Multi-target Detection in Sensor Networks

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 : source matrix : mixing matrix, : unmixing matrix, and : hypothesis of the number of sources and : latent variable, : non-linear transformation function : noise, with variance : marginal distribution of Detailed derivation

6. 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. Centralized vs. Distributed Schemes

7. Distributed Source Number Estimation Scheme • 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. Sensor nodes clustering

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

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

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 Target types Sensor laydown

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

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

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