1. 6.4 Global Positioning of Nodes Advanced Operating Systems Ruizhe Ma September 28, 2015

2. Overview 0. Introduction 1. Fundamentals 2. Current Work 3. Future Work

3. 0. Introduction For many applications, data without position is useless, so sensor nodes have to clearly state its position to be able to transmit “where the specific even is occuring”. Moreover, knowing the position information of sensor nodes can also improve router efficiency, provide network namespaces ， achieve network load balancing, network topology self configuration, etc..

4. 1. Fundamentals Global Positioning of Nodes Example Node Coordinate Inconsistancy of Distance Measures

5. Global Positioning of Nodes When the number of nodes in a distributed system grows, it becomes increasingly difficult for any node to keep track of the others. Important for executing distributed algorithms such as routing, multicasting, data placements, searching, etc.

6. Simple Example Distance corresponds to internode latency. Given nodes P and Q, the distance d(P,Q) reflects how long it would take for a message to travel from P to Q.

7. Node Position Computation Positioning a node in an m- dimensional geometric space requires m+1 distance measures to nodes with known positions.

8. Node Coordinate P can compute its coordinated (Xp,Yp) by solving three equations with the two unknowns Xp and Yp: d generally corresponds to measuring the latency between P and the node at (Xj, Yj), this value will differ over time. The effect is a different positioning whenever P would want to recompute its position. P will also affect the accuracy of the positionin of other nodes.

9. Inconsistancy of Distance Measures Measured distance by different nodes will generally not be consistant. This can be solved simply by computing positions in a two-dimensional space. However, this is not a general solution.

10. Why Simple Solution Doesn’t Work Internet latency measurements may violate the triangle of inequality. It is generally impossible to resolce inconsistencies completely.

11. 2. Current Work Common Algorithms Node Position Distance Estimation Position Estimation

12. Common Algorithms Range based AHLos RADAR Range free Centroid Distance Vector Hop APIT MAP Amorphous Ring Overlapping

13. Node Position Range based measurement: in a sensor network when some of the position information is known, the position of other sensor nodes can be estimated using measurement and position estimation. Range free: takes advantage of network connectivity or topology to estimate the distance, and then uses the trilateration or maximum likelihood to estimate the position.

14. Distance Measurement Methods TOA (Time of Arrival) TDOA (Time Differential of Arrival) AOA (Angle of Arrival) RSS (Received Sinnal Strength)

15. Position Estimation Methods Trilateration Maximum likelihood

16. Future Work (Research Areas) Improved algorithms for efficiency and accuracy for distance measurement and position estimation. Extend distance measurement model to three-dimensional. Applying node positioning to real world applications, such as animal tracking and protection.

17. References Tsui, James Bao-Yen. Fundamentals of global positioning system receivers. Wiley-Interscience, 2000. Čapkun, Srdjan, Maher Hamdi, and Jean-Pierre Hubaux. "GPS-free positioning in mobile ad hoc networks." Cluster Computing 5.2 (2002): 157- 167. Niculescu, Dragoş, and Badri Nath. "DV based positioning in ad hoc networks."Telecommunication Systems 22.1-4 (2003): 267-280. Savarese, Chris, Jan M. Rabaey, and Jan Beutel. "Location in distributed ad-hoc wireless sensor networks." Acoustics, Speech, and Signal Processing, 2001. Proceedings.(ICASSP'01). 2001 IEEE International Conference on. Vol. 4. IEEE, 2001.

18. Thank you Questions?