An Aeromagnetic Compensation Method Based on a Multimodel for Mitigating Multicollinearity
<p>The <math display="inline"><semantics> <mrow> <mi>L</mi> <mi>T</mi> <mi>V</mi> </mrow> </semantics></math> reference system.</p> "> Figure 2
<p>Procedures for calibration and compensation. VIF—variance inflation factor.</p> "> Figure 3
<p>The aircraft used in the experiment.</p> "> Figure 4
<p>Compensation results.</p> "> Figure 5
<p>Comparisons between the three compensation methods: (<b>a</b>) figure-of-merit (FOM), (<b>b</b>) standard deviation (STD), and (<b>c</b>) improvement ratio (IR). LS—least squares; RR—ridge regression; MM—multimodel.</p> "> Figure 6
<p>Compensation results of the three compensation methods. In the legends, <math display="inline"><semantics> <mi>σ</mi> </semantics></math> represents the standard deviation (STD), with unit of nT.</p> "> Figure 7
<p>Compensation results: (<b>a</b>) Line-A and (<b>b</b>) Line-B.</p> "> Figure 8
<p>The tracks of Dataset-C and Dataset-D.</p> "> Figure 9
<p>The compensated signal of Dataset-C. The coefficients are calculated from Dataset-C.</p> "> Figure 10
<p>Comparisons between the three compensation methods in non-standard headings: (<b>a</b>) figure-of-merit (FOM), (<b>b</b>) standard deviation (STD), and (<b>c</b>) improvement ratio (IR).</p> ">
Abstract
:1. Introduction
2. Analysis and Method
2.1. T–L Model
2.2. Analysis of Multicollinearity
2.3. The Multimodel Method
3. Experiment
3.1. Implementation
3.2. Comparison with Conventional Methods
3.3. Compensations in Level Flights
3.4. Compensation in Non-Standard Headings
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Variable | Expression | Pitch | Roll | Yaw |
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0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 | 0 | |||
0 | 0 | |||
0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 |
Variable | Expression | Pitch | Roll | Yaw |
---|---|---|---|---|
0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 | ||||
0 | 0 | |||
0 | ||||
0 | 0 | |||
0 | ||||
0 |
Variables | VIFs | ||||
---|---|---|---|---|---|
FVS | EVS-1 | EVS-2 | EVS-3 | EVS-4 | |
9730.40 | 6640.77 | 5119.77 | — | — | |
159,672.01 | — | — | — | — | |
112,862.35 | 39,651.18 | 23.55 | 23.54 | 23.32 | |
16,679.02 | 9875.18 | 21.07 | 20.81 | 20.78 | |
1907.04 | 1312.74 | 1311.42 | 512.57 | 511.42 | |
4727.15 | 3772.57 | 2369.45 | 509.71 | 507.73 | |
36,281.72 | 35,521.73 | — | — | — | |
26,334.11 | 526.00 | 20.67 | 20.67 | 20.49 | |
626.94 | 626.33 | 623.44 | 619.19 | 15.07 | |
1.60 | 1.60 | 1.60 | 1.46 | 1.43 | |
2.51 | 2.49 | 2.47 | 2.46 | 2.35 | |
488.07 | 488.07 | 487.06 | 482.17 | 443.24 | |
1946.64 | 1945.84 | 1932.61 | 1913.33 | — | |
1169.43 | 1168.18 | 1162.95 | 1154.38 | 25.10 | |
483.08 | 483.08 | 481.86 | 477.28 | 436.85 | |
510.18 | 510.11 | 504.93 | 499.07 | 10.90 |
Variables | VIFs | ||||
---|---|---|---|---|---|
FVS | EVS-1 | EVS-2 | EVS-3 | EVS-4 | |
397,320.73 | — | — | — | — | |
27,811.26 | 27,266.38 | – | — | — | |
(400,873.05) | 2809.42 | 2763.78 | 3.38 | 3.38 | |
35,405.72 | 3384.67 | 3336.12 | — | — | |
3626.27 | 3534.16 | 37.41 | 37.39 | 37.29 | |
51,546.73 | 49.68 | 49.51 | 3.37 | 3.36 | |
138.65 | 3.30 | 3.03 | 2.61 | 1.79 | |
11,488.87 | 11,299.04 | 39.48 | 39.41 | 39.09 | |
328.74 | 324.86 | 222.25 | 219.56 | — | |
71.27 | 67.20 | 66.60 | 66.60 | 66.16 | |
104.81 | 104.04 | 75.54 | 73.93 | 4.41 | |
22.37 | 22.35 | 19.98 | 18.54 | 18.47 | |
1.60 | 1.60 | 1.49 | 1.45 | 1.39 | |
19.68 | 19.67 | 16.97 | 15.74 | 15.72 | |
98.89 | 97.12 | 61.96 | 61.87 | 5.20 | |
69.11 | 65.23 | 64.58 | 64.36 | 63.81 |
Maneuver | North | East | South | West | Sum |
---|---|---|---|---|---|
Roll | 1.19|1.39|1.40|0.72 | 5.11|1.33|1.41|0.61 | 2.01|1.29|1.26|0.34 | 3.88|2.00|1.89|0.86 | 12.19|6.00|5.97|2.53 |
Pitch | 2.71|0.66|0.62|0.47 | 0.89|0.34|0.32|0.36 | 3.04|0.24|0.23|0.15 | 1.83|1.86|1.85|1.74 | 8.47|3.09|3.02|2.73 |
Yaw | 1.25|0.67|0.65|0.31 | 1.84|1.03|1.06|0.42 | 1.10|0.69|0.67|0.17 | 1.82|1.11|1.07|0.88 | 6.01|3.49|3.45|1.78 |
Sum | 5.15|2.72|2.67|1.50 | 7.84|2.70|2.80|1.39 | 6.15|2.21|2.16|0.66 | 7.54|4.96|4.81|3.79 | 26.68|12.59|12.44|7.04 |
Dataset | STD (nT) | IR | ||||
---|---|---|---|---|---|---|
LS | RR | MM | LS | RR | MM | |
Line-A | 0.0223 | 0.0216 | 0.0206 | 2.2695 | 2.3452 | 2.4565 |
Line-B | 0.0579 | 0.0594 | 0.0452 | 1.8594 | 1.8124 | 2.3835 |
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Zhao, G.; Han, Q.; Peng, X.; Zou, P.; Wang, H.; Du, C.; Wang, H.; Tong, X.; Li, Q.; Guo, H. An Aeromagnetic Compensation Method Based on a Multimodel for Mitigating Multicollinearity. Sensors 2019, 19, 2931. https://doi.org/10.3390/s19132931
Zhao G, Han Q, Peng X, Zou P, Wang H, Du C, Wang H, Tong X, Li Q, Guo H. An Aeromagnetic Compensation Method Based on a Multimodel for Mitigating Multicollinearity. Sensors. 2019; 19(13):2931. https://doi.org/10.3390/s19132931
Chicago/Turabian StyleZhao, Guanyi, Qi Han, Xiang Peng, Pengyi Zou, Haidong Wang, Changping Du, He Wang, Xiaojun Tong, Qiong Li, and Hong Guo. 2019. "An Aeromagnetic Compensation Method Based on a Multimodel for Mitigating Multicollinearity" Sensors 19, no. 13: 2931. https://doi.org/10.3390/s19132931