1. Localization for Anisotropic Sensor Networks
Hyuk Lim and Jennifer C. Hou (InfoCom 05)
Sang Rok Kim Dependable Software Lab at KAIST

2. Contents Introduction Background Proximity Characterization
Localization based on PDM
Experiment Result
Conclusion

3. Introduction Node Localization
For some sensor network applications, exact location is critical
Tracking
Monitoring
Sensing
For most Applications, having location information enhance value of information
Also needed in geographic routing

4. Introduction How to determine node location?
May be trivially available if:
Satellite based GPS is feasible and available on all nodes.
All nodes are hand-placed and pre-configured with location coordinates.
Otherwise it is quite challenging (even with a fraction of known reference/beacon nodes).
Typically, one assumes some nodes have position information (e.g., through GPS), but not all.
Triangulation
Lateration

5. Background Localization Problem Notation What to do Sensor Network : S
Beacon node : M
Non-beacon node : N
Location xi ∈ Rd (d-dimensional space)
i = {1,2, …, M , M+1, …,M+N}
Geographical distance between xi, xj
Proximity measure between xi, xj : p ij
What to do
Given xi, p ij and p sj for i,j ∈ {1,..,M}
Estimate : xs for a sensor node s

6. Background Isotropic Assumption Mapping function fp:R2d→Rd
geographic locations (xi, xj) → measured proximity p ij
p ij = fp (xi, xj)
If fp (xi, xj) is a Euclidean distance
p ij = fp (xi, xj) = gp (dij)

7. Background Anisotropic Networks
General network topology for localization models are isotropic
the properties of proximity measurements are identical in all directions.
In practice
Proximities often differ in different direction
depend on the distinct locations of sensor nodes
Square area with obstacle
Irregular radio pattern
Anisotropic terrain condition

8. Background It is necessary to compensate for anisotropic properties
by gathering and utilizing infor.
Topology A : Isotropic network
obstacle
Topology B : Anisotropic network
(geographic structure)
Topology C : Anisotropic network
(different radio range)

9. Background APS basics Ad-hoc Positioning System
Three different propagation method
DV-hop
Distance vector(table) exchange
Average distance per hop
Estimate location by performing lateration algorithm
☞Lateration alg. : simplified version of the GPS triangulation
DV-distance
Received signal strength
Euclidean scheme
Rely on the geometry of neighboring sensor nodes
Hop-by-hop propagation

10. Background MDS basics Multi-Dimensional Scaling
Data analysis technique used to visualize proximity in a low d-space
High dimension → Low(2 or 3) dimension
Shift, Decompose, Selecting eigenvectors
Modified MDS
Assume region is locally isotropic in small regions
Establish local maps and merge them into a global map
Better retain anisotropic characteristics in global map
Performance rely on the choice of region size

11. Background Proposed Method
Is similar to MDS as it use SVD to calculate proximity matrix
Is differs as follows :
Accurate characterization
Less computational complexity
The proximity matrix only between beacon node not all.
Simple protocol operations
No global topology information
No partition into small region
No global coordination and global map
Geographic locations by lateration algorithm

12. Proximity Characterization
Proximity-Distance Map(PDM)
Describe relationship between the proximities and the geographic distance
Diagonal tij of T can be scaling factor
Geo-distance between node s and b is specified
as a weighted sum of proximities to all the beacon node
PDM retain all the proximity characteristics to
all beacon node in all direction
Proximity Matrix P
Optimal linear transformation T : PDM
mapping
Singular value
Decomposition,
Pseudo-inverse
PDM = T = LPT(PPT)-1
Geographic Matrix L
T = LP+
Truncated
pseudo-inverse
T = LP+r
node s with unknown location ls = Tps = LP+rps

13. Localization based on PDM
Localization System Based on PDM
Procedure for Information Collection and Linear Transformation Calculation
P1 : Every node Initializes a beacon list
P2 : Every beacon node broadcasts to neighbor a probing
packet (ID, location, initial proximity)
P3 : calculate new p (hop-count or geo-distance)
whenever a node receives a probing packet
If Pnew<Pold in beacon list then update list and forward to neighbors

14. Localization based on PDM
Localization System Based on PDM
Procedure for Information Collection and Linear Transformation Calculation
P4 : if beacon node b receives P2, it perform P3
and inform other beacon node of its update pb
P5 : if beacon node b receives P4,
update proximity matrix P and geo-distance matrix L.
After all update, the b compute SVD of P and T
P6 : a sensor node s obtains ps from its beacon list,
obtains T from one of beacon node,
calculates geo-distance to beacon node
and estimates its location xs by a lateration algorithm

15. Localization based on PDM
Localization System Based on PDM
Alternatives to Packet Flooding
Can overwhelm the sensor network
Modification
P2 : broadcast → unicast their probing packets to one another
P3 : forward to neighbors → unicast their probing packets to the beacon nodes and obtain its proximity vector
Limit the scope of Packet Flooding
Simple
TTL value setting
Cause inconsistency
Approximate proximity psu

16. Experimental Result
Proximity = hop-count
Proximity = Euclidian distance
Smallest estimation error under all case in case of PDM
Proximity type – radio range
Hop-count : inverse proportion
Geo-distance : direct proportion
Estimation error of PDM is 50%,33% of that of others
Isotropic
Ansotropic

17. Experimental Result Almost same performance in DV-hop and PDM
Proximity = hop-count
Almost same performance in DV-hop and PDM
Isotropic network
Enough strong connection
But anisotropic, PDM is comparatively better
Isotropic
Ansotropic
Radio range r = u, 1.3u, 1.69u

18. Experimental Result As compare to former fig, performance improves
Proximity = Euclidian distance
As compare to former fig, performance improves
Isotropic
Ansotropic
Radio range r = u, 1.3u, 1.69u

19. Experimental Result PDM is much smaller and decrease faster
Power Control :
Alternatives to Packet Flooding
Proximity = Hop count
Isotropic
Ansotropic
PDM is much smaller and decrease faster
PDM capture the topological feature in the case of low power control
In (b), DV-hop, MDS-map don’t show performance improvement when ratio > 0.1
While PDM show same performance improvement

20. Conclusion New PDM based localization method
Retain Anisotropic network topologies
Power Control
Simulation

21. Thank You !