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Table 1 Normalized mean absolute errors (MAE) of centralized and distributed estimation algorithms. A single source field (M=1) with c 1=1, τ 1=1.213, ξ 1=(0.1130,0.2210) is considered and the source parameters estimated from the spatiotemporal samples taken at \(\frac {1}{\Delta t} = 1\) Hz over T=10 s using N=45 sensors, with spatial sensing function families K=1 and K=3. The normalized MAE statistic has been computed with results from 1000 independent trials at different noise levels

From: Physics-driven quantized consensus for distributed diffusion source estimation using sensor networks

 

Centralized

Distributed (Unquantized)

Distributed (Quantized)

 

K=1

K=3

K=1

K=3

K=1

K=3

No noise

c m

0.0811

0.0683

0.0811

0.0684

0.1017

0.0740

 

τ m

0.1375

0.1277

0.1231

0.1128

0.4127

0.1883

 

ξ 1,m

0.0439

0.0306

0.0439

0.0306

0.1151

0.0644

 

ξ 2,m

0.0285

0.0219

0.0285

0.0219

0.0571

0.0313

20 dB

c m

0.4385

0.1025

0.4385

0.1026

0.5939

0.1030

 

τ m

0.2794

0.2565

0.2583

0.2267

0.4928

0.2887

 

ξ 1,m

0.0861

0.0611

0.0861

0.0620

0.1893

0.0767

 

ξ 2,m

0.0600

0.0415

0.0600

0.0415

0.1040

0.0451

10 dB

c m

0.2417

0.2027

0.2417

0.2031

0.2785

0.2171

 

τ m

0.7132

0.7310

0.6952

0.7102

0.8321

0.7240

 

ξ 1,m

0.2081

0.1808

0.2081

0.1874

0.2627

0.1951

 

ξ 2,m

0.1135

0.0990

0.1135

0.0995

0.1310

0.1037