Novel Self-Configurable Positioning Technique for Multihop Wireless Networks Authors ： Hongyi Wu Chong Wang Nian-Feng Tzeng IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3, JUNE 2005

Outline Overview Proposed self-configurable positioning technique Euclidean Distance Estimation Coordinates System Establishment Selection of Landmarks Simulation Conclusion

Overview(1/2) Establish a local positioning system with the following features: Self-configurable : need no assistance from other infrastructure. Independence : independent of other global positioning systems. Robustness : should tolerate possible measurement inaccuracy. High accuracy : provide location information that is accurate enough to support target applications

Overview(2/2) Estimate the Euclidean distance between two nodes Select a number of nodes serving as the landmarks Estimates its distance to other landmarks. Exchange information and establish a coordinate system by themselves without the support of GNSS. The other nodes (called regular nodes) can accordingly contact the landmarks and compute their own coordinates.

Proposed self-configurable positioning technique Euclidean Distance Estimation Coordinates System Establishment Selection of Landmarks

Euclidean Distance Estimation What to do? To have an accurate estimation of the distance between two landmarks or between a regular node and a landmark. How to do? If two nodes are adjacent (within the transmission range of each other) ： RSS, ToA, or TDoA When the two nodes are not adjacent ： Finding the length of the shortest path.

Euclidean Distance Estimation Consisting of N nodes uniformly distributed in a 1  1 area. The transmission range of a node in the network is r << 1. (0,0) (d,0)

Euclidean Distance Estimation There are in average a set Φ of N  r 2 nodes within S’ s transmission range. The distance between node D and a node i (with coordinates (X i,Y i ) ) in Φ is given by where X i and Y i are random variables with a uniform distribution

Euclidean Distance Estimation We can derive the density function of Z i We assume a node  Φ, and has the shortest Euclidean distance to D, is selected as the next hop along the shortest path.

Euclidean Distance Estimation the density function of Z  its mean value where is the cumulative probability distribution of Z i

Euclidean Distance Estimation To derive the coordinates of node , we draw an arc ACB with node D as the center and as the radius

Euclidean Distance Estimation Assuming node is uniformly distributed along AC (or BC ), then the mean length of the first hop along the shortest path from S to D where

Euclidean Distance Estimation Recursively applying the above method, we can obtain the length of the remaining hops along the shortest path. The total length of a shortest path with m hops is

Euclidean Distance Estimation

Coordinates System Establishment 1. Identify the landmarks and determine the landmarks’ coordinates by exchanging information between each other and minimizing an error objective function. 2. Calculate the coordinates of regular nodes.

Determine The Landmarks’ Coordinates Assuming the coordinates of a landmark i is (x i,y i ), then the distance between two landmarks i and j is and the error function is defined to be where L ij can be learned through the Euclidean distance estimation model, is expressed by the coordinates variables The Simplex method is then used to determine the coordinates variables such that is minimized.

Determine The Landmarks’ Coordinates

Calculate The Coordinates of Regular Nodes A regular node needs to know the coordinates of landmarks and its distances to the landmarks.

Calculate The Coordinates of Regular Nodes After obtaining these information, node P(x p,y p ) calculates its coordinates by minimizing an error objective function similar to what mentioned before. and the error function is defined to be Again, the Simplex method can be used to minimize the error function,and determine the coordinates (x p,y p )

Calculate The Coordinates of Regular Nodes After calculating its coordinates, node P may label itself as a “semi-landmark” and respond to the requests of other regular nodes Other regular nodes may decide whether or not to use the information obtained from the semi-landmarks, according to their requirements on delay, accuracy, and/or computational complexity.

Selection of Landmarks Two issues ： 1. How many nodes should be selected to serve as landmarks? 2. Which nodes shall be selected?

Number of Landmarks The more the landmarks, the higher the accuracy of the established coordinates system. It’s not practical to employ a large number of landmarks since the computational complexity increases exponentially with the number of landmarks.

Number of Landmarks After a regular node calculates its coordinates, it may announce itself as a “semi-landmark” if it is stable and computationally powerful. As a result, there are landmarks and semi- landmarks, which are usually sufficient for highly accurate coordinates calculation.

Locations of Landmarks We consider four landmarks in a network with N nodes uniformly distributed in a 1  1 area. Assume that the four landmarks locate at the vertices of a square which is centered at ( X c,Y c ) and has an edge of G.

Experimental results We observe the maximum error when the square with four landmarks as vertices is at the center of the network. The error decreases as the landmarks deviate from the center. the longer the average path length from the regular nodes to the landmarks, thus decreasing the path error. The landmarks should be separated as far as possible

Algorithm : Landmark Selection We develop an algorithm to determine K corner nodes of the network. Initially any node is a candidate of landmark if its stability and computing power are higher than a predefined threshold.

Algorithm : Landmark Selection  ： a set, which includes all landmark candidates. C i ： Candidacy degree for node i. where S i,j is the length of the shortest path from i to j, if node j is in set  ; or otherwise, S i,j = . A node i with the highest value of C i is most probably located at the center of network, and thus should be removed from  first.

The landmarks (∆) locate largely at the corners of the network, except that node 83 seems a better choice than the one selected at the lower-left corner.

The algorithm also works well in a sparse network

Simulation ： Node Density Fig. 9. Euclidean distance. (a) N = 50. (b) N = 100. (c) N = 400.

Simulation ： Node Density Fig. 10. No translation. (a) N = 50. (b) N = 100. (c) N = 400.

Simulation ： Node Density Fig. 11. Center match. (a) N = 50. (b) N = 100. (c) N = 400.

Simulation ： Node Density Fig. 12. GPS tuning. (a) N = 50. (b) N = 100. (c) N = 400.

Simulation ： Node Density

Simulation ： One-Hop Measurement Error

Fig. 15. N = 100. (a) = 2%. (b) = 5%. (c) = 10%. (d) = 20%. (e) = 30%. (f) = 40%.

Simulation ： The Number of Landmarks

Simulation ： Control Overhead The overhead for initial landmark discovery is relatively high because flooding is used to locate the landmarks. However, it happens only during system initialization. We ignore the overhead in the initial stage and focus on the overhead for coordinates update only. The total control overhead increases with the number of nodes

Simulation ： Control Overhead

Conclusion Proposed a self-configurable positioning technique for multihop wireless networks. A number of nodes at the “corners” of the network serve as landmarks for estimating the distances by a Euclidean distance estimation model and establishing the coordinates themselves by minimizing an error objective function Other nodes calculate their coordinates according to the landmarks. The proposed positioning technique is independent of global position information.