Distributed Detection and Classification in Sensor Networks

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Distributed Detection and Classification in
Sensor Networks

• Akbar M. Sayeed
• Electrical and Computer Engineering
• University of Wisconsin-Madison
• akbar_at_engr.wisc.edu
• http//dune.ece.wisc.edu

This work was partially supported by DARPA SensIT
program under grant F30602-00-2-0555
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Wireless Sensor Networks
Wireless Transceiver
Sensing and Processing Unit
Battlefield surveillance, disaster relief, border
control, environment monitoring, etc.
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Two Vital Operations in Sensor Networks

• Information processing Distributed sensing and
  processing of data collected by nodes spatially
  local in general
• Information transport communication of
  information from one part of the network to
  another
• Both operations are fundamentally interconnected
  due to the distributed network topology (joint
  source-channel coding)
• A key goal minimize the burden on the network
• Communication burden (power and bandwidth)
• Computational burden (power)
• Exploiting spatio-temporal statistics of sensed
  data is key to minimizing the communication
  burden on network

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Key Questions Driving This Work

• Distributed decision making --- interplay between
  sensing and communication
• detection and classification of objects/events
  based on the sensed spatio-temporal signal field
• Information communicated to a remote fusion
  center
• Given some a priori information about target
  statistics
• What are optimal node sampling strategies?
• What are optimal strategies for fusing node
  information?
• What are the implications for information
  exchange between nodes?
• What is the impact of network constraints (e.g.,
  power/bandwidth)?

We address these questions in the context of
single target classification using a basic
statistical model for node measurements
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Two Forms of Information Fusion
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Main Messages

• Advantage of spatially distributed node
  measurements
• Unreliable (cheap) local node decisions can be
  fused to yield arbitrarily reliable final decision

• Data versus decision fusion governed by node
  statistics
• Correlated measurements lt-gt data fusion
• Independent measurements lt-gt decision fusion
• A combination of data/decision fusion in general
• Data fusion (high power/bandwidth) limited to
  spatially local nodes
• Decision fusion (low power/bandwidth) is
  sufficient globally across spatially distant
  nodes
• Simple guidelines for spatio-temporal sampling
• Fundamental insights regarding the interplay
  between distributed sensing and communication

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A Simple Model for the Spatio-Temporal Signal
Field
s(x,y,t) stationary complex Gaussian field in
(x,y,t)
spatial bandwidths in x and y dimensions
and
temporal signal bandwidth
Spatial Coherence Region (SCR)
(coherence distance)
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Spatial Sampling via Sensors
Distance-bandwidth (DB) products
K total number of nodes
Spatial DoF
Number of independent SCRs
Spatial Coherence Region (SCR)
Number of nodes in each SCR
(Oversampling per DoF)
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Example Time-Varying Point Sources
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Single Target/Event Classification

• Goal Given K node measurements, determine which
  one of M targets/events is being sensed
• node measurements
• N-dimensional temporal feature vector extracted
  at each node -
• Nodes sense one of M signal spatio-temporal
  fields (M objects/events)

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M-ary Hypothesis Testing

• M hypotheses on sensed measurements

Optimum (ML) centralized classifier
Goal distributed classifiers that approach the
performance of centralized classifier with
minimal communication burden
A challenge exploiting exact spatial correlation
between nodes measurements comes at the cost of
distributed coordination (in addition to
communication)
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Simplified Classifier Structure
The spatial signal is approximately independent
across SCRs
? Independent local decisions in each SCR

• - Ignore fine correlation structure within each
  SCR
• Exploit temporal characteristics of individual
  node measurements
• Exploit independent decisions from different SCRs

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Structure of the distributed classifier implied
by the signal model
Two sources of error 1) noise, and 2) inherent
statistical signal variability
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Interplay between Sensing and Communication

• SCRs imply a structure on information fusion
  that naturally minimizes communication burden
• high-bandwidth (feature level) local information
  exchange (intra SCR)
• low-bandwidth (symbol-level) global information
  exchange (inter SCR)

The nodes in each SCR could form a coherent
virtual array to transport symbol-level
information - many-to-one
capacity power pooling effect (energy saving)
Independent symbol-level information communicated
from different SCRs -
many-to-one MAC capacity
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Three Classifiers (Fusion Schemes)
Noisy comm. links
Noise-free comm. links
Soft decision fusion (benchmark)
Noisy hard decision fusion
Hard decision fusion
Global maximum likelihood decision given the
received measurements at manager node
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Fusion Architecture
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Probability of Error Approximation
D - the smallest (worst) pairwise Chernoff
exponent
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Chernoff Exponent and K-L Divergence
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D decreases from soft to hard decision fusion
D increases with measurement SNR and comm SNR
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Numerical Results

• Acoustic node signals
• 3 vehicle classes AAV, DW and HMWVV
• Stationarity assumption on time series
• N 25 dimensional FFT feature vectors
• Covariance matrices from PSD estimates
• G independent measurements (simulating G SCRs)
• Generated using PSD estimates from experimental
  (SITEX02) data
• Comparison of three classifiers
• Optimal centralized classifier (noise-free soft
  decision fusion)
• Hard decision fusion classifier
• Noisy hard decision fusion classifier (noisy
  comm. Links)

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Acoustic PSDs for the Three Vehicles
AAV tracked (Amphibious Assault Vehicle)
DW wheeled (Dragon Wagon)
HMMWV wheeled (Humvee)
SITEX02 Data. DARPA SensIT Program.
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Probability of Error Versus G
Meas. SNR 0dB
Meas. SNR 10dB
D error exponent decreases from soft to hard
to noisy hard decision fusion
D governed by the worst Kullback-Leibler distance
between pairs of hypotheses
D improves with meas. SNR (data fusion within
each SCR)
A. DCosta, V. Ramachandran, A. Sayeed,
Distributed Classification of Gaussian
Space-Time Sources in Wireless Sensor Networks,
to appear in the IEEE JSAC .
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How Tight are the Approximations?
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Fundamental Advantage of Distributed Measurements
Point sources spatial and temporal measurements
are equivalent
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Type-Based Detection

• How to reduce the loss in error exponent from
  soft to hard decision fusion?
• Quantize soft decisions?
• Analog communication of soft decisions?
• Type-based detection
• Quantize the local measurements or soft decisions
• Transmit the histogram of measurements
• Loss in error exponent controlled by quantization

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Conclusions

• Distributed decision making interplay between
  sensing and communication
• Statistical signal model (spatial coherence
  regions - SCRs)
• Highly correlated measurements within each
  coherence region
• Independent measurements across coherence regions
• Optimal classifier structure
• Local high-bandwidth data (feature) fusion
  coherent averaging in each SCR to improve SNR
• Global low-bandwidth decision fusion Noncoherent
  averaging across SCRs to stabilize the inherent
  signal variability
• Remarkable advantage of spatially distributed
  node measurements
• Local decisions from relatively unreliable
  (cheap) sensors can be fused to yield arbitrarily
  reliable final decisions
• High bandwidth (rapidly varying) spatial fields
  are easier to discriminate (larger number of
  SCRs in a given area)

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Broader Implications of the Signal Model
Communication perspective each coherence region
can act as a point (beamforming)
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Sequential Decision Making Combining Data and
Decision Fusion
Data fusion robustness to noise (improves SNR)
Decision fusion robustness to inherent
statistical signal variations
M
M
M
M
Coherence distance