An Approach for Filter Divergence Suppression in a Sequential Data Assimilation System and Its Application in Short-Term Traffic Flow Forecasting
Abstract
:1. Introduction
2. Representation of Filter Divergence Phenomenon in Sequential Data Assimilation System for Short-Term Traffic Flow Forecasting
3. Methodology
4. Numerical Study
5. Empirical Study
5.1. Study Area and Material Description
5.2. Test Design
6. Results and Discussion
7. Conclusions
- The proposed approach based on the L1-norm constraint can suppress the filter-divergence phenomenon that occurs in the KF assimilation method of the S-DA system.
- The proposed approach based on the L1-norm constraint had a higher assimilation accuracy for suppressing filter divergence than the other two methods.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Forecast | |
Update | |
RMSE | MAPE (%) | |
---|---|---|
KF method | 0.5647 | 31.81 |
C-W method | 0.0368 | 0.16 |
A-KF method | 0.0356 | 0.14 |
Proposed method | 0.0340 | 0.12 |
RMSE | |||||
---|---|---|---|---|---|
KF | C-W | A-KF | Proposed Method | KF (Correct Model) | |
Monday | 842.65 | 394.20 | 152.55 | 85.37 | 77.38 |
Tuesday | 829.18 | 340.98 | 178.67 | 85.69 | 74.59 |
Wednesday | 857.94 | 346.18 | 164.94 | 88.85 | 80.74 |
Thursday | 856.66 | 360.62 | 227.82 | 84.82 | 75.18 |
Friday | 901.86 | 412.18 | 211.86 | 78.56 | 69.80 |
Saturday | 584.92 | 210.12 | 134.08 | 41.29 | 39.22 |
Sunday | 579.88 | 145.76 | 104.04 | 35.77 | 30.16 |
MAPE (%) | |||||
---|---|---|---|---|---|
KF | C-W | A-KF | Proposed Method | KF (Correct Model) | |
Monday | 99.56 | 39.67 | 15.31 | 7.23 | 6.76 |
Tuesday | 99.71 | 35.72 | 17.99 | 7.91 | 6.82 |
Wednesday | 99.70 | 34.62 | 15.15 | 7.58 | 7.00 |
Thursday | 99.69 | 37.70 | 22.18 | 7.56 | 6.66 |
Friday | 99.75 | 40.51 | 20.83 | 7.24 | 6.26 |
Saturday | 99.65 | 35.94 | 22.05 | 6.70 | 6.15 |
Sunday | 99.48 | 28.73 | 21.58 | 6.60 | 5.74 |
RMSE | MAPE (%) | |||||
---|---|---|---|---|---|---|
C-W | A-KF | Proposed Method | C-W | A-KF | Proposed Method | |
Monday | 316.82 | 75.17 | 7.99 | 32.91 | 8.55 | 0.47 |
Tuesday | 266.39 | 104.08 | 11.10 | 28.90 | 11.17 | 1.09 |
Wednesday | 265.44 | 84.20 | 8.11 | 27.62 | 8.15 | 0.58 |
Thursday | 285.44 | 152.64 | 9.64 | 31.04 | 15.52 | 0.90 |
Friday | 342.38 | 142.06 | 8.76 | 34.25 | 14.57 | 0.98 |
Saturday | 170.90 | 94.86 | 2.07 | 29.79 | 15.90 | 0.55 |
Sunday | 115.60 | 73.88 | 5.61 | 22.99 | 15.84 | 0.86 |
RMSE | |||||
---|---|---|---|---|---|
KF | C-W | A-KF | Proposed Method | KF (Correct Model) | |
Monday | 596.29 | 233.39 | 156.14 | 71.47 | 55.70 |
Tuesday | 591.97 | 204.79 | 145.25 | 70.72 | 53.58 |
Wednesday | 607.66 | 208.28 | 143.06 | 72.54 | 54.74 |
Thursday | 606.60 | 213.69 | 161.17 | 95.87 | 52.45 |
Friday | 649.17 | 252.80 | 222.20 | 68.37 | 50.28 |
Saturday | 419.31 | 127.81 | 111.40 | 38.30 | 26.53 |
Sunday | 414.71 | 102.03 | 96.47 | 36.77 | 23.62 |
MAPE (%) | |||||
---|---|---|---|---|---|
KF | C-W | A-KF | Proposed Method | KF (Correct Model) | |
Monday | 98.39 | 31.56 | 21.61 | 9.34 | 7.12 |
Tuesday | 98.88 | 28.13 | 19.98 | 9.63 | 7.19 |
Wednesday | 98.43 | 27.77 | 19.08 | 9.57 | 7.07 |
Thursday | 97.99 | 28.91 | 21.59 | 10.06 | 6.87 |
Friday | 98.15 | 32.42 | 25.47 | 8.90 | 6.55 |
Saturday | 98.50 | 26.12 | 22.56 | 8.86 | 6.42 |
Sunday | 97.94 | 25.80 | 24.11 | 9.23 | 6.71 |
RMSE | MAPE (%) | |||||
---|---|---|---|---|---|---|
C-W | A-KF | Proposed Method | C-W | A-KF | Proposed Method | |
Monday | 177.69 | 100.44 | 15.77 | 24.44 | 14.49 | 2.22 |
Tuesday | 151.21 | 91.67 | 17.14 | 20.94 | 12.79 | 2.44 |
Wednesday | 153.54 | 88.32 | 17.80 | 20.70 | 12.01 | 2.50 |
Thursday | 161.24 | 108.72 | 43.42 | 22.04 | 14.72 | 3.19 |
Friday | 202.52 | 171.92 | 18.09 | 25.87 | 18.92 | 2.35 |
Saturday | 101.28 | 84.87 | 11.77 | 19.70 | 16.14 | 2.44 |
Sunday | 78.41 | 72.85 | 13.15 | 19.09 | 17.40 | 2.52 |
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Tong, X.; Wang, R.; Shi, W.; Li, Z. An Approach for Filter Divergence Suppression in a Sequential Data Assimilation System and Its Application in Short-Term Traffic Flow Forecasting. ISPRS Int. J. Geo-Inf. 2020, 9, 340. https://doi.org/10.3390/ijgi9060340
Tong X, Wang R, Shi W, Li Z. An Approach for Filter Divergence Suppression in a Sequential Data Assimilation System and Its Application in Short-Term Traffic Flow Forecasting. ISPRS International Journal of Geo-Information. 2020; 9(6):340. https://doi.org/10.3390/ijgi9060340
Chicago/Turabian StyleTong, Xiaohua, Runjie Wang, Wenzhong Shi, and Zhiyuan Li. 2020. "An Approach for Filter Divergence Suppression in a Sequential Data Assimilation System and Its Application in Short-Term Traffic Flow Forecasting" ISPRS International Journal of Geo-Information 9, no. 6: 340. https://doi.org/10.3390/ijgi9060340
APA StyleTong, X., Wang, R., Shi, W., & Li, Z. (2020). An Approach for Filter Divergence Suppression in a Sequential Data Assimilation System and Its Application in Short-Term Traffic Flow Forecasting. ISPRS International Journal of Geo-Information, 9(6), 340. https://doi.org/10.3390/ijgi9060340