1. 後卓越計畫進度報告 王晉良老師實驗室 2007/8/13

2. 2 Positioning in Sensor Networks Suppose there are N sensors the (known) location of sensor i. Let be the position of the target. Distance between target and sensor i is Measurement at sensor i can be modeled as where is the noise at sensor i. For example: Received Signal Strength (RSS): Path loss model:

3. 3 2) Initialization: compute 1). Incremental Subgradient Method: [Rabbat & Nowak 2004] 2).Projection Onto Convex Sets (POCS): [Blatt & Hero 2005] 3).Weighted interpolation positioning method (WIP): [C.L. Wang & Y. W. Hong 2007] 4).Weighted Incremental Subgradient method (WIG), weighting factor is. Related Work: Positioning Algorithms d6d6 d1d1 d2d2 d3d3 d4d4 d5d5 d7d7 d8d8 d9d9 00101 1 01001 01 11 110 101 ( 1).Energy consuming (2).Large latency When all distance estimates are known  least squares (LS) method: Centralized Algorithms Decentralized Algorithms is a positive scalar step size, by previous sensor Where The WIG algorithm is implemented as following iterative steps. 1) The first iterative cycle: 3) Iterative step: is the diminishing parameters anddenotes the gradient of at the target’s location estimate d1d1 d2d2 d3d3 d4d4 d5d5 d6d6 1 01 11 101110 111 d7d7 1000

4. 4 Convergence analysis of the WIG method Message passing algorithm - Token passing

5. 5 1.The Moving target velocity is 2 m/sec and that moving from (x=5, y=5) to (x=150, y=150) 2. Iterative cycle k=2 1.The stationary target location are arbitrary 2.Iterative cycle k=10

6. 6 1.The stationary target location at (x=5, y=5) 2.Initialization location at (x=190,y=190) 3.Iterative cycle k=10 1.The Moving target velocity is 2 m/sec and that moving from (x=5, y=5) to (x=150, y=150) 2. Iterative cycle k=2