1. Compressive Sensing for Attitude Determination Rishi Gupta, Piotr Indyk, Eric Price, Yaron Rachlin May 12, 2011 Draper Laboratory

2. Attitude Determination http://pubpages.unh.edu/~cmg65/projectpages/page7.html

3. Attitude Determination

4. Star Trackers 1. Acquire Image 2. Find a few big stars 3. Match constellations to database

5. Compressive Star Trackers 1. Acquire Compressed Image 2. Find a few big stars 3. Match constellations to database 2.5 Decompress

6. 1. Compression (folding)

8. 2. Find a few big stars ● This is just like the regular algorithm ● Except faster, because we have smaller images Fold 1 Fold 2

9. 2.5a Match stars ● Label the stars in Fold 1 ● Find stars that look similar in Fold 2 Fold 1 Fold 2 1 2 3 4 5 1 2 3 4 5

10. 2.5b Decompress Decompress the labels one at a time. x x

11. Compressive Star Trackers 1. Acquire Compressed Image 2. Find a few big stars 3. Match constellations to database 2.5 Label and Decompress 2x

12. Hardware ● Why now? ● Falling cost of computation relative to sensing ● Potential implementations ● Mirrors ● Lenses ● Integrated circuit (CMOS)

13. Generalizations ● Two folds --> Many folds ● Random --> Adversarial star placement ● Stars --> Local, distinguishable objects ● Full paper (with pictures) http://web.mit.edu/rishig/papers/attitude.pdf

14. Empirical Results Std of noise added to each folded pixel Fraction of correct recoveries Tiling is robust to compression