1. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Localization using Signal Strength: TO RANGE OR NOT TO RANGE? Gianni Giorgetti Sandeep K.S. Gupta Gianfranco Manes ACM MELT08 - San Francisco September 19, 2008 IMPACT LAB http://impact.asu.edu Arizona State University

2. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Which approach to use? 51015202530 15 20 25 30 Connectivity Avg Error [m] Range-Free RSS ranging RF-Based Localization: Range-Based Connectivity Localization Results

3. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Outline MOTIVATION: to provide a criteria to choose between a range-based and range-free scheme. TOOLS: Analysis of the Fisher information and Cramér-Rao Bound. We’ll start with a simple, intuitive, 1D case. RESULTS: Yes, it is possible to make an educated choice based on the network connectivity, the parameters of the propagation model, and the number of nodes.

4. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 1D Localization 1 1 0 0 01010101 RSS 1 RSS 2 RSS 3 RSS 4 … 0 0 Proximity-Based Localization 0 0 Ranging using RSS

5. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Log-Normal Shadowing Model We assume both and are known. Path-Loss Exponent

6. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 1 1 Measurement Models Ranging using RSS: -95-90-85-80-75-70-65-60-55-50-45 Connectivity [1] : RSS [dBM] [1] N. Patwari and A. Hero III. Using proximity and quantized RSS for sensor localization in wireless networks. WSNA, 2003.

7. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Fisher Information Both measurements are the outcome of random variables that depends on the unknown parameter d. Fisher Information measures the amount of information available to estimate d. Measurement Models RSS ranging: Connectivity: Max Maximum Likelihood Estimator

8. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Fisher Information Fisher Information: Cramér-Rao bound: 0 0 1 1 Large value of F  Small Error Small value of F  Large Error

9. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Fisher Information 0246810 0 1 2 3 4 5 6 Distance Information Fisher Information for connectivity measurements is about 37% lower than F rss

10. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Optimal Connectivity Threshold 0 0 1 1 2 2 -95-90-85-80-75-70-65-60-55-50-45 RSS [dBM] pdf

11. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Fisher Information - Connectivity 012345678910 0 0.05 0.1 0.15 0.2 dth [m] Fisher Information -95-90-85-80-75-70-65-60-55-50-45 RSS [dBM] 5 m

12. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Comparison Both F RSS and F conn decrease with the square of the distance and with the ratio σ dB /n p F RSS always lower than F conn -95-90-85-80-75-70-65-60-55-50-45 rss Max Range ?

13. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Network Localization Fisher Information Matrix Cramér-Rao Bound: Anchors Blind Nodes

14. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Cramér-Rao Bound 01020304050 0 5 10 15 20 25 Connectivity RMS Err [m] RSS ranging Range-Free RSS ranging Connectivity CRITICAL CONNECTIVITY

15. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Critical Connectivity - CRB Critical connectivity found using CRB analysis CRB not available at run-time because it is based on the node coordinates

16. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Properties of Critical Connectivity Does not change with the node density Does not change with the number of anchors

17. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Properties of Critical Connectivity Changes with the number of nodes Changes with the ratio

18. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Effect of noise on connectivity -95-90-85-80-75-70-65-60-55-50-45 RSS [dBM] pdf

19. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Simulation Results Simulated about 1300 topologies Number of nodes between 20 and 400 Propagation parameters:

20. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Results

21. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Which approach to use? 51015202530 15 20 25 30 Connectivity Avg Error [m] Range-Free RSS ranging RF-Based Localization: Range-Based Connectivity Localization Results 100 nodes, np=3, σ dB =8 dBm Range-FreeRSS Ranging

22. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 http://impact.asu.edu THANKS!

23. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Ranging Errors - distance 5m10m … 35m40m

24. G. Giorgetti, ACM MELT 2008 – San Francisco – September 19, 2008 Ranging Error – Ratio 5m10m -90-80-70-60-50 0.2 0.4 RSS Probability Density Function RSS [dBm] -90-80-70-60-50 0 0.2 0.4 -90-80-70-60-50 0 0.1