1. Ad-Hoc Localization Using Ranging and Sectoring Krishna Kant Chintalapudi, Amit Dhariwal, Ramesh Govindan, Gaurav Sukhatme Computer Science Department, University of Southern California, Los Angeles, California, USA, 90007. （ IEEE Infocom 2004 ）

2. Outline: Introduction Related work Ad-Hoc localization using ranging Using Bearing information for higher localization extent Range-Sector based localization systems Conclusion

3. Ⅰ Introduction （ 1/3 ） Ad-hoc localization system ： Nodes determine their position in a common coordinate system using a number of anchor nodes. Anchor nodes ： already known their location in that coordinate system.(through some external means,such as GPS) Assume all nodes possess a ranging capability and use one of several distributed position fixing techniques to determine their position.

4. Introduction （ 2/3 ） Two characteristics （ design requirements ） in a distributed ad-hoc localization system ： First ： An ad-hoc localization system permits unplanned anchor placement. Second ： relatively few anchors be necessary for obtaining good localization performance. The performance of ad-hoc localization depends upon several factors ： the accuracy of ranging the density of node placement the relative fraction of anchors the particular position fixing scheme

5. Introduction （ 3/3 ） Consider whether adding the ability to estimate bearing to neighboring nodes can qualitatively improve the performance. （ use both range and bearing information ） But it is unclear if accurate bearing estimation devices can be build. More feasible is the ability to approximately detect bearing.Whether devices that enable nodes to place neighbors within sectors.

6. Ⅱ Related work ： Ranging ： estimating distances between nodes.  RF-based ranging Based on measuring received signal strength a receiver can determine its distance to a transmitter. Range error upwards of 10%.  Acoustic ranging Based on measuring the time-of-flight an acoustic or ultrasound signal. Range error ： 1-2% （ over distances of 3-6m ） Position fixing

7. Ⅲ Ad-Hoc localization using ranging Goal ： to fairly extensively evaluate,through analysis and simulation,a representative sampling of such ad-hoc localization schemes,with the intent of understanding their error characteristics as a function of node and anchor density. In this simulation,we use larger topologies, examine a wider range of density and anchor ratios, and use a slightly more sophisticated ranging error model.

8. A Taxonomy of Localization Schemes Following Langendoen et al.,such localization schemes can be divided into three distinct stages:  estimating distance to anchors  getting an initial position estimate  iteratively refining the position estimate Step1 ： estimation of distance to an anchor.  There are two classes of approaches to estimating distance to anchors ： topological and geometric.  Topological approaches ： DV-dist and DV-hop.  Geometric approaches ： Relative localization scheme and Euclidean scheme. K. Langendoen and N. Reijers, “Distributed Localization in Wireless Sensor Networks: A Quantitative Comparison,”

9. Step2 、 3 Initial position estimate and refinement Initial position ： Using multi-lateration approach. Refinement ： Least-Mean-Squared Refinement(LMSR) LMSR attempts to minimize the objective function,

10. The conditional local minima can be written as,the set of |N|-|L| simultaneous equations, the above equations can be re-written as,

11. Evaluating Ad-Hoc Localization System Using simulation The schemes:  Euclidean geometric scheme  Relative localization technique  DV-dist topological scheme Methodology ：  A field of 1000 randomly deployed nodes  Ranging distance to be 10m  Error model ： Guassian with its standard deviation varying linearly with range.

12. Sonar ranging error standard deviation as a function of range Device ： using sonar ranging device (error measurement about 1% over 3-4m) α ： approximately 0.007

13. Metrics ： Mean error ： The extent of localization ： the fraction of non-anchor nodes that are localized to within 2 meters of their ground-truth position.

14. Simulation results ： Localization extent

15. Simulation results ： Localization Error

16. Ⅳ Using bearing information for higher localization extent Goal ： improve localization performance(low mean error and high localization extent even at low node densities) If each node had the ability to estimate bearing to its neighboring nodes. r-θlocalization ： algorithm for range-and-bearing based ad-hoc localization.

17. Iterative Least-Mean-Squares Refinement using Range and Bearing （ LMSRB ） if n i is able to measure its range (r ij ) and its bearing (θ ij ) to another nearby node n j Each r-θmeasurement leads to the equation,

18. Δx ij can be approximated by Gaussian random vector with covariance matrix ： approach seeks to minimize the objective function, The conditions for local minima are given by the set of |N|-|L| simultaneous equations,

19. This gives a set of |N|-|L| simultaneous equations, local minima in this formulation can be written as ：

20. Results ： Localization Extent

21. Localization Error

22. Localization Error for Higher Bearing error

23. Ⅴ Range-Sector based localization systems Iterative Least-Mean-Square Refinement with Range and Sector ： A node gets initial guess using Equation (7) and the center of the sector.

24. Result ： Localization extent for LMSRS

25. Localization Error

26. Conclusion Result:(20% anchors)  Ranging (11-12 node density) localization extent ： 90%,localization error ： 5%  Range and bearing (5 node density, bearing error 4 。 ) localization extent ： 96%,localization error ： 0.5%  Range and sector (5 node density, sector angle 30 。 ) localization extent ： 95%,localization error ： 3% By contrast,new schemes that can use range and bearing estimates,or even range and sector estimates can give good performance.