Strapdown Celestial Attitude Estimation from Long Exposure Images for UAV Navigation
Abstract
:1. Introduction
2. Methods
 Estimate the theoretical curve of the star trail on the image plane by using INS measurements.
 Apply a smoothing filter, morphological operations, and clustering to extract the star trail for each star with brightness above a given magnitude threshold.
 Apply a thinning algorithm on each star trail to remove the effects of Gaussian pointspread diffusion.
 Identify the endpoints of each star trail given the INSsimulated approximation.
 Use the endpoints of the thinned star trails, along with the endpoints of the INS approximation, to compute the weighted least squares approximation for the mean attitude offset throughout the exposure window.
 For each point in the meanerror corrected INS approximation, compute the least squares approximation of the precise attitude offset.
2.1. Image Processing
2.2. Orientation Estimation
 The INS sampling period, ${T}_{s}$, is constant.
 The photon flux density incident on the sensor from a given luminary is constant.
 The path taken by the airframe results in a simple curve on the image plane (i.e., the star trail does not cross itself at any point).
Algorithm 1 Mapping from INS points to real image points. 

3. Results
 A randomvalued constant offset, and
 Perlin noise.
3.1. Simulation Results
3.2. Real Imagery
4. Discussion
 The camera calibration matrix, $\mathbf{K}$ does not perfectly characterize the camera.
 Unmodeled sources of noise caused the image processing techniques not to transfer from simulation to reality.
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Jacobian Matrix Entries
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Mean  Median  Std  Mean + 3$\mathit{\sigma}$  

Max yaw error  0.1053  0.0903  0.0856  0.2828 
Max pitch error  0.0503  0.0414  0.0317  0.1453 
Max roll error  0.0506  0.0418  0.0286  0.1366 
Mean absolute yaw error  0.0428  0.0442  0.0274  0.1294 
Mean absolute pitch error  0.0205  0.0167  0.0128  0.0591 
Mean absolute roll error  0.0217  0.0207  0.0129  0.0604 
Mean yaw error  0.0118  0.01076  0.0322   
Mean pitch error  −0.0080  −0.0061  0.0138   
Mean roll error  −0.0078  −0.0061  0.02124   
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Teague, S.; Chahl, J. Strapdown Celestial Attitude Estimation from Long Exposure Images for UAV Navigation. Drones 2023, 7, 52. https://doi.org/10.3390/drones7010052
Teague S, Chahl J. Strapdown Celestial Attitude Estimation from Long Exposure Images for UAV Navigation. Drones. 2023; 7(1):52. https://doi.org/10.3390/drones7010052
Chicago/Turabian StyleTeague, Samuel, and Javaan Chahl. 2023. "Strapdown Celestial Attitude Estimation from Long Exposure Images for UAV Navigation" Drones 7, no. 1: 52. https://doi.org/10.3390/drones7010052