location, localization, and localizability liu y, yang z, wang x et al. journal of computer science...
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![Page 1: Location, Localization, and Localizability Liu Y, Yang Z, Wang X et al. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY, Mar. 2010 Slides prepared by Lanchao](https://reader030.vdocuments.mx/reader030/viewer/2022032800/56649d2d5503460f94a03484/html5/thumbnails/1.jpg)
Location, Localization, and Localizability
Liu Y, Yang Z, Wang X et al. JOURNAL OF COMPUTER SCIENCE AND
TECHNOLOGY, Mar. 2010
Slides prepared by Lanchao Liu and Zhu HanECE Department, University of Houston
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Outline• Location• Localization– Physical Measurement and Single-Hop Positioning– Network-Wide Localization– Error Control for Network Localization
• Localizability– Network Localizability– Node Localizability
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• Routing• Topology Control• Coverage• Boundary Detection• Clustering
Location information supports many fundamental network services
• Medical care• Smart space• Logistics• Environment monitor• Mobile p2p
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Location-based services for a wide range of wireless networks• Limitation of GPS and local positioning systems• Two stages– Measuring geographic information from the ground
truth of network deployment; – Computing node locations according to the measured
data.
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Outline• Location• Localization– Physical Measurement and Single-Hop Positioning– Network-Wide Localization– Error Control for Network Localization
• Localizability– Network Localizability– Node Localizability
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Physical Measurement and Single-Hop Positioning
Physical measurement classification
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Directly obtain the position without any further computation• GPS• Deliberated deployed
Location Distance Angle Area Hop Count Neighborhood
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Location Distance Angle Area Hop Count Neighborhood
Multilateration*: The distances from an unknown node to several references constrain the presence of this node
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• Radio Signal Strength (RSS): noisy but cheap
Location Distance Angle Area Hop Count Neighborhood
Received power at distance
Received power at some reference distance
path-loss exponent fading effects
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Location Distance Angle Area Hop Count Neighborhood
Need line-of-sight conditions
• TDoA: better resolution but costy
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Location Distance Angle Area Hop Count Neighborhood
a b
c
D
𝜑2 𝜑1
• Angle Of Arrival:
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• Area measurement– Single Reference Area Estimation
distance and angle, etc.
Location Distance Angle Area Hop Count Neighborhood
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• Multi-Reference Area Estimation– Approximate point in triangle (APIT)• The triangle formed by three arbitrary references• The node then decides whether it is inside or outside a
given triangle.
– Range measurement calibration and node density
Location Distance Angle Area Hop Count Neighborhood
The node simply finds the intersection of all overlapping coverage regions, and chooses the centroid as its position estimate
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• Hop Count Measurements D =
Location Distance Angle Area Hop Count Neighborhood
The expected number of neighbors per node
Number of hops Communication range
D =
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Location Distance Angle Area Hop Count Neighborhood
Failed in anisotropic network !
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• Neighborhood Measurement Reference nodes periodically emit beacons including their location IDs. Unknown nodes use the received locations as their own location, achieving a course-grained localization. Very cheap K-nearest neighbor approximation
Location Distance Angle Area Hop Count Neighborhood
Centroid
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Comparative Study & Future work
Promising technique: UWB and Chirp Spread Spectrum
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Outline• Location• Localization– Physical Measurement and Single-Hop Positioning– Network-Wide Localization– Error Control for Network Localization
• Localizability– Network Localizability– Node Localizability
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Network-Wide Localization
• Computation Organization– Centralized: Network nodes collect environmental
data and send back to a base station for analysis.• Multi-dimension scaling (MDS)• Semi-Definite programming (SDP)
– Distributed:• Beacon-based, top-down manner• Local map based, bottom-up manner
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• Multi-Dimensional Scaling (MDS) – Generate an n * n matrix M, whose (i; j) entry contains the
estimated distance between nodes i and j– Apply classical metric-MDS on M to determine a map that
gives the locations of all nodes in relative coordinates– Transform the solution into global coordinates based on
some number of fixed anchor nodes
Centralized Distributed
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• Semi-Definite Programming (SDP) Geometric constraints between nodes are represented as linear matrix inequalities (LMIs). The LMIs can be combined to form a single semi-definite program, which is solved to produce a bounding region for each node.
Centralized Distributed
Concise problem formulation, clear model representation, and elegant mathematic solution……but the constraints should be convex.
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An example:
Biswas, P. and Yinyu Ye, “Semidefinite programming for ad hoc wireless sensor network localization”, IPSN,2004
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• Beacon Based Localization (top down manner)– Distance vector(DV)-hop: to the reference node– DV distance: if inter-node distance is known– Iterative localization: unknown to known, step by step
Centralized Distributed
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Multilateration-based algorithms require an average node degree beyond 10.
To make localization applicable for sparse networks, Sweeps partially relaxes the requirement of node dependence. In this example, two possible locations
Centralized Distributed
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• Coordinated System Stitching (jig-saw puzzle)
Centralized Distributed
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• Coordinated System Stitching – Split the network into small overlapping
subregions. Very often each sub-region is simply a single node and its one-hop neighbors.
– For each sub-region, compute a “local map”, which is essentially an embedding of the nodes in the sub-region into a relative coordinate system.
– Merge sub-regions using a coordinate system registration procedure.
Centralized Distributed
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• How to produce robust local maps
Centralized Distributed
Shortest side Smallest angle Threshold
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• Component Based Localization
Centralized Distributed
Rigid Structure
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• Beacon nodes– In a convex hull around the network– In the center of the network
• Node Density– High density may not be always true
• Accuracy– Location accuracy trades off with location precision
• Cost– Hardware cost: node density, beacon density, and
measurement equipment– Energy cost: communication
Comparative Study & Future work
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• Obtaining a Pareto improvement is a major challenge
• Device-Free Localization
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Outline• Location• Localization– Physical Measurement and Single-Hop Positioning– Network-Wide Localization– Error Control for Network Localization
• Localizability– Network Localizability– Node Localizability
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Error Control for Network Localization
• Noisy Distance Measurement– Extrinsic: Physical effects on the measurement
channel (multipath, shadowing…)– Intrinsic: Hardware limitation
1. Errors in Distance Measurements
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• Negative Impact of Noisy Ranging Results– Uncertainty– Non-Consistency– Error Propagation
Error Control for Network Localization
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• Error Characteristics of Localization– Creamer Rao Lower Bound (CRLB)
– CRLB for Multihop Localization*– CRLB for One-Hop Localization
Error Control for Network Localization
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Error Control for Network Localization
• Geographic Dilution of Precision
Variance of the estimate location Angle between each pair of reference nodes
• The ranging error• The geometric relationship of references and to be localized nodes
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Geographic Dilution of Precision (GDoP):
Highest location accuracy would be achieved if reference nodes are evenly separated
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Error Control for Network Localization
• Location Refinement– Framework of Location Refinement• Node Registry: Location + Confidence• Reference Selection: Selects the reference achieving
the highest estimate confidence• Registry Update
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Framework of location refinement
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Error Control for Network Localization
• Location Refinement– Framework of Location Refinement– Metrics for Location Refinement• Analyze the performance both on noisy distance
measurements and location uncertainly of reference.• Quality of Trilateration
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Location Estimate
Estimated location error caused by noisy distance measurements
The error due to location uncertainty of references
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Error Control for Network Localization• Robust Localization Severe errors can be seen as outliers of measurements that significantly deteriorate localization accuracy.
Amortize errors
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Outline• Location• Localization– Physical Measurement and Single-Hop Positioning– Network-Wide Localization– Error Control for Network Localization
• Localizability– Network Localizability– Node Localizability
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Localizability can assist network operation and management
Location-uniqueness
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Network Localizability• Globally Rigid Graphs
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• Conditions for Network Localizability– Theorem 1: A graph with n >= 4 vertices is globally
rigid in 2 dimensions if and only if it is 3-connected and redundantly rigid.
– Theorem 2: A network is uniquely localizable if and only if its distance graph is globally rigid and it contains at least three anchors.
Network Localizability
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• Inductive Construction of Globally RigidGraphs
Network Localizability
Deficiency of trilateration
WHEEL!
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Outline• Location• Localization– Physical Measurement and Single-Hop Positioning– Network-Wide Localization– Error Control for Network Localization
• Localizability– Network Localizability– Node Localizability
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Node Localizability• The results derived for network localizability
cannot be directly applied• Given a network configuration, whether or not a
specific node is localizable? • How many nodes in a network can be located and
which are them?
u is uniquely localizable, although the 3 connectivity property does not hold
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Node Localizability
Studies show that a vertex is localizable if it belongs to the redundantly rigid component of B in which there exists 3 vertex-disjoint paths connecting it to 3 beacon vertices.(RR3P)
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Location
LocalizationLocalizability
Conclusion
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Thank You!
Q & A