Mobile sensor networks have been widely used to predict the spatio-temporal physical phenomena for various scientific and engineering applications. To accommodate the realistic models of mobile sensor networks, we incorporated probabilistic wireless communication links based on packet reception ratio (PRR) with distributed navigation. We then derived models of mobile sensor networks that predict Gaussian random fields from noise-corrupted observations under probabilistic wireless communication links. For the given model with probabilistic wireless communication links, we derived the prediction error variances for further sampling locations. Moreover, we designed a distributed navigation that minimizes the network cost function formulated in terms of the derived prediction error variances. Further, we have shown that the solution of distributed navigation with the probabilistic wireless communication links for mobile sensor networks are uniformly ultimately bounded with respect to that of the distributed one with the R-disk communication model. According to Monte Carlo simulation results, agent trajectories under distributed navigation with the probabilistic wireless communication links are similar to those with the R-disk communication model, which confirming the theoretical analysis.

References

1.
Hu
,
L.
, and
Evans
,
D.
,
2004
, “
Localization for Mobile Sensor Networks
,”
10th Annual International Conference on Mobile Computing and Networking
,
MobiCom’04
, ACM, New York, pp.
45
57
.
2.
Ailamaki
,
A.
,
Faloutos
,
C.
,
Fischbeck
,
P. S.
,
Small
,
M. J.
, and
VanBriesen
,
J.
, “
An Environmental Sensor Network to Determine Drinking Water Quality and Security
,”
SIGMOD Rec.
,
32
(
4
), pp.
47
52
.
3.
Choi
,
J.
,
Oh
,
S.
, and
Horowitz
,
R.
,
2009
, “
Distributed Learning and Cooperative Control for Multi-Agent Systems
,”
Automatica
,
45
(
12
), pp.
2802
2814
.
4.
Choi
,
J.
,
Oh
,
S.
, and
Horowitz
,
R.
,
2007
, “
Cooperatively Learning Mobile Agents for Gradient Climbing
,” 46th
IEEE
Conference on Decision and Control
, Dec. 12–14, pp.
3139
3144
.
5.
Lynch
,
K. M.
,
Schwartz
, I
. B.
,
Yang
,
P.
, and
Freeman
,
R. A.
,
2008
, “
Decentralized Environmental Modeling by Mobile Sensor Networks
,”
IEEE Trans. Rob.
,
24
(
3
), pp.
710
724
.
6.
Leonard
,
N. E.
,
Paley
,
D. A.
,
Lekien
,
F.
,
Sepulchre
,
R.
,
Fratantoni
,
D. M.
, and
Davis
,
R.
,
2007
, “
Collective Motion, Sensor Networks, and Ocean Sampling
,”
Proc. IEEE
,
95
(
1
), pp.
48
74
.
7.
Xu
,
Y.
,
Choi
,
J.
, and
Oh
,
S.
, “
Mobile Sensor Network Navigation Using Gaussian Processes With Truncated Observations
,”
IEEE Trans. Rob.
,
27
(
6
), pp.
1118
1131
.
8.
Cortés
,
J.
,
2009
, “
Distributed Kriged Kalman Filter for Spatial Estimation
,”
IEEE Trans. Autom. Control
,
54
(
12
), pp.
2816
2827
.
9.
Graham
,
R.
, and
J.
Cortés
,
2012
, “
Adaptive Information Collection by Robotic Sensor Networks for Spatial Estimation
,”
IEEE Trans. Autom. Control
,
57
(
6
), pp.
1404
1419
.
10.
Xu
,
Y.
,
Choi
,
J.
,
Dass
,
S.
, and
Maiti
,
T.
,
2012
, “
Sequential Bayesian Prediction and Adaptive Sampling Algorithms for Mobile Sensor Networks
,”
IEEE Trans. Autom. Control
,
57
(
8
), pp.
2078
2084
.
11.
Xu
,
Y.
, and
Choi
,
J.
,
2012
, “
Spatial Prediction With Mobile Sensor Networks Using Gaussian Processes With Built-In Gaussian Markov Random Fields
,”
Automatica
,
48
(
8
), pp.
1735
1740
.
12.
Xu
,
Y.
, and
Choi
,
J.
,
2012
, “
Stochastic Adaptive Sampling for Mobile Sensor Networks Using Kernel Regression
,”
Int. J. Control, Autom. Syst.
,
10
(
4
), pp.
778
786
.
13.
Varagnolo
,
D.
,
Pillonetto
,
G.
, and
Schenato
,
L.
,
2012
, “
Distributed Parametric and Nonparametric Regression With On-Line Performance Bounds Computation
,”
Automatica
,
48
(
10
), pp.
2468
2481
.
14.
Murray
,
R. M.
,
2007
, “
Recent Research in Cooperative Control of Multivehicle Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
129
(
5
), pp.
571
583
.
15.
Xu
,
Y.
, and
Choi
,
J.
,
2011
, “
Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks
,”
Sensors
,
11
(
3
), pp.
3051
3066
.
16.
Choi
,
J.
, and
Milutinović
,
D.
,
2015
, “
Tips on Stochastic Optimal Feedback Control and Bayesian Spatio-Temporal Models: Applications to Robotics
,”
ASME J. Dyn. Syst., Meas., Control
,
137
(
3
), p.
030801
.
17.
Choi
,
S.
,
Jadaliha
,
M.
,
Choi
,
J.
, and
Oh
,
S.
,
2015
, “
Distributed Gaussian Process Regression Under Localization Uncertainty
,”
ASME J. Dyn. Syst., Meas., Control
,
137
(
3
), p.
031007
.
18.
Manyika
,
J.
, and
Durrant-Whyte
,
H.
,
1995
,
Data Fusion and Sensor Management: A Decentralized Information-Theoretic Approach
,
Prentice Hall PTR
,
Upper Saddle River, NJ
.
19.
Oh
,
S.
, and
Sastry
,
S.
,
2006
, “
Distributed Networked Control System With Lossy Links: State Estimation and Stabilizing Communication Control
,” 45th
IEEE
Conference on Decision and Control
, Dec. 13–15, pp.
1942
1947
.
20.
Mostofi
,
Y.
,
Chung
,
T. H.
,
Murray
,
R. M.
, and
Burdick
,
J. W.
,
2005
, “
Communication and Sensing Trade-Offs in Decentralized Mobile Sensor Networks: A Cross-Layer Design Approach
,”
4th International Symposium on Information Processing in Sensor Networks
,
IPSN’05
,
IEEE Press
,
Piscataway, NJ
, Paper No. 16.
21.
Nevat
,
I.
,
Peters
,
G.
, and
Collings
,
I.
,
2013
, “
Random Field Reconstruction With Quantization in Wireless Sensor Networks
,”
IEEE Trans. Signal Process.
,
61
(
23
), pp.
6020
6033
.
22.
Mesbahi
,
M.
, and
Egerstedt
,
M.
,
2010
,
Graph Theoretic Methods in Multiagent Networks
,
Princeton University Press
,
Princeton, NJ
.
23.
Bullo
,
F.
,
Cortés
,
J.
, and
Martínez
,
S.
,
2009
,
Distributed Control of Robotic Networks
(Applied Mathematics Series),
Princeton University Press
,
Princeton, NJ
.
24.
Zuniga
,
M.
, and
Krishnamachari
,
B.
,
2004
, “
Analyzing the Transitional Region in Low Power Wireless Links
,” First Annual
IEEE
Communications Society Conference on Sensor and Ad Hoc Communications and Networks
, Oct 4–7, pp.
517
526
.
25.
Seada
,
K.
,
Zuniga
,
M.
,
Helmy
,
A.
, and
Krishnamachari
,
B.
,
2004
, “
Energy-Efficient Forwarding Strategies for Geographic Routing in Lossy Wireless Sensor Networks
,”
2nd International Conference on Embedded Networked Sensor Systems
,
SenSys'04
,
ACM
,
New York
, pp.
108
121
.
26.
Rasmussen
,
C.
,
2004
, “
Gaussian Processes in Machine Learning
,”
Advanced Lectures on Machine Learning
(Lecture Notes in Computer Science), Vol.
3176
,
O.
Bousquet
,
U.
von Luxburg
, and
G.
Ratsch
, eds.,
Springer
,
Berlin/Heidelberg
, pp.
63
71
.
27.
Oh
,
S.
,
Schenato
,
L.
,
Chen
,
P.
, and
Sastry
,
S.
,
2007
, “
Tracking and Coordination of Multiple Agents Using Sensor Networks: System Design, Algorithms and Experiments
,”
Proc. IEEE
,
95
(
1
), pp.
234
254
.
28.
Suh
,
J.
,
You
,
S.
,
Choi
,
S.
, and
Oh
,
S.
,
2014
, “
Vision-Based Coordinated Localization for Mobile Sensor Networks
,”
IEEE Trans. Autom. Sci. Eng.
,
13
(
99
), pp.
611
620
.
29.
Bertsekas
,
D. P.
, and
Tsitsiklis
,
J. N.
,
1989
,
Parallel and Distributed Computation: Numerical Methods
, Vol.
23
,
Prentice Hall
,
Englewood Cliffs, NJ
.
30.
Bertsekas
,
D. P.
,
1999
,
Nonlinear Programming
,
Athena Scientific Belmont
,
Belmont, MA
.
31.
Khalil
,
H. K.
, and
Grizzle
,
J. W.
,
2002
,
Nonlinear Systems
,
Prentice Hall
,
Englewood Cliffs, NJ
.
32.
Hirsch
,
M. W.
,
Smale
,
S.
, and
Devaney
,
R. L.
,
2004
,
Differential Equations, Dynamical Systems, and an Introduction to Chaos
,
Academic Press
,
Waltham, MA
.
You do not currently have access to this content.