Collaborative Signal Processing

1. Collaborative Signal Processing CS 691 – Wireless Sensor Networks Mohammad Ali Salahuddin 04/22/03

2. Introduction to CSP • Need for CSP • Features: • Distributed Processing • Goal-Oriented on demand processing • Information Fusion • Multi-resolution Processing

3. Space-Time Sampling and Space-Time Cells • Space and Time for useful information • Moving object in a region corresponds to a peak in the spatial signal field that moves with time

4. Detection and Tracking • Tracking a single target in a distributed network • Routing protocols being used in the Sensor Networks: • Data-Centric • Node-Centric • Geographic-Centric (UW) • Geographic region divided in spatial cells • Some nodes are designated Manager nodes

5. Single Target

6. Single Target (contd.) • Assumptions: • Potential target may enter the region via one of the four corners, four cells A, B, C and D • Nodes in each of the four corner cells are activated to detect potential target • Nodes run an energy detection algorithm, sampling at a priori fixed sampling-rate • Suppose a target enters cell A

7. Single Target (contd.) • Algorithm: • Some or all nodes in A detect the target, send the CPA and energy detector output to the manger nodes at N successive time intervals • At each time instance, the manager nodes determine the location of the target from the energy detector outputs. • Manager node use locations of the target at N successive time instants to predict the location of the target at M<N future time intervals • The predicted positions of the target are used to create new cells that the target is likely to enter • Once the target is detected in one of the new cells, it is designated as the new active cell and the node in the original active cell (cell A) may be put to sleep The above steps are repeated for the new active cell and so on, thus forming the basis of detecting and tracking a single target

8. Multiple Targets • Two scenarios: • Multiple targets sufficiently separated in space or time i.e. they occupy distinct space-time cells • Then the same procedure as described for single targets can be used, initialing and maintaining a separate track for each target • Multiple targets are not separated in space or time • Needs classification algorithms that operate on target signatures to classify them • Needs temporal processing, FFT • The output from the classification, active classifiers, are reported to the manager node as opposed to the energy detector outputs • Then the same procedure as described for single targets can be used, initialing and maintaining a separate track for each target

9. Signal Processing • Detection • Target Localization • Tracking

10. Detection • An event is detected when the detector output exceeds a threshold value • Noise component in the detector may be modeled as a Gaussian random variable whose mean and variance can be determined from the statistics of the background noise • The Threshold is dynamically adjusted according to the noise variance of the detector output in order to maintain a CFAR • Detector outputs below CFAR are used to update the Threshold • Output parameters sent to the manager node consists of: • Time when the detector output exceeds the Threshold • Time of maximum CPA • Detector output of CPA time • Time when the detector output falls below the threshold

11. Target Localization • Need for Complex Algorithms: • Accurate localization methods based on time-delay estimation require accurate synchronization among nodes, which comes at a high cost • Exchange of time series data among nodes, as required by some algorithms, consume too much energy to be feasible • Algorithm (4 or more nodes): • Energy-based algorithm, which assumes an isotropic exponential attenuation for the target energy source: where, yi(t) is the energy reading at the ith sensor, r(t) denotes the unknown coordinates of source with respect to a fixed reference, ri are coordinates of ith sensor, s(t) is the unknown target signal energy, alpha is the decay component

12. Target Localization (contd.) • The algorithm first computes the ratio yi(t)/yj(t) for all pair of sensors to eliminate the unknown variable s(t) • The unknown r(t) is estimated by solving a nonlinear least square problem of the form: where, (x,y) are the unknown coordinates of the target, (oi,x, oi,y) are the center coordinates, and pi is the radius of the circle associated with the ith ratio

13. Target Localization (contd.)

14. Target Tracking • Given target locations at time instants in the past, it is possible to fit data samples into a dynamic model to predict future target locations • For single moving targets, data can be fitted into a linear or polynomial model using a least square fit • Is complicated when it comes to tracking multiple targets as targets can cross paths resulting in data association problems • Classification algorithms can provide a solution to the above problem

15. Target Classification • Needed for tracking multiple targets • Feature Vector • Categories • Building block: p (wc | x) = p (wc) p (x | wc) p(x)

16. Future Research • To study the feasibility of introducing parallel computations in classification in CSP (Self) • Choosing between DATA fusion and DECISION fusion

17. References [KWHS] D. Li, K.D. Wong, Yu H. Hu and A.M. Sayeed, “Detection, Classification and Tracking of Targets in Distributed Sensor Networks”, Department of Electrical and Computer Engineering, University of Wisconsin-Madison [S] A. Sayeed, “Collaborative Signal Processing”, MobiComm 2003 [R] T.S. Rognvaldsson, “Introduction to classification”, Learning and Self- Organizing Systems, January 21, 2001 [DS] A. D’Costa and A. M. Sayeed, “Collaborative Signal Processing for Distributed Classification in Sensor Networks”, Department of Electrical and Computer Engineering, University of Wisconsin-Madison

18. References (contd.) [M] D. J. Mackay, “Introduction to Gaussian Processes”, Department of Physics, Cambridge University [R] P. Ramanathan, “Location-centric Approach for Collaborative Target Detection, Classification, and Tracking”, University of Wisconsin- Madison

19. Question and Comments