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Research Papers

A Distributed Navigation Strategy for Mobile Sensor Networks With the Probabilistic Wireless Links

[+] Author and Article Information
Aqeel Madhag

Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48823
e-mail: madhagaq@msu.edu

Jongeun Choi

Associated Professor
Mem. ASME
School of Mechanical Engineering,
Yonsei University,
Seoul 03722, South Korea
e-mail: jongeunchoi@yonsei.ac.kr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 7, 2015; final manuscript received October 10, 2016; published online January 10, 2017. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 139(3), 031004 (Jan 10, 2017) (11 pages) Paper No: DS-15-1370; doi: 10.1115/1.4035008 History: Received August 07, 2015; Revised October 10, 2016

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.

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Figures

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Fig. 1

Undirected communication graph

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Fig. 2

PRR versus distance from the model (1), (a) γ in Eq. (1) is a function of d and other parameters (i.e., transmitted, noise floor, and path loss powers), which are random processes, (b) γ in (1) is a function of d and other parameters (i.e., transmitted, noise floor, and path loss powers), which are set as fixed values. There are three regions: full reception (as a connected region), no reception (as a disconnected region), and between those some level of reception (as a transitional region).

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Fig. 3

The network of agents with the probabilistic wireless links. The ball in the center represents agent i. The right side and left side balls represent agents within NRP[i] in which agent i accepts their packets and agents within NR[i] who dropped them from agent i, respectively.

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Fig. 4

Simulations results of agents under distributed navigation with the R-disk communication model. (a) True field, (b) predicted field, and (c) prediction error variance. The true and predicted fields are obtained from the spatio-temporal Gaussian process model z(s, t) (2) with a covariance function defined in Eq. (3). Target points are shown as stars. Agents' trajectories and initial agents' positions are shown as solid lines and crosses, respectively.

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Fig. 5

Simulation results of agents under distributed navigation with the probabilistic wireless links. (a) True field, (b) predicted field, and (c) prediction error variance. The true and predicted fields are obtained from the spatio-temporal Gaussian process model z(s, t) (2) with a covariance function defined in Eq. (3).Target points are shown as white stars. Agents' trajectories and initial agents' positions are shown as solid white lines and yellow crosses, respectively.

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Fig. 6

(a) The individual cost functions produced by an agent under distributed navigation with the R-disk communication model (circles), and the probabilistic wireless links (triangles). The X-axis shows the number of iterations and Y-axis is the prediction error variance. (b) The local collective network performance cost functions produced by agents under distributed navigation with the R-disk communication model (circles), and the probabilistic wireless links (triangles). The X-axis shows the number of iterations, and Y-axis shows the local collective network performance cost functions.

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Fig. 7

Monte Carlo simulations results for case 1: (a) R-disk communication model and (b) probabilistic wireless links. Target points are shown as stars. Agents' trajectories and initial agents' positions are shown as solid lines and crosses, respectively.

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Fig. 8

Monte Carlo simulations results for case 2 with initial position of the agents around the center of the ring: Target points are shown as stars. Agents' trajectories and initial positions are shown as solid lines and crosses, respectively. (a) R-disk communication model and (b) probabilistic wireless links.

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Fig. 9

Monte Carlo simulations results for case 2 with initial position of the agents near the target points: (a) R-disk communication model and (b) probabilistic wireless links. Target points are shown as stars. Agents' trajectories and initial agents' positions are shown as solid lines and crosses, respectively.

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Fig. 10

Monte Carlo simulations results for case 3: (a) R-disk communication model and (b) probabilistic wireless links. Target points are shown as stars. Agents' trajectories and initial agents' positions are shown as solid lines and crosses, respectively.

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Fig. 11

Monte Carlo simulations results for case 4: (a) R-disk communication model and (b) probabilistic wireless links. Target points are shown as stars. Agents' trajectories and initial agents' positions are shown as solid lines and crosses, respectively.

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Fig. 12

Simulations results of time computation complexity. X-axis shows the number of agents, and Y-axis shows the computation time. The circles and triangles for distributed navigation with probabilistic wireless links and distributed navigation with R-disk communication model, respectively.

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