1. Multi-target Detection in Sensor Networks Xiaoling Wang ECE691, Fall 2003

2. Target Detection in Sensor Networks Single target detection Energy decay model: Constant false-alarm rate (CFAR) Multiple target detection Blind source separation (BSS) problem Targets are considered as the sources “Blind”: there is no a-priori information on  the number of sources  the probabilistic distribution of source signals  the mixing model Independent component analysis (ICA) is common technique to solve the BSS problem source

3. BSS in sensor networks BSS problem involves Source number estimation Source separation Assumptions Linear, instantaneous mixture model Number of sources = number of observations This equality assumption is not the case in sensor networks due to the large amount of sensors deployed

4. Source Number Estimation Source number estimation: Available source number estimation algorithms Sample-based approach: RJ-MCMC (reversible- jump Markov Chain Monte Carlo) method Variational learning Bayesian source number estimation

5. Bayesian Source Number Estimation (BSNE) Algorithm : sensor observation matrix : hypothesis of the number of sources : source matrix : mixing matrix, : unmixing matrix, and : latent variable, and : non-linear transformation function : noise, with variance : marginal distribution of Detailed derivation

6. Centralized vs. Distributed Schemes Centralized scheme: long observed sequences from all the sensors are available for source number estimation Centralized processing is not realistic in sensor networks due to: Large amount of sensor nodes deployed Limited power supply on the battery-powered sensor node Distributed scheme: Data is processed locally Only the local decisions are transferred between sensor clusters Advantages of distributed target detection framework: Dramatically reduce the long-distance network traffic Therefore conserve the energy consumed on data transmissions.

7. Distributed Source Number Estimation Scheme Sensor nodes clustering The distributed scheme includes two levels of processing: An estimation of source number is obtained from each cluster using the Bayesian method The local decisions from each cluster are fused using the Bayesian fusion method and the Dempster’s rule of combination.

8. Distributed Hierarchy Unique features of the developed distributed hierarchy M-ary hypothesis testing Fusion of detection probabilities Distributed structure Structure of the distributed hierarchy

9. Posterior Probability Fusion Based on Bayes Theorem Since where Sinceare independent, for Therefore,

10. Dempster’s Rule of Combination Utilize probability intervals and uncertainty intervals to determine the likelihood of hypotheses based on multiple evidence Can assign measures of belief to combinations of hypotheses

11. Performance Evaluation of Multiple Target Detection Sensor laydown Target types

12. Results Comparison: Log-likelihood and Histogram

13. Results Comparison: Kurtosis, Detection Probability, and Computation Time

14. Discussion The distributed hierarchy with the Bayesian posterior probability fusion method has the best performance, because: Source number estimation is only performed within each cluster, therefore, the effect of signal variations are limited locally and might contribute less in the fusion process The hypotheses of different source numbers are independent, exclusive, and exhaustive set which is in accordance with the condition of the Bayesian fusion method. The physical characteristics of sensor networks are considered, such as the signal energy captured by each sensor node versus its geographical position

15. Derivation of the BSNE Algorithm Choosethen since where are constants. Suppose noise on each component has same variance,then where (1) Assume the integral in (1) is dominated by a sharp peak at Laplace approximation of the marginal integral, then by using

16. Therefore, where Then where (2) Assume the density function ofis sharply peaked at and use Laplace approximation,

17. Assume Then and Using the maximum-likelihood estimation, gives