GPS-free Positioning in Ad-Hoc Networks Yu-Min Tseng

Target  Not rely on GPS  Use the distances between nodes to build a relative coordinate system Distance measurement method Distance measurement method Signal strength methodSignal strength method Angel of Arrival (AOA) methodAngel of Arrival (AOA) method Time of Arrival (TOA) methodTime of Arrival (TOA) method

Build Local Coordinate System

 Detect one-hop neighbors (K i )  Measure the distances to one-hop neighbors (D i )  Send K i & D i to all one-hop neighbors  Choose node p & q Local View Set for node i as a set of nodes LVS i (p,q) K i such that, node i can compute the location of node j Local View Set for node i as a set of nodes LVS i (p,q) K i such that, node i can compute the location of node j

Coordinate System Direction

Coordinate System  Problem The motion of node i will cause that all the nodes have to re-compute their positions The motion of node i will cause that all the nodes have to re-compute their positions Cause a large inconsistency Cause a large inconsistency Only used in small area networks, low mobility Only used in small area networks, low mobility  Solution Compute the center of the coordinate system Compute the center of the coordinate system Message broadcast Message broadcast Stable coordinate system Stable coordinate system

Location Reference Group  Location Reference Group (LRG) The density of the nodes in the LRG is the highest in the network The density of the nodes in the LRG is the highest in the network Network center is a relative position dependent on the topology of the LRG Network center is a relative position dependent on the topology of the LRG Average speed of LRG center is much smaller than the average speed of nodes Average speed of LRG center is much smaller than the average speed of nodes

Location Reference Group  How to obtain the LRG center Every node broadcast hello packet to its n-hop neighborhood to obtain node IDs, their mutual distances, the directions of their coordinate systems Every node broadcast hello packet to its n-hop neighborhood to obtain node IDs, their mutual distances, the directions of their coordinate systems Compute positions of the n-hop neighbors Compute positions of the n-hop neighbors Compute the n-hop neighborhood centers Compute the n-hop neighborhood centers

Location Reference Group Compute n-hop neighborhood direction as average of coordinate system directions Compute n-hop neighborhood direction as average of coordinate system directions Compute density factor Compute density factor Density factor is the ratio between the number of nodes & the size of the observed areaDensity factor is the ratio between the number of nodes & the size of the observed area

Location Reference Group

 How to maintain the LRG Every node broadcast hello packet to its n- hop neighborhood to obtain node IDs, their mutual distances, the directions of their coordinate systems (same as init) Every node broadcast hello packet to its n- hop neighborhood to obtain node IDs, their mutual distances, the directions of their coordinate systems (same as init) Compare the n-hop neighbors list with the list of the LRG members Compare the n-hop neighbors list with the list of the LRG members The node that is a n-hop neighbor of LRG master & the highest number of LRG nodes still in its n- hop neighborhood is elected to be the new LRG masterThe node that is a n-hop neighbor of LRG master & the highest number of LRG nodes still in its n- hop neighborhood is elected to be the new LRG master

Location Reference Group If the node doesn’t have the LRG master in its n- hop neighborhood, and the node doesn’t receive the new position information issued by LRG master, it starts the init procedureIf the node doesn’t have the LRG master in its n- hop neighborhood, and the node doesn’t receive the new position information issued by LRG master, it starts the init procedure

Location Reference Group If we finds at least 3 modes have same topology in both C1 & C2, then adjust the direction of C2 to direction of C1

Simulation

Drawback  Relative positioning  When the reference moves, positions have to be recomputed for nodes that have not moved  If intermediate nodes move, fixed nodes depending on them also have to recompute position

Ad Hoc Positioning System  At least 3 nodes (called landmarks) are GPS enhanced  An arbitrary node has estimates to a number (>= 3) of landmarks, it can compute its own position in the plain  Use propagation method, all nodes infer their distance to landmarks  Complexity of signaling is driven by the number of landmarks, and by the average degree of each node

DV-Hop propagation method  Each node maintain a table {X i,Y i,h i } & exchanges updates only with its neighbors  The correction a landmark (X i,Y i ) computes is

DV-Hop propagation method Assume A gets its correction from L2, its estimate distance to the 3 landmarks would be: to L1, 3x16.42 ; to L2, 2x16.42 ; to L3, 3x16.42 Then plugged into the triangulation procedure to get an estimate location

DV-distance propagation method  Similar to DV-hop method  Measured by using radio signal strength & is propagated in meters rather than in hops  Less coarse than DV-hop method Not all hops have same size Not all hops have same size  Sensitive to measurement errors

Euclidean propagation method AB AC BC are known by estimation, and known by node A The estimated distance of AL is obtained by applying Pithagora’s generalized theorem in triangles ACB BCL ACL It is possible that A is on the different side of BC  A’, the choice is made by voting or by examining relation with other common neighbors of B and C

Summary Setup coordinate by perimeter nodes Setup coordinate by every node Setup coordinate by landmarks GPS No GPS. Landmarks need GPS. Coordinate system AbsoluteRelativeAbsolute Flooding When init LRG need broadcast all, Other nodes broadcast n-hop Propagation