Mobile Agent Based Progressive Multiple Target Detection in Sensor Networks

1. Mobile Agent Based Progressive Multiple Target Detection in Sensor Networks Xiaoling Wang ECE691, Fall 2003

2. Multiple Target Detection • Similar to BSS (blind source separation) problem • It is normally assumed in BSS that the number of targets equals the number of sensors • In sensor networks, the number of sensors usually exceeds the number of targets • The first step is to estimate the number of sources in real time

3. Environment Sensor i Sensor n Sensor 1 x1 x2 x3 Fusion Center Source Number Estimation • Bayesian estimation approach • Traditional centralized scheme(Roberts,98) …… ……

4. Centralized Bayesian SNE • Suppose denotes the hypothesis that there is m targets in the field, then the Bayesian objective function is: Bayes theorem Eq.1

5. Centralized Bayesian SNE where : sensor observation matrix : mixing matrix : unmixing matrix, and and : latent variable, : non-linear transformation function : noise, with variance : marginal distribution of

6. Progressive SNE • Motivation • Reduce data transmission • Conserve energy • Basic idea of progressive scheme • At sensor i, process data locally • Upon receiving a partial result from its previous sensor, update the estimation of the log-likelihood and the mixing matrices • Transmit the updated result to its next sensor

7. Progressive Scheme Environment x3 xn x2 x1 I(2) I(n-1) I(1) …… Sensor 2 Sensor 3 Sensor n Sensor 1 m

8. Progressive Estimation of the Log-likelihood Function Denote each term in Eq.1 as T, then T3 depends on the updating rule of mixing matrix A

9. The updating rule of T7 depends on the updating rule of matrix A Progressive estimation of mixing matrix A: BFGS method

10. Algorithm of Progressive SNE /*Initialization*/ At sensor 1, for each possible m: Set A (1 by m) to random numbers; Compute W and a; Compute estimation error; Compute each term in Eq.1; Compute L(m); /*Progressive Updating*/ While (max L(m)<threshold) Send A, latent variables a, estimation error and the seven terms in Eq.1 to next sensor i; At sensor i, for each possible m: Add one row to A with random numbers; while (!converge) Update A using BFGS method; Update the accumulated estimation error; Update each term in Eq.1; Compute L(m); /*Generate the final estimation*/ Decide m=arg max L(m); Output m;

11. Mobile Agent Implementation Step 2 Step 1 Step 3 Step 4

12. Data transmitted Raw data Processing unit Fusion center Scheme Centralized Data transmitted Mixing matrix A Latent variables a Estimation error Each term in Eq.1 Processing unit Each sensor Scheme Serial Mobile agent implementation Comparison Progressive SNE Centralized SNE

13. Experiment 1 Targets Signals: 1-second acoustic, 500 samples each

14. Experiment 2 & 3 Targets: diesel truck and pick- up truck

15. Progressively Estimated Log-likelihood (Exp.1)

16. Progressively Estimated Log-likelihood (Exp.2)

17. Progressively Estimated Log-likelihood (Exp.3)

18. Discussion • Progressive SNE provides the greatest support to the true number of sources • Progressive SNE can achieve progressive accuracy with the migration of MA • By using MAF, the progressive SNE can stop at any time if the required accuracy is achieved • Progressive SNE can reduce the amount of transmitted data • Experiment 1: 10 sensors, 1-second segment, 500 samples each • Centralized: 144,000 bits • Progressive: 12,096 bits • 8.4%