Transcript Distributed Information Storage and Retrieval in 3D Sensor

3D Surface Localization with Terrain Model
Yang Yang, Miao Jin, Hongyi Wu
Presenter: Buri Ban
The Center for Advanced Computer Studies (CACS)
University of Louisiana at Lafayette
Applications of Wireless Sensor
Networks
Localization in Sensor Networks
 Location information is important
•
Devices need to know where they are.
•
We want to know where the data is from.
•
It helps infrastructure establishment. For examples,
geographical routing, sensor coverage, et al.
Localization in Sensor Networks
 Wireless Sensors
•
Deployed on 2D plane (ground)
•
Deployed on 3D space (air, underwater)
•
Deployed on 3D surface (terrain)
3D Surface Localization
 Applications
•
•
Volcano Monitoring
ZebraNet
Challenges in 3D Surface Localization
 Connectivity and surface distance information
only are not enough for 3D surface localization.
(a)
A 2D
Surface
(b)
Deformation
to cylinder.
(c)
Deformation
to wave
shape.
Previous Methods
 Y. Zhao, H. Wu, M. Jin, S. Xia, "Localization in 3D Surface
Sensor Networks: Challenges and Solutions”, INFOCOM'12, pp.
55-63 ,2012.
Y. Zhao, H. Wu, M. Jin,Y.Yang, H. Zhou, and S. Xia, “Cut-andsew:A distributed autonomous localization algorithm for 3d surface
wireless sensor networks,” MobiHoc'13, pp. 69-78, 2013.
Previous Methods
 Assume each sensor node knows the distance
between its neighboring nodes.
 Assume each sensor node can measure its own
height information.
Our Approach
 To reduce the cost of hardware, is it possible not
using height information?
 If possible, we still need some extra information,
since a surface network is non-localizable with pure
connectivity and surface distance information.
Digital Terrain Model (DTM)
 A 3D representation of a terrain’s surface.
 Commonly built using remote sensing technology.
 Available to public with a variable resolution up to
one meter.
Outline
 Theoretical background and motivation of
our approach
 Our approach
 Discussions
 Simulations
 Conclusion and future works
Theoretical Background
 Conformal structure is an intrinsic geometric
structure of surfaces:
•
•
Tolerate a small local deformation of a surface;
Surfaces sharing the same conformal structure exist
conformal mapping between them.
 A conformal mapping is a one-to-one and
continuous mapping/function that preserves angles and
local shape.
Motivation of Our Approach
The triangular mesh of a DTM and the triangular
mesh extracted from the connectivity graph of a
network deployed over the terrain surface approximate
the geometric structure of the same terrain surface.
Theoretically, the two triangular meshes share the
same conformal structure.There exists a conformal
mapping between them.
DTM mesh
Sensor Network mesh
M1
M2
Motivation of Our Approach
It is extremely difficult to directly construct a conformal
mapping between two 3D surfaces. We can conformally
map the two surfaces to 2D plane, and then construct a
conformal mapping between the mapped two planar
domains. The three conformal mappings induces a
conformal mapping between the two 3D surfaces.
Based on this mapping, each sensor node of the network
can easily locate reference grid points from the DTM to
calculate its own geographic location.
Outline
 Theoretical background and motivation of
our approach
 Our approach
 Discussions
 Simulations
 Conclusion and future works
Overview of Our Approach
DTM mesh
M1
2D triangular mesh
D1
Alignment
Localization
Sensor Network mesh
M2
2D triangular mesh
D2
Step 1: Conformal Mapping to Plane
 Construct Triangular Mesh for both DTM and
Sensor Network.
•
•
A DTM is represented by a grid of squares. It is
straightforward to convert the grid into a
triangulation, e.g., by simply connecting a
diagonal of each square.
For Sensor Network with one-hop distance
information available, a simple distributed
algorithm can extract a refined triangular mesh
from the network connectivity graph.
Step 1: Conformal Mapping to Plane
 Given a triangular mesh M embedded in 3D. We
apply Discrete Surface Ricci Flow to conformally map M to
a planar region, denoted as D in 2D. The mapping result
is stored at each vertexV as a complex number, which
serves as the planar coordinates of V when M is mapped
to D.
Overview of Our Approach
DTM mesh
M1
2D triangular mesh
D1
Alignment
Localization
Sensor Network mesh
M2
2D triangular mesh
D2
Step 2: Alignment
 Randomly deployed three Anchor Nodes (Sensors
with GPS information)
Sensor Network mesh
M2
2D triangulation mesh
D2
Step 2: Alignment
 A Mobius Transformation is a conformal mapping
between complex plane to itself, with a set of three
points mapped to another set of three points.
Property:
aligns to
D2
D1
Overview of Our Approach
DTM mesh
M1
2D triangular mesh
D1
Alignment
Localization
Sensor Network mesh
M2
2D triangular mesh
D2
Step 3: Localization
 If DTM has a high density, a sensor node simply
determines its own 3D coordinates according to the
nearest triangle vertex of DTM.
 If DTM has a low density, with the aligned planar
coordinates, each sensor node locates three nearest grid
points on D1, and use the Barycentric Coordinates and
grid points’3D coordinates to get sensors’ approximate
3D location.
Step 3: Barycentric Coordinates
 Barycentric Coordinates provides a convenient way
to interpolate a function on triangles as long as the
function’s value is known at all vertices.
b
b
b
Outline
 Theoretical background and motivation of
our approach
 Our approach
 Discussions
 Simulations
 Conclusion and future works
Discussions: Performance with # of
Anchor Nodes
The size of Anchor Nodes
Discussions: Anchor Node Free
Outline
 Theoretical background and motivation of
our approach
 Our approach
 Discussions
 Simulations
 Conclusion and future works
Simulations: Different Digital Terrain
Models
Different Digital Terrain Models
Simulations: The Distribution of
Localization Errors under Different
Sets of Anchor Nodes
The distribution of localization errors
under different sets of anchor nodes
Simulations: Terrain models with
Various Resolutions
Simulations: Range Distance
Measurement Error
Simulations: Connectivity Only
Networks with Connectivity Information Only
Outline
 Theoretical background and motivation of
our approach
 Our approach
 Discussions
 Simulations
 Conclusion and future works
Conclusion and Future Works
 A fully distributed algorithm to localize a wireless
sensor network deployed on the surface of complex
3D terrains with range distance measurement only.
Both the 3D terrain surface and the network can
be any complicated shape, not necessarily convex.
 Future works: Incorporate those useful contour
features of surfaces like the peaks of valleys
into the alignment algorithm.
Q&A
Thank You !