Article Figures & Data
Figures
- FIGURE 1
Illustration showing the DOV as the angle of the effective gravity vector relative to the ellipsoidal normal
- FIGURE 2
Trajectory of an RNP 0.3 approach into Runway 02 of the Kahului Airport
- FIGURE 3
North-south DOV for an approach into Runway 02 of Kahului Airport
- FIGURE 4
Simulated approach onto Runway 33 at Ted Stevens Anchorage International Airport
- FIGURE 5
North-south DOV for an approach onto Runway 33 of Ted Stevens Anchorage International Airport
- FIGURE 6
Visualization of gravitational forces acting on Object 1 as it moves on a path offset from Object 2
- FIGURE 7
Normalized along-track and cross-track components of the gravitational force experienced as Object 1 passes Object 2 that is offset from the trajectory
- FIGURE 8
Normalized spatial power spectra demonstrating differences between the along-track and cross-track components of the gravitational forces
- FIGURE 9
Block diagram demonstrating the generation of the total simulated gravity model error
- FIGURE 10
DOV profiles as determined from EGM2008 and DEFLEC data sets for a simulated approach into Ted Stevens International Airport in Anchorage, Alaska
- FIGURE 11
Block diagram outlining the process for using system identification to analyze measured data, identify, and validate representative ARMA models
- FIGURE 12
Example differences between EGM2008 and xDEFLEC19 cross-track components of DOV for select trajectories
- FIGURE 13
Example differences between EGM2008 and XDEFLEC19 along-track components of DOV for select trajectories
- FIGURE 14
Mean of the BIC for each of the selected cross-track runs
- FIGURE 15
Pole-zero plot showing the cross-track and along-track pole results from system identification of each of the trajectories
- FIGURE 16
Comparison of the measured data PSD to the simulated data to show validation of the AR(2) model specified in Equation (5)
- FIGURE 17
Mean of the model order selection criteria (i.e., BIC) over a range of (p,q) combinations up to ARMA(15,15)
- FIGURE 18
Pole-zero plot showing the ARMA(2,2) poles and zeros for model fits in addition to the roots selected for the ARMA(2,2) model used for validation
- FIGURE 19
The measured data PSD with confidence bounds compared to the PSD produced by the ARMA(2,2) model in Equation (7)
- FIGURE 20
Complementary CDF showing that Gaussian distribution bounds the tails of the model errors
- FIGURE 21
Block diagram demonstrating the use of ARMA models to generate simulated reference model
- FIGURE 22
Example simulated reference gravity model errors using the models given in Equations (5) and (7) and a model standard deviation of σx = 16.3 arc-seconds
- FIGURE 23
Block diagram demonstrating an example of low-fidelity architecture
- FIGURE 24
Sample cross-track total DOV for a select trajectory
- FIGURE 25
Sample along-track total DOV for a select trajectory
- FIGURE 26
Mean BIC values for each ARMA(p,q) combination for the cross-track (left) and along-track (right)
- FIGURE 27
Pole-zero plots showing roots of the ARMA(1,1) fits to the low-order cross-track and along-track
- FIGURE 28
PSDs of the measured data compared to the spectrum of the simulated data generated by Equation X and Equation Y
- FIGURE 29
DOV for a trajectory over Puerto Rico showing the large low-frequency effects and gravitational effects of the trench
- FIGURE 30
Mean BIC for the cross-track low-fidelity residuals from areas near Hawaii and Puerto Rico
- FIGURE 31
Pole-zero plot demonstrating the results of the system identification on cross-track DOV of trajectories near Hawaii and the Puerto Rico trench using AR(2)
- FIGURE 32
Pole-zero plot demonstrating the results of the system identification on DOV of trajectories near Hawaii and the Puerto Rico trench using AR(3)
- FIGURE 33
Low-fidelity Geographic Area #2 along-track
- FIGURE 34
Pole-zero plot demonstrating the results of the system identification on along-track DOV of trajectories near Hawaii and the Puerto Rico trench using AR(2)
- FIGURE 35
Low-fidelity Geographic Area #2 along-track
- FIGURE 36
The measured data PSD with confidence bounds compared to the PSD produced by AR(2) cross-track model in Equation (10)
- FIGURE 37
The measured data PSD with confidence bounds compared to the PSD produced by AR(2) along-track model in Equation (11)
- FIGURE 38
Complementary CDF showing that Gaussian distribution bounds the tails of the low-fidelity model errors
- FIGURE 39
Example cross-track and along-track data generated using the model as specified in Equation (10) and Equation (11)
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- Article
- Abstract
- 1 INTRODUCTION
- 2 GRAVITY COMPENSATION AND MIS-MODELING
- 3 EFFECTS OF A STATIONARY MASS ON A MOVING OBJECT
- 4 HIGH-FIDELITY GRAVITY SIMULATION ARCHITECTURE
- 5 HIGH-FIDELITY STOCHASTIC MODEL DEVELOPMENT APPROACH
- 6 EXAMPLE HIGH-FIDELITY STOCHASTIC MODEL
- 7 LOW-FIDELITY STOCHASTIC MODEL DEVELOPMENT APPROACH AND EXAMPLE
- 8 CONCLUSION AND RECOMMENDATIONS
- HOW TO CITE THIS ARTICLE
- ACKNOWLEDGEMENTS
- REFERENCES
- Figures & Data
- Supplemental
- References
- Info & Metrics
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