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Data Fusion Improves the Coverage of Wireless Sensor Networks
Guoliang Xing1, Rui Tan2, Benyuan Liu3, JianpingWang2, Xiaohua Jia2,Chih-wei Yi4
1Michigan State University, 2City University of Hong Kong, 3University of Massachusetts Lowell, 4National Chiao Tung
University, Taiwan
Outline• Motivation
– Limitations of current studies on sensing coverage
• Problem definition– (α,β)-coverage under disc and fusion models
• Scaling laws of network density for coverage– Disc model vs. data fusion model
• Simulations2
Mission-critical Sensing Applications
• Large spatial deployment region• Resource-constrained sensor nodes• Stringent performance requirements
– High sensing prob., e.g., 99%, low false alarm rate, e.g., 1%3
100 seismometers in UCLA campus [Estrin 02] acoustic sensors detecting AAV http://www.ece.wisc.edu/~sensit/
• Fundamental requirement of critical apps– How well is a region monitored by sensors?– Full coverage: any point in a region is covered
• Network density to achieve full coverage– Critical metric for deployment cost and lifetime
Sensing Coverage
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State of the Art• Numerous studies on coverage protocols/analysis
– Our earlier work [sensys 03] cited >600 on Google Scholar– K-coverage and barrier coverage
• Most existing results are based on simplistic models– All 5 related papers since MobiCom 04 assumed disc model– Ignored sensing uncertainties and collaboration
• Collaborative signal processing theories– Focused on small-scale networks– Made performance analysis of large networks difficult
5
6
Sensing Model✘ The (in)famous disc model
✘ Any target within r is detected✘ Deterministic and independent sensing
✔ Real-world event sensing• Probabilistic, no cookie-cutter like “sensing range”!• Collaborative sensing is a must
r
Real Acoustic Vehicle Detection Experiments [Duarte 04]
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Sensor Measurement Model• Reading of sensor i is yi = si + ni
• Decayed target energy
• Noise energy follows normal distribution ni ~ N(μ,σ2) • Signal to noise ratio (SNR) is S /σ
, 2 ≤ k ≤ 5
Real Acoustic Vehicle Detection Experiments [Duarte 04]
k
i
iiix
xwxwSs1
)();(
N – CDF of Normal distributionsi – Energy reading of sensor i
Data Fusion Model• Sensors within distance R from target fuse their readings
– The sum of readings is compared again a threshold η– R is the fusion range
• False alarm rate PF = 1-N(n· η)
• Detection probability PD = 1 –N(n·η - Σsi)
R
8
Outline• Motivation
– Limitations of current studies on sensing coverage
• Problem definition– (α,β)-coverage under disc and fusion models
• Scaling laws of network density for coverage– Disc model vs. data fusion model
• Simulations9
(α,β)-Coverage• A physical point p is (α,β)-covered if
– The system false alarm rate PF ≤ α – For target at p, the detection prob. PD ≥ β
• (α,β)-coverage is the fraction of points in a region that are (α,β)-covered– Full (α,β)-coverage: any point is (α,β)-covered
• Random network deployment– Nodes deployed by Poisson process of density ρ
10
Disc and Fusion Coverage• Coverage under the disc model
– Sensors independently detect targets within sensing range r
• Coverage under the fusion model– Sensors collaborate to detect targets within fusion range R
11
grayscale represents PD
(α,β)-Coverage under Disc Model
• Choose sensing range r s.t. if any point is covered by a sensor, the region is (α,β)-covered
ρd: density of networkQ-1: inverse Complementary CDF of std Normal distr.
12
2
1Coverage rde
SNR
QQw
)()(r
111
[Liu 2004]
(α,β)-Coverage under Fusion Model
• The (α,β)-coverage of a network of density ρf
Г(R) is function of fusion range R, α, β and w(.)
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optimal fusion range
2
2)(Coverage
R
RRQ
d
d
opt fusion range
grows w density!
Outline• Motivation
– Limitations of current studies on sensing coverage
• Problem definition– (α,β)-coverage under disc and fusion models
• Scaling laws of network density for coverage– How does network density grow when coverage 1– Disc model vs. data fusion model
• Simulations14
15
Full Coverage with Opt Fusion Range
• ρf and ρd are densities of random networks under fusion and disc models
• When k=2 (acoustic signals)
• Density significantly reduced via data fusion!
5k2 ,/11 kdf
df
Network Density vs. SNR
• For full coverage with fixed fusion range R
• Disc model is good for high SNR and small k– Most low-power sensors have low SNRs, and k ≥ 2
16
k
d
f SNR2
Coverage with Non-opt Fusion Range
• Density ratio ρf/ρd satisfies
• ρf << ρd for high coverage requirement– Fusion range R may grow with network density– Sensing range r is a constant
2
22
R
r
d
f
17
SNR
QQw
)()(r
111
18
Trace-driven Simulations• Data traces collected from 75 acoustic sensors in vehicle
detection experiments [Duarte 04]– α=0.05, β=0.95, deployment region: 1000m x 1000m
fusion saves more sensors
Conclusions
• Reveal limitations of current analytical results– Only applicable for slowly decaying signals with high SNRs– Disc model significantly underestimates coverage
• Provide insights into fusion design of large networks– Data fusion can significantly improve coverage!– Fusion parameters (e.g., fusion range) are critical
• First step toward bridging the gap bw CSP and performance analysis of sensor networks
19
Future Work
• Fusion-based coverage for regular deployments
• Fusion-based coverage for moving targets
• Deployment algorithms for fusion-based coverage
Simulation on Synthetic Data
• k=2, target position is localized as the geometric center of fusing nodes
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Coverage under Disc Model• Deterministic deployment
– Optimal topology is hexagon• Random deployment
– Sensors deployed by a Poisson point process of density ρ– The coverage (fraction of points covered by at least one sensor):
deterministic deployment random deployment 22
[Liu 2004]
Contributions
• Introduce probabilistic and collaborative sensing models in the analysis of coverage– Data fusion: sensors combine data for better inferences
• Derive scaling laws of network density for full coverage
• Compare the performance of disc and fusion models– Data fusion can significantly improve coverage!
23