Sampling great circles at their rate of innovation

• Main Authors: Deslauriers-Gauthier, Samuel, Marziliano, Pina
• Other Authors: Van De Ville, Dimitri
• Format: Conference or Workshop Item
• Language: English
• Published: 2014
• Subjects: DRNTU::Engineering::Electrical and electronic engineering::Antennas, wave guides, microwaves, radar, radio
• Online Access: https://hdl.handle.net/10356/100670; http://hdl.handle.net/10220/18606
• Institution: Nanyang Technological University

In this work, we show that great circles, the intersection of a plane through the origin and a sphere centered at the origin, can be perfectly recovered at their rate of innovation. Specifically, we show that 4K(8K − 7) + 7 samples are sufficient to perfectly recover K great circles, given an appropriate sampling scheme. Moreover, we argue that the number of samples can be reduced to 2K(4K − 1) while maintaining accurate results. This argument is supported by our numerical results. To improve the robustness to noise of our approach, we propose a modification that uses all the available information, instead of the critical amount. The increase in accuracy is demonstrated using numerical simulations.