1. REST for interacting multi- target tracking Jesse McCrosky Surrey Kim

2. Overview Signal Model –SDE –Analysis –Simulation Observation Model –SONAR Filtering –REST –New Layout Conclusions

3. Signal Model Model multiple submarines Currently using Fish School model –Four forces (drift): Cohesion – fish stay close together Separation – fish don’t collide Alignment – fish point in same direction Containment – fish don’t leave domain –Also diffusion

4. Simulation WARNING: equations ahead…

5. Signal Model SDE

8. Analysis Problems with converting SDE into measure valued process form –Modify SDE to simplify –Solution must exist: find it

9. Basic Sonar Systems Active –Transducers –Echo Ranging Systems –Gives range information –May have a higher FOM in some cases Passive –Usually hydrophones only (Listening Systems) –Does not give away searching vessel’s position. –Enables the listener to gain information on the contact’s characteristics, speed, aspect

10. Acoustic Every target sub emits sound SL = 10 log(I 1 / I o ) –Where SL is the source level, I 1 is the intensity for sound emitted by target from 1 meter away DT = (SL-TL) – NL –where DT is the detection threshold, –TL is the range dependent transmission loss from the target to sonobuoy, and –NL is the noise level

11. Sources for Noise Biological –Produced by marine life (Whales, dolphins, Loch Ness) Seismic –Movement of the earth (earthquakes). Hydrodynamic –Caused by the movement of water. –Includes tides, current, storms, wind, rain, etc.

12. Optimal Control Problem –Estimation of Buoy range (filter’s estimate on target’s speed) –Deciding when to deploy –Deciding where to deploy The Buoy Deployment Problem

13. Acoustic Basics p = C x f –Where p is pressure and f is velocity C = D x V –Where D = fluid density (kg/m 3 ) and V = propagation velocity (m/s) –For sea water C = 1.54x10 6 kgm -2 s -1 I = p 2 / C –Where I is the power per unit area –I o = 6.504 x 10 -19 W/m 2 (Standard Intensity)

14. Acoustic Basics SL = 10 log(I 1 / I o ) –Where SL is the source level, I 1 is the intensity for sound emitted by target from 1 meter away DT = (SL-TL) – (NL-DI) where DT is the detection threshold, TL is

15. Source Level (SL) dependent on Speed (f) Time differences of arrival TDOA Tracking/Prediction Problem

16. REST layout Traditional, single-target REST uses cells laid out in signal space. Particle flow is between signal-space neighbours But multi-target REST uses counting measure cells

17. Counting measure cells For two dimensional signal space with three targets: This cell has particle flow with any cell where only one target moves horizontally or diagonally: 0000 0100 0100 0001 0000 0000 0200 0001

18. Problem In this case there is no natural concept of “negative neighbor in 2 nd dimension” –Could artificially build cells into grid Need higher dimensionality than signal space –Some other concept of adjacency?