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後卓越進度報告

後卓越進度報告. 蔡育仁老師實驗室 2006/06/05. MSE of Est. Estimator 1. Estimator 2. CRLB. Sensor Location. Step-by-Step Deployment of Location Sensors by Cram é r-Rao Lower Bound. Cramér-Rao Lower Bound (CRLB) is a lower bound of the mean square error of the unbiased estimators.

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後卓越進度報告

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  1. 後卓越進度報告 蔡育仁老師實驗室 2006/06/05

  2. MSE of Est. Estimator 1 Estimator 2 CRLB Sensor Location Step-by-Step Deployment of Location Sensors by Cramér-Rao Lower Bound • Cramér-Rao Lower Bound (CRLB) is a lower bound of the mean square error of the unbiased estimators. • CRLB of location estimations depends on the propagation model and the topology of the sensor network. • Propose a step-by-step deployment method to minimize the CRLB in a low complexity manner.

  3. Step-by-Step Deployment Procedure • Let the x- and y-axis location vectors of the deployed nodes is denoted as X, Y. • From CRLB, the mean squared error of the estimated location (x,y) has a lower bound given by [1] where are Fisher Information Matrices • Given the deployed location vectors XandY, we want to find the next best deploying position (x*,y*), i.e.X*=[X x*],Y*=[Y y*],to minimize or minimize

  4. Step-by-Step Deployment (100×100 unit2) —the 5th Node Deployed Locations Avg. CRLB (unit2) Occurs the Minimum CRLB Sensor Location

  5. Step-by-Step Deployment (100×100 unit2) —the 6th Node Deployed Locations 5th Deployed Loc. Avg. CRLB (unit2) Occurs the Minimum CRLB Sensor Location

  6. Step-by-Step Deployment (100×100 unit2) — 9 Nodes with Different Initial Conditions (Begin with 4 Nodes) 100 units 100 units Avg. CRLB (unit2) Avg. CRLB (unit2)

  7. Future Works & Reference • Apply the minimum estimation error deployment to an irregular deploying area • Find the analytical Global Minimum CRLB Location without heuristic search • [1] N. Patwari et al., “Relative location estimation in wireless sensor networks,” IEEE Trans. Sig. Proc., vol. 51, pp. 2137-2147, Aug. 2003

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