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What is a Wireless Sensor Network ?
Entities
- Sensor Nodes
- Beacon Nodes
- Gateway Nodes
Function
- Sample
- Process
- Communicate
Localization Error Analysis in Wireless Sensor Networks Uday Kiran - - PowerPoint PPT Presentation
Localization Error Analysis in Wireless Sensor Networks Uday Kiran - - PowerPoint PPT Presentation
Localization Error Analysis in Wireless Sensor Networks Uday Kiran Pulleti What is a Wireless Sensor Network ? Entities Sensor Nodes Beacon Nodes Gateway Nodes Function Sample Process Communicate
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Wireless Sensor Networks
Why WSNs ?
Small size, Low cost, High Reliability and Accessibility
Unique challenges
Power, Random Deployment, Unreliable Communication
Applications
Habitat monitoring, Battle fields, Surveillance, Nuclear power plants, etc.
Functions
Parameter measurement, Target localization and tracking.
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Localization
Node Localization Source Localization Differences
- Cooperative/Non-cooperative
- Node Density
- Computational Complexity
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Localization – A generic definition
Given a set of entities (nodes) with known
locations and a source entity, the problem is to estimate the location of the source.
Location aware --- Sensor node Location unaware --- Source
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Localization
Measurements Modalities
- Received Signal Strength (RSS)
- Time of Flight (TOF)
- Time of Arrival (TOA)
- Time Difference of Arrival (TDOA)
- Direction of Arrival (DOA)
Measurements
- Range
- Range Difference
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Localization Algorithms
Mostly non iterative Range Difference
- Locus is a hyperbola
- At least four nodes are required
- Least Square Estimation
Range
- Locus is a circle
- At least three nodes are required
- Also Least Square Estimation
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Localization Error
Network Parameters
- Node density
- Available energy resources
- Circuit noise
- Location errors
Environmental Parameters
- Sensing modality and its propagation model
- Terrain’s geographical topology
- Ambient noise levels
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Problem Formulation
To characterize the localization error with
respect to the network and environmental parameters in an algorithm independent manner
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Notation
- ( xs , ys) --- source location
- -- estimated source location
( xi , yi ) --- ith sensor node ri --- distance between the source and ith node mi --- range measurement at the ith sensor node. mij --- range-difference measurement between ith
and the jth sensor nodes
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Error models
Range Measurements
- Gaussian error
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Error models
Range Difference Measurements
- Joint Gaussian error
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Error models
Range Difference Measurements
- Derived Gaussian error
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Data Collection Techniques
Closest N Activation Model (CNAM) Fixed Radius Activation Model (FRAM)
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Post-deployment and a priori error performance
Given sensor network Random network (Poisson points)
- CNAM
- FRAM
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Cramer-Rao Lower Bound
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Cramer-Rao Lower Bound
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Range Measurements – Post- deployment CRLB
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Constrained optimization
Re-deployment stratagies
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Range Measurements – A priori CRLB
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CNAM
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CNAM : K = 0
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CRLB 3D plot for the nearest 6 nodes as a function of and
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FRAM
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Error Comparisons
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Error Comparisons
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Error Comparisons
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Error Comparisons
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Error Comparisons
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Range Difference Measurements
Joint Gaussian model
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Joint Gaussian model
CNAM FRAM
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Derived Gaussian model
CNAM FRAM
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Error Comparisons
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Error Comparisons – Joint Gaussian Model
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Error Comparisons – Derived Gaussian Model
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