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APPL: Anchor Path Planning –based Localization for Wireless Sensor Networks Imane BENKHELIFA and Samira MOUSSAOUI LSI, Computer Science Department Houari.

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Presentation on theme: "APPL: Anchor Path Planning –based Localization for Wireless Sensor Networks Imane BENKHELIFA and Samira MOUSSAOUI LSI, Computer Science Department Houari."— Presentation transcript:

1 APPL: Anchor Path Planning –based Localization for Wireless Sensor Networks Imane BENKHELIFA and Samira MOUSSAOUI LSI, Computer Science Department Houari Bourmediene University of Science and Technology Algiers, Algeria Imane BENKHELIFA and Samira MOUSSAOUI LSI, Computer Science Department Houari Bourmediene University of Science and Technology Algiers, Algeria

2 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) 2 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Outline

3 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation Introduction Motivation Introduction 22/07/20113 Battlefield Surveillance Maritime Surveillance Forest Fire Detection Precision AgricultureMonitoring Patients Monitoring Animals Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011)

4 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation Introduction Motivation Introduction 22/07/20114 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) WSN Attractive Caracteristics (Fast Deployment, Fault Tolerance, reduced cost,… etc) Why Sensor Localization is important?  A detected event is only useful if an information relative to its geographical position is provided

5 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) 5 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Outline

6 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction RSSI Technology AoA Technology Introduction RSSI Technology AoA Technology 22/07/20116 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Localization = to assign accurate or estimated position to a sensor Why not a GPS (Global Posionning System) in each node? Solution: to equip some nodes with GPS  Anchors Measurement Technologies: ToA (Time of Arrival) TDoA (Time difference of Arrival) RSSI (Received Signal Strength Indicator) AoA (Angle of Arrival) Costly

7 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction RSSI Technology AoA Technology Introduction RSSI Technology AoA Technology 22/07/20117 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) RSSI (Radio Signal Strenght Indicator) Considers the power loss of a signal between its emission and reception This loss varies with the distance between two sensors. More the sensors are distant (resp. close), more the loss is important (resp.weak) This loss is then converted to a distance

8 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction RSSI Technology AoA Technology Introduction RSSI Technology AoA Technology 22/07/20118 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) AoA (Angle of Arrival) Each sensor has an oriented antenna and a reference axis Absolute AoA :( θ i + Δθ )(mod 2 π), i = {1,2}

9 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) 9 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Outline

10 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory 22/07/201110 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Many anchors equipped with GPS  Energy comsuption & high costs Solution: using a mobile anchor (robot, plane, drone, vehicle, tractor…)

11 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory 22/07/201111 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Other than serving as a mobile anchor, the mobile node can perform other tasks necessary for the network operations Tasks: Reconfigures or recalibrates sensors, Synchronizes the clocks, Collects data from the sensors, Deploys new sensors, and disables existing ones

12 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory 22/07/201112 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Method using a mobile Anchor [Kouts. 07] Goal:  Planning the anchor trajectory  Reducing the Localization error and Time Principle:  Based on RSSI (conversion of signal to distance)  Bayesian Inference (Probabilistic approch) Trajectories: -SCAN -DOUBLE SCAN -HILBERT

13 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory 22/07/201113 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) D= (L/R+1)x L+(L/R)x R= (L/R+2)x L Advantages: Good coverage of nodes Short traveled distance Reduced localization time Drawbacks: Abscissa-error is bigger than ordinate- error if resolution >> transmission range Straight lines introduce collinearity L R

14 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory 22/07/201114 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) D= 2x D SCAN = 2 (L/R+2)x L Advantages: Scans 2 dimensions (horizontal & vertical) Ensures error-similarity along both axis Drawbacks: Double distance / resolution Higher localization time/error L R

15 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL : Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory Introduction Scan Trajectory Double Scan Trajectory Hilbert Trajectory 22/07/201115 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) D= (L/R+2)x L +R Advantages: Traveled distance differs only in R from SCAN Diffusion of non-colinear messages Similar error between x/y axis Drawbacks: Some nodes cannot receive anchor messages (square holes) L R

16 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) 16 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Outline

17 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory 22/07/201117 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) APPL (Anchor Path Planning based Localization) Principle: – One single Mobile Anchor – Anchor Trajectory is chosen in advance – At Each reception of anchor message, the static node rebuilds an Anchor Box – The Anchor Box is built based on distances deduced from the received RSSI – The node draws N samples from this box – The estimated position is the mean of samples

18 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory 22/07/201118 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Building the Anchor Box Actual Position Estimated Position r1 r2 r3

19 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory 22/07/201119 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Anchor Path Planning To offer network coverage  any deterministic trajectory with properly selected parameters To provide good quality beacons  non-collinear messages, and signal strengths can be mapped to their distances from the sensor Anchor Trajectories - Squares - Archimedean Spiral - Waves

20 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory 22/07/201120 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Squares Trajectory 20 Advantages: Same traveled distance as Scan Good node coverage 2 dimentional scan Similar error between x/y axis Drawbacks: Straight lines introduce collinearity if resolution >> transmission range L R L D= R+4 [(L-2R)+(L-4R)+(L-6R)+….+(L-2[L/2R]R)] = (L/R+2)x L

21 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory 21 Archimedean Spiral Trajectory 21 Advantages: Traveled distance less than SCAN with + 37%  Localization time reduced Reception of non-colinear messages Similar error between the two axis Drawbacks: Coverage of the four corners If the deployment area increases, turns become larger  the amount of non- collinearity reduces R Distance ≤ Rπn/4 (4n-1) with n= [L/2R] + 1 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011)

22 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory Estimation Technique Anchor Path Planning Squares Trajectory Archimedian Spiral Trajectory Waves Trajectory 22 Waves Trajectory 22 3R/2 R Advantages: Reception of many non-colinear messages from only one segment Traveled Distance less than SCAN with 16% Good network coverage x/y error similarity D=2R/3 ( [ 2L/3]-1 ) + (1+ ([L/R ]-1) ([ 2L/3R ])) (π R/2 ) 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011)

23 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) 23 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Outline

24 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 24 Simulation Environment: – NS2 Simulator on Linux (Ubuntu 9.10) – Deplyment area =200m x 200m – Number of nodes =100 – Transmission range =30m – Anchor speed =20m/s Evaluation Metrics: – Path Length and Travel Time – Localization Coverage (Number of localized nodes) – Localization Error (Distance between estimated position and real position) 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011)

25 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 25 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Path =Squares, Resolution =20m (% end time)

26 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 26 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Path =Squares, Resolution =20m (% end time)

27 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 27 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Resolution =20m TrajectoriyPath Length (m)Travel Time (s)Gain over Scan Double Scan4800240-100% Hilbert2420121-0,82% Scan24001200% Squares24001200% Waves2003,6100,18+16,5% Spiral150075+37,5%

28 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 28 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Resolution =60m

29 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 29 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Path= Squares

30 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 30 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) Resolution =60m

31 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error Simulation Environment Estimation Technique Evaluation Path Length and Travel Time Localization Coverage Localization Error 31 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) x/y error gap Resolution =60m

32 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) 32 Motivation & Introduction Localization in Wireless Sensor Networks Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Outline

33 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Conclusion Future Directions Conclusion Future Directions 33 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) APPL uses a very simple localization algorithm that makes a good combination of RSSI measurements and anchor positions Proposed Trajectories (SQUARES, ARCHILEDEAN SPIRAL and WAVES) are specifically designed with better localization accuracy, coverage and path length in mind Squares gives the quickest coverage Sipral gives the shortest distance Waves gives the best accuracy When the path resolution is much larger than the transmission range, the collinearity becomes more significant. In such cases, WAVES outperforms previously proposed path types.

34 Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Motivation & Introduction Localization in Wireless Sensor Networs Localization using a Mobile Anchor APPL: Anchor Path Planning based Localization Evaluation Conclusion & Future Directions Conclusion Future Directions Conclusion Future Directions 34 22/07/2011 Imane BENKHELIFA Mosharaka International Conference on Communications, Computers and Applications (MIC-CCA2011) The static paths work well when the sensors are assumed to be uniformly deployed. However, in the cases where such assumption is not valid, there is a strong intensive to dynamically adjust the path during the localization procedure

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