Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model
<p>The architecture of ELM.</p> "> Figure 2
<p>The workflow of the proposed SSA-ELM algorithm.</p> "> Figure 3
<p>The residual plot of the RB clock as a reference clock. (<b>a</b>) The residual value of C08 predicted after 6 h. (<b>b</b>) The residual value of C22 predicted after 6 h. (<b>c</b>) The residual value of C29 predicted after 6 h.</p> "> Figure 4
<p>The residual plot of the Rb-II clock as the reference clock. (<b>a</b>) The residual value of C08 predicted after 6 h. (<b>b</b>) The residual value of C22 predicted after 6 h. (<b>c</b>) The residual value of C29 predicted after 6 h.</p> "> Figure 5
<p>The residual plot of the PHM clock as the reference clock. (<b>a</b>) The residual value of C08 predicted after 6 h. (<b>b</b>) The residual value of C22 predicted after 6 h. (<b>c</b>) The residual value of C29 predicted after 6 h.</p> "> Figure 6
<p>The ISUP-ISC residuals of three atomic clocks. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> "> Figure 7
<p>The ISUO-ISC residuals of three atomic clocks. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> "> Figure 8
<p>The ISUP-ISUO residuals of three atomic clocks. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> "> Figure 9
<p>The residual plot of the ISUP model using the initial hour update ultra-fast clock product of the next day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 10
<p>The residual plot of QP model using the initial hour update ultra-fast clock product of the next day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 11
<p>The residual plot of GM model using the initial hour update ultra-fast clock product of the next day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 12
<p>The residual plot of the SSA-ELM model using the initial hour update ultra-fast clock product of the next day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 13
<p>The residual plot of the ISUP model using the 6th hour update ultra-fast clock product of the day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 14
<p>The residual plot of the QP model using the 6th hour update ultra-fast clock product of the day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 15
<p>The residual plot of the GM model using the 6th hour update ultra-fast clock product of the day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 16
<p>The residual plot of the SSA-ELM model using the 6th hour update ultra-fast clock product of the day. (<b>a</b>) The residual value of BDS-2 predicted after 6 h. (<b>b</b>) The residual value of BDS-3 predicted after 6 h.</p> "> Figure 17
<p>The prediction accuracies of BDS for 6 h obtained using 6 h of SCB data.</p> "> Figure 18
<p>The prediction accuracies of BDS for 6 h obtained using 12 h of SCB data.</p> "> Figure 19
<p>The initial residual value with a DOY of 196.</p> "> Figure 20
<p>The initial residual value with a DOY of 198.</p> "> Figure 21
<p>Multiday average prediction accuracy of BDS-2.</p> "> Figure 22
<p>Multiday average prediction accuracy of BDS-3.</p> "> Figure 23
<p>Multiday prediction residual statistics of the ISUP model. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> "> Figure 24
<p>Multiday prediction residual statistics of the QP model. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> "> Figure 25
<p>Multiday prediction residual statistics of the GM model. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> "> Figure 26
<p>Multiday prediction residual statistics of the SSA-ELM model. (<b>a</b>) The residual distribution of the RB clock. (<b>b</b>) The residual distribution of the Rb-II clock. (<b>c</b>) The residual distribution of the PHM clock.</p> ">
Abstract
:1. Introduction
2. Basic Principles
2.1. Extreme Learning Machine Algorithm
2.2. Sparrow Search Algorithm
2.3. SSA-ELM Model
3. Ultra-Fast Clock Bias Data Analysis
3.1. Single-Day Accuracy Analysis
3.2. Multiday Accuracy and Stability Analysis
4. Accuracy Analysis of Ultra-Fast Clock Bias Prediction
4.1. Prediction Analyses of Clock Bias Data with Different Fitting Times
4.2. Clock Bias Prediction with Different Fitting Time Lengths
4.3. Analysis of Multiday Clock Bias Prediction
4.4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Satellite | Clock Type | PRN |
---|---|---|
BDS-2 | Rb | C01, C02, C03, C04, C05, C06, C07, C08, C09, C10, C11, C12, C13, C14 |
BDS-3 | Rb-II | C19, C20, C21, C22, C23, C24, C32, C33, C36, C37 |
PHM | C25, C26, C27, C28, C29, C30, C34, C35 |
Reference Clock | C11 | C20 | C27 | ||||||
---|---|---|---|---|---|---|---|---|---|
Second Difference | Rb | Rb-II | PHM | Rb | Rb-II | PHM | Rb | Rb-II | PHM |
ISUP-ISC | 2.68 | 6.00 | 4.75 | 6.41 | 0.92 | 1.97 | 4.30 | 1.89 | 0.87 |
ISUO-ISC | 2.60 | 5.32 | 4.18 | 5.54 | 0.89 | 1.86 | 3.61 | 1.65 | 0.68 |
ISUP-ISUO | 1.89 | 0.83 | 0.77 | 1.78 | 0.39 | 0.42 | 1.74 | 0.46 | 0.49 |
Mean | 2.39 | 4.05 | 3.23 | 4.58 | 0.73 | 1.42 | 3.22 | 1.33 | 0.68 |
Reference Clock | Rb | Rb-II | PHM | ||||||
---|---|---|---|---|---|---|---|---|---|
Second Difference | Rb | Rb-II | PHM | Rb | Rb-II | PHM | Rb | Rb-II | PHM |
ISUP-ISC | 6.74 | 5.72 | 4.49 | 9.60 | 1.10 | 2.12 | 7.58 | 2.37 | 1.41 |
ISUO-ISC | 5.32 | 5.33 | 4.27 | 8.08 | 0.70 | 1.59 | 6.36 | 1.72 | 0.80 |
ISUP-ISUO | 3.57 | 3.02 | 2.71 | 3.60 | 0.93 | 1.15 | 3.04 | 1.15 | 1.05 |
Mean | 5.21 | 4.69 | 3.82 | 7.10 | 0.91 | 1.62 | 5.66 | 1.75 | 1.09 |
Second Difference | Rb | Rb-II | PHM | Mean |
---|---|---|---|---|
ISUP-ISC | 3.71 | 1.41 | 0.99 | 2.03 |
ISUO-ISC | 2.78 | 0.73 | 0.63 | 1.38 |
ISUP-ISUO | 2.97 | 1.04 | 0.91 | 1.64 |
Mean | 3.15 | 1.06 | 0.84 |
Model | ISUP | QP | GM | SSA-ELM | Enhancement with ISUP (%) | Enhancement with QP (%) | Enhancement with GM (%) |
---|---|---|---|---|---|---|---|
Rb | 1.75 | 1.09 | 2.88 | 0.97 | 44.67 | 11.58 | 66.32 |
Rb-II | 1.65 | 0.56 | 1.37 | 0.55 | 66.57 | 1.99 | 59.85 |
PHM | 1.62 | 0.50 | 0.50 | 0.49 | 70.01 | 2.81 | 3.20 |
Mean | 1.67 | 0.72 | 1.58 | 0.67 | 60.42 | 5.46 | 57.59 |
Model | ISUP | QP | GM | SSA-ELM | Enhancement with ISUP (%) | Enhancement with QP (%) | Enhancement with GM (%) |
---|---|---|---|---|---|---|---|
Rb | 3.19 | 1.88 | 3.93 | 1.13 | 64.66 | 39.93 | 71.25 |
Rb-II | 3.35 | 1.48 | 2.09 | 0.80 | 76.04 | 45.71 | 61.72 |
PHM | 3.19 | 1.48 | 1.27 | 0.76 | 76.10 | 48.31 | 40.05 |
Mean | 3.25 | 1.61 | 2.43 | 0.90 | 72.27 | 44.65 | 62.96 |
Model | QP | GM | SSA-ELM | Enhancement with QP (%) | Enhancement with GM (%) |
---|---|---|---|---|---|
Rb | 2.62 | 2.12 | 1.01 | 61.43 | 52.35 |
Rb-II | 1.34 | 1.64 | 0.71 | 47.21 | 56.79 |
PHM | 1.17 | 1.09 | 0.58 | 50.84 | 47.14 |
Mean | 1.71 | 1.62 | 0.76 | 53.16 | 52.09 |
Model | QP | GM | SSA-ELM | Enhancement with QP (%) | Enhancement with GM (%) |
---|---|---|---|---|---|
Rb | 1.89 | 2.40 | 0.97 | 48.33 | 59.40 |
Rb-II | 1.68 | 1.60 | 0.93 | 44.56 | 41.46 |
PHM | 1.08 | 1.24 | 0.77 | 29.08 | 38.28 |
Mean | 1.55 | 1.75 | 0.89 | 40.66 | 46.38 |
Clock Type | Rb | Rb-II | PHM | Mean |
---|---|---|---|---|
0h | 9.75 | 9.42 | 9.64 | 9.60 |
6h | 5.16 | 4.96 | 5.13 | 5.08 |
Model | ISUP | QP | GM | SSA-ELM | Enhancement with ISUP (%) | Enhancement with QP (%) | Enhancement with GM (%) |
---|---|---|---|---|---|---|---|
Rb | 7.08 | 6.88 | 7.50 | 4.54 | 35.90 | 33.98 | 39.43 |
Rb-II | 5.54 | 5.76 | 6.07 | 4.39 | 20.79 | 23.86 | 27.72 |
PHM | 5.72 | 6.06 | 5.86 | 4.36 | 23.86 | 28.17 | 25.72 |
Mean | 6.11 | 6.23 | 6.48 | 4.43 | 26.85 | 28.67 | 30.96 |
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Ya, S.; Zhao, X.; Liu, C.; Chen, J.; Liu, C. Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model. Sensors 2023, 23, 2453. https://doi.org/10.3390/s23052453
Ya S, Zhao X, Liu C, Chen J, Liu C. Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model. Sensors. 2023; 23(5):2453. https://doi.org/10.3390/s23052453
Chicago/Turabian StyleYa, Shaoshuai, Xingwang Zhao, Chao Liu, Jian Chen, and Chunyang Liu. 2023. "Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model" Sensors 23, no. 5: 2453. https://doi.org/10.3390/s23052453
APA StyleYa, S., Zhao, X., Liu, C., Chen, J., & Liu, C. (2023). Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model. Sensors, 23(5), 2453. https://doi.org/10.3390/s23052453