© The Institution of Engineering and Technology
In this study a distributed maximum likelihood estimator (MLE) has been presented to estimate ML function of traffic flow and mean traffic speed in a freeway. This algorithm uses traffic measurements including volume, occupancy and mean speed which gathered by some inductive loop detectors. These traffic detectors (traffic sensors) located in certain distances in the freeway network such that they establish a distributed sensor network (DSN). The presented distributed estimator has employed a distributed expectation maximisation algorithm to calculate MLE. In the Estep of this algorithm, each sensor node independently calculates local sufficient statistics by using local observations. A consensus filter is used to diffuse local sufficient statistics to neighbours and estimate global sufficient statistics in each node. In the Mstep of this algorithm, each sensor node uses the estimated global sufficient statistics to update model parameters of the Gaussian mixtures, which can maximise the loglikelihood in the same way as in the standard EM algorithm. As the consensus filter only requires each node to communicate with its neighbours, the distributed algorithm is scalable and robust. A set of field traffic data from Minnesota freeway network has been used to simulate and verify the proposed distributed estimator performance.
References


1)

R. Cervero
.
(1998)
The transit metropolis.

2)

F. Akyildiz ,
W. Su ,
Y. Sankara subramaniam
.
A survey on sensor networks.
IEEE Trans. Commun. Mag.
,
8 ,
102 
114

3)

Estrin, D., Govindan, R., Heidemann, J., Kumar, S.: `Next century challenges: scalable coordination in sensor networks', Proc. ACM/IEEE Int. Conf. on Mobile Computer Network, 1999, Seattle, WA, p. 263–270.

4)

R.D. Nowak
.
Distributed EM algorithms for density estimation and clustering in sensor networks.
IEEE Trans. Signal Process.
,
8 ,
2245 
2253

5)

Sheng, Y., Hu, X., Ramanathan, P.: `Distributed particle filter with GMM approximation for multiple targets localization and tracking in wireless sensor networks', Proc. Fourth Int. Symp. Information Processing Sensor Network, April 2005, Los Angeles, CA, p. 181–188.

6)

R. Kamimura
.
Cooperative information maximization with Gaussian activation functions for selforganizing maps.
IEEE Trans. Neural Netw.
,
4 ,
909 
918

7)

C. Constantinopoulos ,
A. Likas
.
Unsupervised learning of Gaussian mixtures based on variational component splitting.
IEEE Trans. Neural Netw.
,
3 ,
745 
755

8)

X. Nguyen ,
M.I. Jordan ,
B. Sinopoli
.
A kernelbased learning approach to ad hoc sensor network localization.
ACM Trans. Sensor Netw.
,
1 ,
134 
152

9)

S. Simic
.
A learning theory approach to sensor networks.
IEEE Pervasive Comput.
,
4 ,
44 
49

10)

F. Zhao ,
J. Shin ,
J. Reich
.
Informationdriven dynamic sensor collaboration for tracking applications.
IEEE Signal Process. Mag.
,
2 ,
61 
72

11)

OlfatiSaber, R.: `Distributed Kalman filter with embedded consensus filters', Proc. 44th IEEE Conf. Decision Control, 12–15 December 2005, p. 8179–8184.

12)

A. Dempster ,
N. Laird ,
D. Rubin
.
Maximum likelihood estimation from incomplete data via the EM algorithm.
J. Roy. Statist. Soc.
,
1 
38

13)

P. Gupta ,
P. Kumar
.
The capacity of wireless networks.
IEEE Trans. Inf. Theory
,
2 ,
388 
404

14)

R.M. Neal ,
G.E. Hinton ,
M.I. Jordan
.
(1998)
A view of the EM algorithm that justifies incremental, sparse, and other variants.

15)

OlfatiSaber, R., Shamma, J.S.: `Consensus filters for sensor networks and distributed sensor fusion', Proc. 44th IEEE Conf. Decision Control, 12–15 December 2005, p. 6698–6703.

16)

W. Ren ,
R.W. Beard
.
Consensus seeking in multiagent systems under dynamically changing interaction topologies.
IEEE Trans. Autom. Control
,
5 ,
655 
661

17)

L. Xu ,
M.I. Jordan
.
On convergence properties of the EM algorithm for Gaussian mixtures.
Neural Comput.
,
1 ,
129 
151

18)

M. Sato ,
S. Ishii
.
Online EM algorithm for the normalized Gaussian network.
Neural Comput.
,
407 
432
http://iet.metastore.ingenta.com/content/journals/10.1049/ietits.2010.0189
Related content
content/journals/10.1049/ietits.2010.0189
pub_keyword,iet_inspecKeyword,pub_concept
6
6