1. Probability Grid: A Location Estimation Scheme for Wireless Sensor Networks Presented by cychen Date ： 3/7 In Secon (Sensor and Ad Hoc Communications and Networks) 2004Sensor and Ad Hoc Communications and Networks

2. Outline  Introduction  The Probability Grid Localization Scheme  The Localization Scheme  Performance Evaluation  System Implementation And Evaluation

3. Introduction  Propose a location estimation scheme completely decentralized not require special location or range finding infrastructure uses a probabilistic approach makes use of additional knowledge of topology deployment

4. Introduction  Assume a sensor network is deployed in a controlled manner The goal is to form a grid topology. The deployment is not completely random  an approximation to a uniform or even grid distribution

5.  The anchor nodes only a small percentage either equipped with GPS or can acquire their location information through other means. do not have any increased communication range  The remaining sensor nodes are unaware of their location The sensor nodes

6. The Probability Grid Localization Scheme  Assumption ： the nodes are deployed in a grid topology the unit length of the grid is known to all the nodes in the network  allow small errors in the true positioning of nodes around the vertexes of a grid.  Our localization problem To identify the correct position in the grid for each sensor node.  The localization error leave for future research

7. Parameter Definitions  M x N ： the dimensions of the grid topology  S ： the set of all the nodes  A ： the set of all the anchors Both sets, S and A, are sets of ordered pairs (i,j) representing the grid points where the nodes are located.  ： hop-count vector the hop count from each of the anchors in the set A to the node ‘ k ’ is the hop count from anchor 1 to node k.

8. The Probability Grid Matrix  ： the probability of node ‘ k ’, positioned at (i, j), to be hops from the l-th anchor. observe that is a discrete random variable that represents the number of hops for a particular Euclidian distance

9. The Probability Grid Matrix  The main features that the distribution function needs to exhibit are: ： the distance between the node and one anchor  ： the number of hops existent between the node and the anchor

10. The Probability Grid Matrix  Narrow and skewed positively for small values of λ For smaller values of λ  τ has a limited range of possible values with higher and higher values being less and less probable (positively skewed).  Become broader and relatively symmetric for larger values of λ. λ increases, the number of possibilities for the hop count (τ) increases and the distribution becomes bell-shaped

11. The Probability Grid Matrix  Through simulations, a Poisson distribution is a good approximation  Define

12. The Probability Grid Matrix  Obtain the Probability Grid Matrix  Let The position of node k in the grid ： The location of node k ：

13. The Localization Scheme  Our localization protocol is similar to the DV-Hop scheme  But it improves upon it by exploiting deployment information.

14. Phase 1 - Flooding  The anchors flood the network with packets containing their IDs, their location and a hop count, initially set to zero. global flooding or controlled flooding (all nodes are expected to hear from at least three anchors).  During the flooding period, sensor nodes keep track of the shortest distance (number of hops) to each of the anchors they heard from.

15. Phase 2 - Compute the correction factor  Correction factor ： an estimation for the Euclidian distance of one hop  Anchor positioned at (x i, y i ) compute ： where is the number of hops between the current anchor, positioned at (x i, y i ), and the anchor positioned at (x j, y j ).

16. Phase 2 - Compute the correction factor  The correction factor is received only by the sensor nodes in the vicinity of the anchor.  Sensor node only uses the “ first ” correction factor it received to estimate its location.

17. Phase 3 - Invoke The Probability Grid algorithm 1.Calculate λ the distance, in hop count units, between the evaluated grid point and one anchor.  PS. is the actual hop count 2.Calculate, and the Probability Grid matrix F k to estimation the location of node k,  k S-A

18. Performance Evaluation  Experimental results obtained through Simulations using GloMoSim, a discrete-event simulator developed at UCLA

19. Localization Error versus Anchors Percentage

20. Localization Error versus Network Size

21. Localization Error versus Number of Neighbors

22. Localization Error versus Imprecision in Anchor Positioning

23. System Implementation & Evaluation  The implementation was done on MICA2 motes from Berkeley. consisted of 25 motes, positioned in a 5x5 grid, approximately 12 meters apart.

24. Real System Evaluation Results