1. Distributed Signal Processing Woye Oyeyele March 4, 2003

2. AICIP Seminar Spring 2003 2 Outline Distributed Signal Processing Matched Filter Detection Examples

3. AICIP Seminar Spring 2003 3 Definition Distributed Signal Processing is – Distributed topology – Distributed task; sensing,localization,tracking – Distributed hypothesis

4. AICIP Seminar Spring 2003 4 Why Distributed concept? Offers opportunities for improved line of sight Finite energy budget at nodes Communications consumes significant power – Need to transmit minimal data

5. AICIP Seminar Spring 2003 5 Two Dimensions Hardware DSP – Focus on distributed computation – Efficient computation strategies Software DSP – Distributed Sensing,Fusion, Detection

6. AICIP Seminar Spring 2003 6 Software Distributed Signal Processing Distributed Detection – Identify presence of phenomenon Distributed Estimation – Determine particular target, locate and track

7. AICIP Seminar Spring 2003 7 Typical Topologies[1][3] Parallel Serial or tandem Tree

8. AICIP Seminar Spring 2003 8 Parallel Topology Phenomenon s1s1 s2s2 s3s3 S n-1 snsn... Fusion Center u0u0 Fusion Center may be omitted to form a variant of this topology y1y1 y2y2 y3y3 y N-1 yNyN

9. AICIP Seminar Spring 2003 9 Serial or Tandem topology Phenomenon s1s1 s2s2 s3s3 S n-1 snsn … u1u1 u2u2 u3u3 u n-1 u 0 =u n

10. AICIP Seminar Spring 2003 10 Tree Topology s4s4 s3s3 s5s5 s6s6 s2s2 s1s1 s0s0 u3u3 u5u5 u4u4 u6u6 u0u0 u1u1 u2u2

11. AICIP Seminar Spring 2003 11 Mobile Agent topology Combined parallel, serial and short hierarchical

12. AICIP Seminar Spring 2003 12 Overall aims Maximize probability of detection Minimize probability of error Maximize accuracy of classification

13. AICIP Seminar Spring 2003 13 Outline Distributed Signal Processing Matched Filter Detection Examples

14. AICIP Seminar Spring 2003 14 Matched Filter Approach to Distributed Detection Two fold – Restricted matched filter(RMF) – restricted to choice of sensors – Match observations to a template of expected cues/features

15. AICIP Seminar Spring 2003 15 Aims and objectives Model as a distributed antenna problem Cast problem in proper domain – Frequency, time, time-frequency Develop robust, scalable and highly reliable algorithms

16. AICIP Seminar Spring 2003 16 Sequential vs. Fixed Sample size detection Number of observations combined to reach decision is dependent on nature of observations Stopping rule is required at each sensor Number of observations used is random Operate on observation size predetermined during design SequentialFixed Sample size

17. AICIP Seminar Spring 2003 17 Matched Filter Algorithm Perform FFT Construct matched signal Correlator -Filter response -To be based on knowledge of expected target signatures -Omitted in testing phase Knowledge Base Normally, possible transmissions are built to be easily differentiated, but target signatures are more complicated. output input

18. AICIP Seminar Spring 2003 18 General Challenges Information is spatially distributed Data is multimodal – Common statistics not sufficient to differentiate – Measurement variability exists for different temporal measurements of same mode Asynchronous nature of observations – Data captured in out-of-order fashion

19. AICIP Seminar Spring 2003 19 General Challenges – contd. Energy Efficiency – Can algorithm recover/slowly degrade on power failure Hierarchical data – Local, global

20. AICIP Seminar Spring 2003 20 RMF detection aims Obviate high communication costs occurring due to use of all sensor observations Choose adequate subset – Optimal subset balances signal energy and noise correlation

21. AICIP Seminar Spring 2003 21 Mobile Agent RMF challenges Size constraints – Limit for buffer growth vs. attainment of sufficient threshold Communication costs – Need to minimize Time – Need to serve real time environments

22. AICIP Seminar Spring 2003 22 RMF algorithm Criterion: Balance signal Energy and noise correlation Matched to sufficient statistic l Select Sensors Filter h[i] l j=0 yykyk l = s k T  -1 y k =  h[i] y[i] y k = n k – target absent(noise) s k + n k – target present {

23. AICIP Seminar Spring 2003 23 RMF Characteristics Optimal choice of sensors ensures maximum SNR Sufficient statistic (with tolerance) is a threshold for evaluating likelihood of hypothesis Spatial processing independent of algorithm topology

24. AICIP Seminar Spring 2003 24 Focus of current work Focus is on filter design i.e. second stage of algorithm Future – technique for estimating noise correlation between sensors – assumption that noise is independent between sensors may not be right

25. AICIP Seminar Spring 2003 25 Distributed Signal Processing Matched Filter Detection Examples

26. AICIP Seminar Spring 2003 26 Example from SensIT data ChannelMode 1Seismic 2Acoustic 3PIR -SITEX00 Data used -Event 08020830 (Dragon Wagon) -Sensor Node A01

27. AICIP Seminar Spring 2003 27 Signal Plot –Channel 1

28. AICIP Seminar Spring 2003 28 Signal Plot – Channel 2

29. AICIP Seminar Spring 2003 29 Signal Plot – Channel 3

30. AICIP Seminar Spring 2003 30 Power Spectral Density – Channel 1

31. AICIP Seminar Spring 2003 31 Power Spectral Density – Channel 2

32. AICIP Seminar Spring 2003 32 Power Spectral Density – Channel 3

33. AICIP Seminar Spring 2003 33 Time domain plot - 3 seconds

34. AICIP Seminar Spring 2003 34 Freq. domain plot

35. AICIP Seminar Spring 2003 35 Filter Response

36. AICIP Seminar Spring 2003 36 Final Output

37. AICIP Seminar Spring 2003 37 Recap Distributed Detection and Estimation offers tremendous benefits Matched Filter forms a conceptual basis for sensor selection and local processing

38. AICIP Seminar Spring 2003 38 Research Directions Develop spatial techniques for matched filter detection – Combine with beamforming and direction of arrival mechanisms to detect and localize target (target tracking is continuous localization) Algorithm to select optimal sensor subset – Estimate noise correlation between sensors – Achieve optimal ROC - quadratic

39. AICIP Seminar Spring 2003 39 References 1. R. Viswanathan and P. K. Varshney, "Distributed detection with multiple sensors: Part I - fundamentals," Proceedings of the IEEE, vol. 85, no. 1, pp. 54-63, Jan. 1997 2. R. Viswanathan and P. K. Varshney, "Distributed detection with multiple sensors: Part I - fundamentals," Proceedings of the IEEE, vol. 85, no. 1, pp. 54-63, Jan. 1997 3. Couch II, Leon W., Digital and Analog Communications Systems, Fourth Edition, Macmillan Publishing Co, 1993, ISBN 0-02-325281-2. 4. P. K. Varshney, Distributed Detection and Data Fusion, Springer-Verlag 1996 5. D. Estrin, L. Girod, G. Pottie, M. Srivastava, Instrumenting the world with Wireless Sensor Networks. 6. Charles Sestok, Alan Oppenheim, The Restricted Matched Filter for distributed detection(presentation), DARPA SensIT PI Meeting, Jan. 16, 2002.