後卓越進度報告 蔡育仁老師實驗室 2006/06/05

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. MSE of Est. Sensor Location Estimator 1 Estimator 2 CRLB

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 X and Y, we want to find the next best deploying position (x*,y*), i.e. X*=[X x*], Y*=[Y y*], to minimize or minimize

Step-by-Step Deployment (100 × 100 unit 2 ) — the 5th Node Sensor Location Avg. CRLB (unit 2 ) Occurs the Minimum CRLB Deployed Locations

Step-by-Step Deployment (100 × 100 unit 2 ) — the 6th Node Sensor Location Avg. CRLB (unit 2 ) 5th Deployed Loc. Deployed Locations Occurs the Minimum CRLB

Step-by-Step Deployment (100 × 100 unit 2 ) — 9 Nodes with Different Initial Conditions (Begin with 4 Nodes) 100 units Avg. CRLB (unit 2 )

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 , Aug. 2003