |
TC UKF | 5.81 | 7.91 | 9.74 | 13.83 | 1.70 | 1.14 | 0.95 | 2.25 | |
Sec 2 | MPS 3D LS | 5.01 | 5.24 | 10.30 | 12.60 | 1.98 | 1.96 | 3.22 | 4.25 |
LC EKF | 5.47 | 6.08 | 11.66 | 14.25 | 1.15 | 1.16 | 2.95 | 3.37 | |
LC UKF | 5.63 | 6.04 | 11.62 | 14.25 | 1.16 | 1.05 | 2.43 | 2.89 | |
TC EKF | 5.60 | 5.82 | 11.76 | 14.27 | 1.14 | 1.16 | 1.76 | 2.40 | |
TC UKF | 5.78 | 5.68 | 11.30 | 13.90 | 1.20 | 1.25 | 0.97 | 1.99 | |
Sec 3 | MPS 3D LS | 5.83 | 6.83 | 5.66 | 10.62 | 2.09 | 2.20 | 3.35 | 4.52 |
LC EKF | 6.56 | 7.27 | 6.96 | 12.02 | 1.12 | 1.30 | 3.02 | 3.48 | |
LC UKF | 6.78 | 7.61 | 7.38 | 12.58 | 1.14 | 1.27 | 2.59 | 3.10 | |
TC EKF | 6.43 | 7.22 | 7.90 | 12.49 | 1.16 | 1.39 | 1.91 | 2.63 | |
TC UKF | 6.77 | 7.68 | 7.86 | 12.91 | 1.04 | 1.51 | 1.44 | 2.34 | |
Total | MPS 3D LS | 5.08 | 6.16 | 8.22 | 11.46 | 2.01 | 1.99 | 2.87 | 4.03 |
LC EKF | 5.73 | 6.87 | 9.68 | 13.18 | 1.34 | 1.19 | 2.52 | 3.10 | |
LC UKF | 5.91 | 6.98 | 9.73 | 13.35 | 1.42 | 1.17 | 2.10 | 2.79 | |
TC EKF | 5.67 | 6.77 | 9.97 | 13.32 | 1.37 | 1.22 | 1.58 | 2.42 | |
TC UKF | 6.02 | 7.05 | 9.79 | 13.48 | 1.37 | 1.29 | 1.13 | 2.19 |
Set1 | Navigation Method | Position RMSE [Centimeter] | Attitude RMSE [Deg] | ||||||
East | North | Up | 3D | Roll | Pitch | Yaw | 3D | ||
Sec 1 | TC UKF | 4.99 | 7.27 | 7.51 | 11.58 | 1.21 | 1.04 | 0.85 | 1.81 |
TC SUKF | 6.06 | 5.56 | 7.62 | 11.21 | 1.05 | 1.06 | 0.89 | 1.74 | |
Sec 2 | TC UKF | 5.46 | 5.95 | 10.05 | 12.90 | 2.15 | 1.76 | 1.29 | 3.07 |
TC SUKF | 4.38 | 6.03 | 10.62 | 12.97 | 1.86 | 1.53 | 1.46 | 2.81 | |
Sec 3 | TC UKF | 6.16 | 9.95 | 8.10 | 14.23 | 1.34 | 1.28 | 0.83 | 2.03 |
TC SUKF | 6.33 | 9.40 | 7.79 | 13.75 | 1.24 | 1.20 | 0.96 | 1.98 | |
Total | TC UKF | 5.55 | 8.21 | 8.21 | 12.87 | 1.51 | 1.31 | 0.93 | 2.20 |
TC SUKF | 5.82 | 7.42 | 8.27 | 12.54 | 1.34 | 1.22 | 1.04 | 2.09 |
Set 2 | Navigation Method | Position RMSE [Centimeter] | Attitude RMSE [Deg] | ||||||
---|---|---|---|---|---|---|---|---|---|
East | North | Up | 3D | Roll | Pitch | Yaw | 3D | ||
Sec 1 | TC UKF | 5.81 | 7.91 | 9.74 | 13.83 | 1.70 | 1.14 | 0.95 | 2.25 |
TC SUKF | 5.32 | 7.39 | 9.43 | 13.10 | 1.62 | 1.10 | 0.99 | 2.19 | |
Sec 2 | TC UKF | 5.78 | 5.68 | 11.30 | 13.90 | 1.20 | 1.25 | 0.97 | 1.99 |
TC SUKF | 5.62 | 5.64 | 11.17 | 13.72 | 1.20 | 1.22 | 1.01 | 1.98 | |
Sec 3 | TC UKF | 6.77 | 7.68 | 7.86 | 12.91 | 1.04 | 1.51 | 1.44 | 2.34 |
TC SUKF | 6.51 | 7.41 | 7.60 | 12.45 | 1.07 | 1.44 | 1.50 | 2.33 | |
Total | TC UKF | 6.02 | 7.05 | 9.79 | 13.48 | 1.37 | 1.29 | 1.13 | 2.19 |
TC SUKF | 5.72 | 6.75 | 9.57 | 13.03 | 1.33 | 1.24 | 1.17 | 2.16 |
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Share and Cite
Seo, J.; Kwon, D.; Lee, B.; Sung, S. Robust MPS-INS UKF Integration and SIR-Based Hyperparameter Estimation in a 3D Flight Environment. Aerospace 2025, 12, 228. https://doi.org/10.3390/aerospace12030228
Seo J, Kwon D, Lee B, Sung S. Robust MPS-INS UKF Integration and SIR-Based Hyperparameter Estimation in a 3D Flight Environment. Aerospace. 2025; 12(3):228. https://doi.org/10.3390/aerospace12030228
Chicago/Turabian StyleSeo, Juyoung, Dongha Kwon, Byungjin Lee, and Sangkyung Sung. 2025. "Robust MPS-INS UKF Integration and SIR-Based Hyperparameter Estimation in a 3D Flight Environment" Aerospace 12, no. 3: 228. https://doi.org/10.3390/aerospace12030228
APA StyleSeo, J., Kwon, D., Lee, B., & Sung, S. (2025). Robust MPS-INS UKF Integration and SIR-Based Hyperparameter Estimation in a 3D Flight Environment. Aerospace, 12(3), 228. https://doi.org/10.3390/aerospace12030228