1. Distributed Radiation Detection Daniel Obenshain Arthur Rock SURF Fellow

2. Motivation Professor Ryan McLean and others at Caltech have developed a new, cheaper radiation sensor using CdZnTe materials. Professor K. Mani Chandy and the Infospheres research group have developed algorithms for aggregating the data collected by many of these sensors working in concert. This paper considers the optimal placement for such sensors.

3. Motivation The threat of nuclear proliferation and dirty bombs is very real. It is our goal to combat this threat through better radiation detection.

4. Motivation Professor Ryan McLean and others at Caltech have developed a new, cheaper radiation sensor using CdZnTe materials.

5. Motivation Professor K. Mani Chandy and the Infospheres research group have developed algorithms for aggregating the data collected by many of these sensors working in concert.

6. Motivation In this SURF, I examined the implications of these algorithms on stationary sensor grids.

7. The Situation A single terrorist carrying a dirty bomb is somewhere in a field. Several stationary agents are attempting to locate the terrorist.

8. The Situation The agents communicate fully in real time. The terrorist does not move.

9. Simulation Methodology The simulation stores a heat map of probabilities for possible terrorist locations. Initially, all probabilities are equal. After each iteration, the Baysian update formula is applied.

10. Simulation Methodology After 50% of the total probability on the heat map is confined to 1% of the total area, the terrorist is considered to be found. In each simulation, neither the terrorist nor the agents may move.

11. Bayesian Update The probability that the terrorist is in a specific cell (x,y) of the heat map is approximated as ((((lambda * T) ^ n) * e ^ (-lambda * T)))/ n! where lambda * T is the expected number of hits (assuming the terrorist is in that cell) and n is the actual number of hits.

12. Bayesian Update The probability is found this way for each agent. The probabilities are multiplied together to get the whole network’s probability. This probability is multiplied by the old entry in the heat map to update the heat map.

13. Bayesian Update The heat map is then normalized to a total probability of 1, to correct for errors. The process is repeated until the terrorist is found.

14. What this means If the terrorist is in the cell (x,y), the number of hits received will closely match the number of hits expected (within a margin of error). Thus, the probability will increase for (x,y).

15. What this means If the terrorist is not in the cell (x,y), the number of hits will not closely match the number of hits expected. Thus, the probability will decrease for (x,y).

16. What this means Since radiation goes as 1/r^2, the closer a sensor is to the source, the better resolution there is between different cells in the heat map. If the radiation source is far away, there is very little radiation (1/r^2 ~ 0), and thus little information about the location.

17. Four Experiments These four experiments will show some of the implications of this algorithm.

18. Line Experiment A group of sensors is trying to determine a radiation source’s position. The sensors spread out in a line. For simplicity, assume neither the sensors nor the source can move.

19. Line Experiment Nine agents in a line One terrorist The terrorist is some fixed distance perpendicularly away from the line of sensors

20. Results

21. Results – Explanation The time to interdiction increases exponentially! So, having many sensors in a line is a bad sensor placement.

22. Expanding Field Here, we examine how increased field size affects interdiction time. For simplicity, we place one sensor on each corner of the field.

23. Expanding Field One terrorist in the center of the field Four agents at the four corners of the field Fixed field size L x L

24. Results

25. Results – Explanation So, as we increase field size, the time to interdict goes as L^2. This is reasonable, since we are also increasing the area by L^2. Not promising, since low interdiction times are important.

26. Expanding Sensor Grid Given a certain field of fixed size, how should we place sensors? We consider several different size square sensor grids.

27. Expanding Sensor Grid Fixed field size of 300 m x 300 m One terrorist in the center of the field Four agents in a square of fixed size L x L, where L <= 300 m

28. Results

29. Results - Explanation Dip at 2/3 of Field length. Appeared in many different field sizes. Caused by edge effects. Still not very good interdiction time. Interdiction time goes exponentially.

30. Off-center Radiation Source What if the terrorist isn’t in the center? We consider several different size square sensor grids, with the source at different distances from center.

31. Off-center Radiation Source Fixed field size of 300 m x 300 m. One terrorist, off- center by some distance S. Four agents in a square of fixed side length L.

32. Results

33. Results – Explanation 15 and 20 meters from center were different because of edge effects. Interdiction time still goes exponentially.

34. Conclusion Because the time to interdiction increases so quickly with distance, it is imperative that some sensors be close to the terrorist. Static sensors would have to be ubiquitous for this to be true, which is not cost effective.

35. Conclusion Instead, mobile sensors should be used. Since mobile sensors can react in real time, they would be able to approach the radiation source to gain more information and decrease interdiction time.

36. Further Work Mobile sensors Dealing with background radiation Screening for false positives (medical radiation, smoke detectors, etc.)

37. Acknowledgements Many thanks to Professor Mani Chandy, Professor Ryan McLean, Annie Liu, Mathew Wu, Concetta Pilotto, Mason Smith, the Arthur Rock Foundation, and everyone else who contributed to this project.