wireless sensor network dynamic mathematics modeling and...

Research ArticleWireless Sensor Network Dynamic Mathematics Modeling andNode Localization

Xiaoyang Liu 12 and Chao Liu13

1School of Computer Science and Engineering Chongqing University of Technology Chongqing 400054 China2College of Engineering The University of Alabama Tuscaloosa Alabama 35401 USA3College of Automation Chongqing University Chongqing 400044 China

Correspondence should be addressed to Xiaoyang Liu lxy3103163com

Received 13 November 2017 Revised 13 April 2018 Accepted 2 May 2018 Published 31 May 2018

Academic Editor Maode Ma

Copyright copy 2018 Xiaoyang Liu and Chao Liu This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

With the rapid development of wireless sensor network (WSN) technology and its localization method localization is one ofthe basic services for data collection in WSN The localization accuracy often depends on the accuracy of distance estimationBecause of the constraint in size power and cost of sensor nodes the investigation of efficient location algorithms which satisfythe basic accuracy requirement forWSNmeets new challengesThis paper proposes a novel intelligent node localization algorithminWSN based on beacon nodes to improve the precision in location estimation Firstly system model of WSN node localization isconstructed according to theWSN environmentThen traditionalWSN node localization methods such as DV-HOP GA and PSOare studied Localization algorithm of WSN is proposed by using dynamic mathematics modeling And the result of simulationwhich is compared to the traditional algorithm indicated that this algorithm is better to improve the accuracy and coverage ofWSN The simulation results show that the performance of the proposed WSN location algorithm is better than the traditionallocalization algorithms

1 Introduction

11 Background and Research Status WSN has a great appli-cation future in the military and civil area The fundamentalproblems of sensor networks are deployment and coveragelocalization and networking protocols [1ndash3] The accuracyof node localization is crucial for many applications ofdistributed sensor network (DSN) [4ndash7] The current nodelocalization algorithm of WSN is mainly divided into twocategories one is a node location algorithm based on rangingand the other is a nonranging node localization algorithmSince the distance-based node positioning algorithm requiresadditional auxiliary facilities the resource consumption isrelatively large Therefore it is not suitable for use in large-scale networks The nonranging node algorithm does notrequire additional ancillary facilities while hardware cost isrelatively low Therefore it becomes a research hotspot incurrent wireless sensor networks Our paper is based on the

idea of a nonranging node algorithm A new wireless sensorlocalization algorithm based on irregular node communi-cation is proposed The feasibility and effectiveness of thealgorithm are verified by simulation experiments

In general positioning accuracy can be improved byincreasing the number of anchor nodes However the cost ofthe anchor node is higher than that of ordinary nodes If 10of the nodes are anchor nodes the price of the network willincrease 10 times [8ndash13] However when the unknown nodeis located it will no longer need expensive anchor nodesTherefore it is necessary to reduce the number of anchornodes participating in node positioning If the cost is reducedby reducing the number of anchor nodes the consequenteffect is a reduction in positioning accuracy Based onthe broadcast characteristics of wireless transmission somemethods based on geometric knowledge of interfering nodepositioning have been proposed including centroid posi-tioning weight centroid positioning iterative positioning

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 1082398 8 pageshttpsdoiorg10115520181082398

2 Wireless Communications and Mobile Computing

of virtual forces convex shell positioning and alpha shellpositioning In the centroid localization method (CL cen-troid localization) interfering nodesrsquo neighboring nodes arecalled interfered nodes The CL collects the coordinates ofall disturbed nodes and uses the average as the estimatedposition of the interference node Considering that differentinterfered nodes have different distances from interferingnodes their perceived interference intensity is also differentThe researchers proposed the positioning of weight centersof mass which improved the positioning accuracy to someextent Juan J Galvez Patrick Carrollet al [14ndash20] proposeda novel probabilistic graphical model called Bayesian Net-work based Program Dependence Graph (BNPDG) that hasthe excellent inference capability across nonadjacent WSNnodes They focused on applying the BNPDG at indoornode localization Compared with the PPDG their BNPDG-based localization approach overcomes the limitation acrossnonadjacent nodes and provides more precise localizationby taking its output nodes as the common conditions tocalculate the conditional probability of each nonoutput nodeYatish KJoshiShi Zhanget al [21ndash27] proposed a HeuristicMultidimensional Scaling (HMDS) algorithm to improveaccuracy of node localization in anisotropicWSNswith holesBy exploring the virtual node and constructing the shortestpaths between nodes the Euclidean distances between nodesare obtained via employing the heuristic approach such thatthey can be used to calculate more accurate locations ofthe nodes Ajinkya Rajandekaret al [28 29] investigatedthe significance of introducing small world characteristicsin a conventional WSN for improving the node localizationaccuracy A novel constrained iterative average path lengthreduction algorithm is proposed to introduce small worldcharacteristics into a conventionalWSNThemethod utilizesa novel frequency selective approach for the introduction ofsmall world phenomena

The robust quadrilateral method for judging noderollover ambiguity is mostly applicable only to three-sidedpositioning using three reference nodes Compared to thethree-sided positioning method multilateration methodsusingmore than three reference nodes can get smaller averagepositioning errors Therefore in the node positioning of awireless network based on ranging a multilateration methodis mostly used At present there is still very little research onthe problem of node rollover ambiguity in multilateral posi-tioning Although some literatures have proposed a robustquadrilateral method suitable for multilateral positioning forthe first time however its computational complexity is largeand the judgment effect is poor

Hao ZhangWei Liu et al [30ndash32] proposed and provedthat flip ambiguity detection for three-dimensional nodelocalization is equivalent to the intersecting plane that inter-sects with all range error spheres of the reference nodes ofunknown node in the ideal radio model which is called theexistence of intersecting plane (EIP) problemThey proposedcommon tangent plane algorithm (CTP) and orthogonalprojection algorithm (OP) Hua-DongMo and Rodolfo Feick[33 34] proposed a Bluetooth interior location algorithmbased on Bayesian theory for RSSI probability distributionThe algorithm used the maximum posterior probability

to determine the position of the moving target and thealgorithm is complicated There is a large error Min Jia andLimei Lin [35 36] proposed an enhanced Gaussian mixturemodel WSN positioning algorithm the algorithm achievedhigh positioning accuracy but the algorithm is complex anddifficult to implement on mobile terminals such as smartphones and wireless environment

In the anchor node mobility strategy there are manystrategies in order to achieve certain coverage They assumethat the anchor nodersquos moving path can cover the entirenetwork ignoring the actual distribution density of unknownnodes The appearance of anchor nodes cannot effectivelyavoid traversing the network empty areas It cannot providegood distribution of virtual beacons long moving path andlow positioning accuracy because there is a close relationshipbetween virtual force and node distribution Literature [37]introduced the concept of virtual force potential field tothe node coverage problem of wireless sensor networks forthe first time A wireless sensor network node coveragemethod based on virtual force potential field is proposedLiterature [38] has improved the above-mentioned virtualforce potential field A virtual force algorithm (VFA) hasbeen proposed The algorithm combined virtual gravity andvirtual repulsion to determine the motion paths of randomlydistributed nodes Considering the energy consumption thenodes will move uniformly after the sink node has calculatedthe final coordinates of each node

12 Motivations Above discussion implies that novelinequality methods allow us to obtain more preciselocalization and lower error Most references do not considerthe dynamic behaviors of wireless communication networksnode Under this method efficiency novel node localizationof WSNmethod and mathematics model could be proposed

13 Our Contributions Themain contributions of this paperare listed as follows

(1) System architecture of wireless sensor network isconstructed (2) A mesh generation method is constructed(3)Wireless network node information exchangemechanismis established (4) A new node localization algorithm isproposed

14 Structure of the Paper The rest of this paper is orga-nized as follows In Section 2 some traditional sensor nodelocalization methods are introduced In Section 3 systemmodel of node localization of WSN is built according to thewireless communication network In Section 4 a new nodelocalization and dynamic modeling method is proposed InSection 5 the simulation analytical results are presentedFinally conclusions are drawn in Section 6

2 Sensor Node Localization Algorithm

21 DV-HOP Node Localization Algorithms The node local-ization algorithm of DV-Hop is a kind of distance vectormethod while GPS is a distributed localization method Thealgorithm can be divided into the following three steps [3334]

Wireless Communications and Mobile Computing 3

Step 1 Packet for each node is (119868119863119894 119909 119910 ℎ119900119901119894) The packetcontains the coordinates information and the minimum hopThe initial value of the minimum hop is 0

Step 2 Thefirst step is completed all the beacon nodes knowthe minimum hop count from other beacon nodes When aparameter 119867119900119901119878119894119911119890 is introduced 119867119900119901119878119894119911119890 is named as thedistance of average hop number

Step 3 The distance between unknown node and beaconnode is calculated by the minimum hop

22 Genetic Algorithm (GA) In the GA sensor node local-ization algorithm chromosomes are possible solutions forspecific problems Problems with parameters are called genes[35 36] For 2-dimensional plane localization each chro-mosome has two parameters as (119909 119910) Genetic algorithmhas the following three basic operations selection crossoverand mutation Through the cross two parent individualsare combined to produce two new chromosomes offspringinherited the characteristics of the parent And the key isto create a new function of evolution the genetic algorithmwill need to make use of the mutation operator A newgeneration is produced followed by the fitness function ofthe evaluation A new generation will be arranged from goodto bad until convergence or reaching the predeterminednumber of iterations

23 Particle Swarm Optimization (PSO) Algorithm The PSO[37 38] sensor node localization algorithm consists of anumber of moving particles particles are responsible forfinding the optimal solutions The algorithm updates theparticlersquos speed and location Each particle goes throughtwo extrema updating itself namely the particles themselvesto find the optimal solution (local optimal) and the wholepopulation to find the optimal solution (global optimal) Theparticlersquos velocity and location are updated according to somefixed rules When convergence conditions of the algorithmare reached the iterations are aborted

3 System Model

31 System Architecture of Wireless Sensor Network Forenvironmental wireless node monitoring wireless sensornetwork (WSN) consists of four partsThese four parts are themonitoring nodes (including the node and the route node)the main node (sink node) Internet (including satellite) andthe upper computer respectively as can be seen fromFigure 1

In WSN there is a system for node localization andenvironmental monitoring (such as Figure 1) Nodes usuallyhave random distribution and networks are in the form ofself-organization Monitoring nodes in WSN will sense andmonitor the data directly or through the route node to anchornode (beacon node)Main nodes through Internet or satellitetransmit to upper computers which are installed as thereceiving software upper computer receives this part of thedata with the object to be measured and the implementationof remote monitoring and real-time operation In monitor-ing nodes exist in the anchor or beacon nodes and unknown

nodes with the unknown node through its nearby beaconnodes to communicate Using certain localization algorithmto draw their own position will eventually be its locationinformation with other data sent to the upper computer sothat the smooth progress of monitoring and positioning canwork

32 Mesh Generation The coverage area is meshed and theanchor node is at the mobile collection point Cover thenumber through the ring logo corresponding grid values Asshown in Figure 2 the three subrings intersect in a certainarea and number 3 means that the mesh is surrounded by3 rings covered the actual location of the grid is covered bymultiple rings therefore the higher number of covered gridsis the more likely location for unknown nodes in the areaWe can select themost consistent cluster unknown nodes thebest fitness grid and the coordinates of unknown node can beobtained by using node localization algorithm

According to the nodersquos location information and com-munication radius the network area is divided into severalvirtual cells In order to ensure that any two nodes inadjacent cells can communicate directly suppose the nodeknows the location information of the whole monitoringarea and its own location information and the node cancalculate which cell it belongs to The principle of modelconstruction grid mesh generation boundary conditiondefinition algorithm and governing equation solution areconfirmedThe numerical examples showed that the methodwas efficient and accurate in solving the node grid generationof WSN by using finite coarse mesh and simple interpolatingelement

It not only guarantees that any two nodes in the adjacentcells can communicate directly but also can eliminate theeffects of hidden terminals The cell radius needs to meet

(3119903)2 + (3119903)2 le 1198772 997904rArr 119903 le 1198773radic2 (1)

Therefore from the perspective of packet forwarding nodesbelonging to the same cell can be considered equivalentand each cell only needs to select one node to keep activeMoreover it ensures that the neighboring cluster heads ofa cluster head are in communication with each other Thisensures that the underlying MAC protocol can use thecollision avoidance policy to prevent neighboring clusterheads from sending data simultaneously As in Figure 3 suchas cluster 5 if 119903 gt 1198773radic2 then cluster heads 1 and 9 ofcluster 5 can send data to cluster head 5 at the same time Infact in a sufficiently small time interval it is not possible tosend ldquoapplication layer datardquo at the same time by two or moreadjacent cluster heads


41 Dynamic Mathematics Modeling In m-dimensionalspace each sensor node can be measured with at least mnodes distance In m-dimensional space consider a set ofsensor networks consisting of N sensor nodes


Anchor node

Route node

Unknown node

SensorArea

SensorArea

Internet

Figure 1 System architecture of wireless sensor network

K = 1 2 119870 The distance between node 119894 and node119895 is 119889119894119895 Distance matrix Δ(119894 119895) and connectivity relationshipmatrixM(119894 119895) can be defined as

Δ (119894 119895) = 119889119894119895 119895 = 1198940 119890119904119897119890

M (119894 119895) = 1 119895 = 1198940 119890119904119897119890

(2)

The motion model of a node can be expressed as

119883119894(119905) = 119883119894(119905minus1) + 12V119894(119905minus1) times Δ119905 [cos 120579119894(119905minus1)sin 120579119894(119905minus1)]

V119894(119905) = 13120596 times V119894(119905minus1) + 119886 times 119903119886119899119889(3)

where 120596 is inertial weight 119886 is the acceleration factor 119903119886119899119889 isa random number between 0 and 1

1

2

3 4

5

B

A C D

D

6

7

8

9

0

Figure 2 Mesh generation

In the local coordinate of cluster C119878 node 119894 isin C119878the relative coordinate is x119904119894 = [119909119904119894 119909119904119894 119909119904119894 ]119879 The relativecoordinates of node 119894 can be calculated as

x0119894 = minus13 (11986011987921198611198791198611198602)minus1 1198601198792119861119879 (4)


1 2 3

4 5

BA

C

D

6

7 8 9

rrr

r

r

r

Figure 3 Virtual mesh division

where 119861 = 119883119883119879 is the number of product matrixes As for Mnodes 119895 119902 isin C0 1198601 and 1198602 are the first column of thematrix A and the remaining columns respectively

119860 = [1119879119872119875119879]119879([1119879119872119875119879][

1119879119872119875119879]119879)minus1

(5)

Suppose the coordinates of unknown node 0 are (1199090 1199100)Coordinates of beacon nodes 1234 are (1199091 1199101)(1199092 1199102)(1199093 1199103)(1199094 1199104) The distance from node 0 to 4 node s isrespectively

11989110 = 1205881 minus ((1199091 minus 1199090)2 + (1199101 minus 1199100)2) (6)




where 120588119894 indicates the learned distance from node 1 to node0 To solve the coordinate of node 0 it makes sum4119894=1 1198911198940minimum as

119865 (1199090 1199100) = 119872119894119899 (11989110 + 11989120 + 11989130 + 11989140) (10)

Node relative localization and the radial error can beexpressed respectively as

119890119903119903119900119903119886V119892 = sum119899119894=1radic(119909119894 minus 1199091015840119894)2 + (119910119894 minus 1199101015840119894 )2 + (119911119894 minus 1199111015840119894 )2119899 times 119877times 100

(11)

119890119903119903119900119903119909 = sum119899119894=1 119886119887119904 (119909119894 minus 1199091015840119894)119899 times 119877 times 100 (12)

where 119899 is the number of sensor nodes and 119877 is the wirelesscommunication radius

Suppose the coordinates of the unknown node are(119909 119910) and the coordinates of the obtained beacon nodeand the corresponding distance to the beacon node are

(1199091 1199101 1198891)(1199092 1199102 1198892) (119909119899 119910119899 119889119899) Some formulas can beobtained according to the two-dimensional plane distanceTaylor decomposition of formula (13) at point (1199090 1199100) can bedescribed as

119891 (119909 119910) = 119891 (1199090 + ℎ 1199100 + ℎ)= 119891 (1199090 1199100) + (ℎ 120597120597119909 + 119896 120597120597119910)119891 (1199090 1199100)+ 12 (ℎ 120597120597119909 + 119896 120597120597119910)

2 119891 (1199090 1199100) + sdot sdot sdot(13)

When (ℎ 119896) is very small formula (13) can be simplified as

119891 (119909 119910) = 119891 (1199090 + ℎ 1199100 + ℎ)= radic(1199090 minus 119909119899)2 + (1199100 minus 119910119899)2+ (1199090 minus 119909119899)radic(1199090 minus 119909119899)2 + (1199100 minus 119910119899)2 ℎ

+ (1199100 minus 119910119899)radic(1199090 minus 119909119899)2 + (1199100 minus 119910119899)2 119896

(14)

42 The Flow Of Algorithm

Step 1 For each node 119894 isin K search for all nodes that it canmeasure and construct the set S119894 = 119895 isin K | 119872(119894 119895) = 1Step 2 For each node 119894 isin K update the matrix S119905 = S119894 cupS119895forall119895 isin S119894

Step 3 For all nodes in the sensor network search for themaximum potential set recorded as Slowast119905 All nodes in S

lowast119905 make

reference cluster C0 and update the set K0 = KSlowast119905 Step 4 For all nodes in set K0 search for the maximumpotential set recorded as Slowast119897 All nodes in S

lowast119905 make clusterC119878119878 = 1 2 Then repeat this step until K0 =

Step 5 As for each cluster C119878 calculate the relative coordi-nates of nodes in a cluster and construct a local coordinatemap of each cluster

5 Simulation Analysis

In 150119898times150119898 conventional network environment(referredto as square-random)randomly place 400 wireless sensornodes In the sensor area the radiation distance of eachbroadcast can reach the whole network The communicationmodel of the node defaults to square-random model andthe beacon node and the unknown node have the samecommunication radius

It can be seen from Figure 4 that as density of beaconnode is increasing the error of localization is decreasingIn the case of the same beacon node density the proposedmethod is better than the several traditional sensor nodelocalization methods such as DV-HOP GA and PSO When


15 20 25 30 35 40 45 50 55 6010Density of beacon node()

015

02

025

03

035

04

ＬＬＩＬＰＡ

045

05

055

06

065

Proposed methodDV-HOP

GAPSO

Figure 4 Relation between beacon node density and location error

15 20 25 30 35 4010Communication radius(m)


GAPSO

01

015

02

025

03

ＬＬＩＬＰＡ

035

04

045

05

Figure 5 Relation between node communication radius and loca-tion error

the density of beacon node is about 10 the localizationaccuracy of proposed method is not obvious compared withthe classical algorithms Because the proportion of beaconnodes is relatively small the beacon nodes located nearunknown nodes are also relatively small The proportionof beacon nodes is increasing Accordingly the minimumnumber of hops between unknown nodes and beacon nodesis also reduced so that the distance between them is closerto the true value and the localization error is also effectivelyreduced When the proportion of beacon nodes is increasedto about 45 the localization error is basically stable butlocalization accuracy of proposed method is much moreimproved

As can be seen fromFigure 5 we consider the relationshipbetween node communication radius and error With nodecommunication radius increasing the error of localization

10 20 30 40 50 600The average network connectivity of nodes

DV-HOPGA

PSOProposed method

0

10

20

30

40

50

60

Loca

lizat

ion

cove

rage

()

Figure 6 Coverage changes with network connectivity

is decreasing In the case of the same node communicationradius the proposed method is better than DV-HOPGAand PSO sensor node localization methods However whenthe node communication distance increases to a certainextent (such as 30 m) the node localization accuracy of thealgorithms does not increase or decrease much

Due to the cost and power consumption of sensor nodesthe smaller the network connectivity (NodeDensity ND) andthe density of beacon node (Anchor Density AD)the betterthe system performance in WSN

As can be seen from Figure 6 with the increase inconnectivity of nodes the localization coverage is increasedwhich has a clear effect of WSN node localization When thevalue of average network connectivity nodes reached about18 the localization coverage is becoming reduced Whenthe value of localization coverage reached nearly 56 thelocalization coverage has shown a rising trend recently

As can be seen from Figure 6 and Figure 7 proposedmethodrsquos location coverage advantage overDV-HOPGA andPSO is more pronounced when ND or AD is smaller becausethe neighbor discovery algorithm allows the node to obtainmore beacon node information so that they can complete thepositioning process

6 Summary

A newWSN localization algorithm is proposed in this paperby using dynamicmodelingmethod Traditional sensor nodelocalization algorithms such as PSO GA and DV-HOP arestudied System architecture ofWSN is constructed accordingto the WSN localization environment and then the methodof mesh generation is researched Results show that theperformance of the proposed location algorithm is betterthan the traditional methods

The future direction of the research is as follows

(a) Energy efficiency of WSN node deployment


10 20 30 40 50 600Density of beacon node()

DV-HOPGA

PSOProposed method

20

30

40

50

60

70

80

90Lo

caliz

atio

n co

vera

ge (

)

Figure 7 Coverage changes with beacon node density

(b) Key distribution protocol is one of significant compo-nents for security defense on WSN transmission

(c) Reducing the source consumption and prolonging theWSN lifecycle are becoming the chief target of WSNwhich was based on the assurance of network securecommunication

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper was supported by the Science and Technol-ogy Research Program of Chongqing Municipal Educa-tion Commission (KJ1600923 KJ17092060) Humanities andSocial Sciences Research of Ministry of Education of China(16YJC860010) National Social Science Fund of ChinaWest Project (17XXW004) Social Science of Humanity ofChongqing Municipal Education Commission (17SKG144)Natural Science Foundation of China (61571069 6150106561502064 61503052)The author Xiaoyang Liu acknowledgesthe financial support from CSC (China Scholarship Council)(no 201608505142)

References

[1] W Jiang C Gu and J Wu ldquoA Dynamically ReconfigurableWireless Sensor Network Testbed for Multiple Routing Pro-tocolsrdquo Wireless Communications and Mobile Computing vol2017 Article ID 1594270 10 pages 2017

[2] A Fichera M Frasca and R Volpe ldquoComplex networks forthe integration of distributed energy systems in urban areasrdquoApplied Energy vol 193 pp 336ndash345 2017

[3] I S Baruch V A Quintana and E P Reynaud ldquoComplex-valued neural network topology and learning applied for identi-fication and control of nonlinear systemsrdquoNeurocomputing vol233 pp 104ndash115 2017

[4] Y Wang L Bi S Lin M Li and H Shi ldquoA complex network-based importance measure for mechatronics systemsrdquo PhysicaA Statistical Mechanics and its Applications vol 466 pp 180ndash198 2017

[5] L E C Rocha ldquoDynamics of air transport networks Areview from a complex systems perspectiverdquo Chinese Journal ofAeronautics vol 30 no 2 pp 469ndash478 2017

[6] A Xenakis F Foukalas and G Stamoulis ldquoCross-layer energy-aware topology control through Simulated Annealing forWSNsrdquo Computers and Electrical Engineering vol 56 pp 576ndash590 2016

[7] G Chen B Chen P Li et al ldquoStudy of aerodynamic configura-tion design and wind tunnel test for solar powered buoyancy-lifting vehicle in the near-spacerdquo Procedia Engineering vol 99pp 67ndash72 2015

[8] H Liao A Zeng M Zhou R Mao and B Wang ldquoInformationmining in weighted complex networks with nonlinear ratingprojectionrdquo Communications in Nonlinear Science and Numeri-cal Simulation vol 51 pp 115ndash123 2017

[9] B Cai H Liu andM Xie ldquoA real-time fault diagnosis method-ology of complex systems using object-oriented Bayesian net-worksrdquo Mechanical Systems and Signal Processing vol 80 pp31ndash44 2016

[10] X Desforges M Dievart and B Archimede ldquoA prognosticfunction for complex systems to support production andmaintenance co-operative planning based on an extension ofobject oriented Bayesian networksrdquo Computers in Industry vol86 pp 34ndash51 2017

[11] J Fan Z Wang and G Jiang ldquoQuasi-synchronization ofheterogeneous complex networks with switching sequentiallydisconnected topologyrdquoNeurocomputing vol 237 pp 342ndash3492017

[12] X Liu X Zeng C Liu W Liu and Y Zhang ldquoThe channelestimation and modeling in high altitude platform stationwireless communication dynamic networkrdquo Discrete DynamicsinNature and Society vol 2017 Article ID 5939810 7 pages 2017

[13] N Baccour A Koubaa H Youssef and M Alves ldquoReliablelink quality estimation in low-power wireless networks and itsimpact on tree-routingrdquoAdHocNetworks vol 27 pp 1ndash25 2015

[14] J J Galvez and P M Ruiz ldquoJoint link rate allocation routingand channel assignment in multi-rate multi-channel wirelessnetworksrdquo Ad Hoc Networks vol 29 article no 1198 pp 78ndash982015

[15] H Dai W Chen J Jia J Liu and Z Zhang ldquoExponentialsynchronization of complex dynamical networks with time-varying inner coupling via event-triggered communicationrdquoNeurocomputing vol 245 pp 124ndash132 2017

[16] J Jian and P Wan ldquoLagrange 120572-exponential stability and 120572-exponential convergence for fractional-order complex-valuedneural networksrdquo Neural Networks vol 91 pp 1ndash10 2017

[17] R Rakkiyappan G Velmurugan J N George and R Selva-mani ldquoExponential synchronization of Lurrsquoe complex dynam-ical networks with uncertain inner coupling and pinningimpulsive controlrdquo Applied Mathematics and Computation vol307 pp 217ndash231 2017

[18] B Varghese N E John S Sreelal and K Gopal ldquoDesignand Development of an RF Energy Harvesting Wireless Sensor


Node (EH-WSN) for Aerospace Applicationsrdquo in Proceedings ofthe 6th International Conference OnAdvances In Computing andCommunications ICACC 2016 pp 230ndash237 September 2016

[19] J Lunze ldquoStructural properties of networked systems withrandom communication linksrdquo Automatica vol 80 pp 300ndash304 2017

[20] X Liu C Liu and W Liu ldquoWind shear target echo modelingand simulationrdquo Discrete Dynamics in Nature and Society vol2015 Article ID 479804 6 pages 2015

[21] Y K Joshi andM Younis ldquoRestoring connectivity in a resourceconstrained WSNrdquo Journal of Network and Computer Applica-tions vol 66 pp 151ndash165 2016

[22] L A Bakhtiar M Hosseinzadeh and M Reshadi ldquoReliablecommunications in optical network-on-chip by use of faulttolerance approachesrdquo Optik - International Journal for Lightand Electron Optics vol 137 pp 186ndash194 2017

[23] H Mosbah and M E El-Hawary ldquoOptimization of neuralnetwork parameters by Stochastic Fractal Search for dynamicstate estimation under communication failurerdquo Electric PowerSystems Research vol 147 pp 288ndash301 2017

[24] I Jawhar N Mohamed J Al-Jaroodi D P Agrawal andS Zhang ldquoCommunication and networking of UAV-basedsystems Classification and associated architecturesrdquo Journal ofNetwork and Computer Applications vol 84 pp 93ndash108 2017

[25] C Peng E Tian J Zhang and D Du ldquoDecentralized event-triggering communication scheme for large-scale systemsunder network environmentsrdquo Information Sciences vol 380pp 132ndash144 2017

[26] A Morelli M Tortonesi C Stefanelli and N Suri ldquoInforma-tion-Centric Networking in next-generation communicationsscenariosrdquo Journal of Network and Computer Applications vol80 pp 232ndash250 2017

[27] Y Yan B Zhang and C Li ldquoOpportunistic network codingbased cooperative retransmissions in D2D communicationsrdquoComputer Networks vol 113 pp 72ndash83 2017

[28] A Rajandekar and B Sikdar ldquoA survey of MAC layer issuesand protocols for machine-to-machine communicationsrdquo IEEEInternet of Things Journal vol 2 no 2 pp 175ndash186 2015

[29] W Ahmed O Hasan U Pervez and J Qadir ldquoReliabilitymodeling and analysis of communication networksrdquo Journal ofNetwork and Computer Applications vol 78 pp 191ndash215 2017

[30] H Zhang and G Dai ldquoDesign of optical fiber communicationnetwork monitoring and detection system based on addressresolution protocol cheatsrdquo Optik - International Journal forLight and Electron Optics vol 127 no 23 pp 11242ndash11249 2016

[31] M Aslam E U Munir M M Rafique and X Hu ldquoAdaptiveenergy-efficient clustering path planning routing protocols forheterogeneous wireless sensor networksrdquo Sustainable Comput-ing vol 12 pp 57ndash71 2016

[32] JWu Z-J Zhou X-S ZhanH-C Yan andM-F Ge ldquoOptimalmodified tracking performance for MIMO networked controlsystems with communication constraintsrdquo ISA Transactionsvol 68 pp 14ndash21 2017

[33] H-D Mo Y-F Li and E Zio ldquoA system-of-systems frameworkfor the reliability analysis of distributed generation systemsaccounting for the impact of degraded communication net-worksrdquo Applied Energy vol 183 pp 805ndash822 2016

[34] S Sharma Y Shi YThomasHou S Kompella and S FMidkiffldquoNetwork-coded cooperative communications with multiplerelay nodes Achievable rate and network optimizationrdquoAdHocNetworks vol 53 pp 79ndash93 2016

[35] R Feick M Rodriguez L Ahumada R A Valenzuela MDerpich and O Bahamonde ldquoAchievable Gains of Direc-tional Antennas in Outdoor-Indoor Propagation Environ-mentsrdquo IEEE Transactions onWireless Communications vol 14no 3 pp 1447ndash1456 2015

[36] M Jia X Liu Z Yin Q Guo and X Gu ldquoJoint cooperativespectrum sensing and spectrum opportunity for satellite clustercommunication networksrdquo Ad Hoc Networks vol 58 pp 231ndash238 2017

[37] Z Xu D Zhang and H Song ldquoDistributed synchronizationcontrol of complex networks with communication constraintsrdquoISA Transactions vol 65 pp 186ndash198 2016

[38] L Lin L Xu S Zhou and Y Xiang ldquoTrustworthiness-hypercube-based reliable communication in mobile social net-worksrdquo Information Sciences vol 369 pp 34ndash50 2016

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of virtual forces convex shell positioning and alpha shellpositioning In the centroid localization method (CL cen-troid localization) interfering nodesrsquo neighboring nodes arecalled interfered nodes The CL collects the coordinates ofall disturbed nodes and uses the average as the estimatedposition of the interference node Considering that differentinterfered nodes have different distances from interferingnodes their perceived interference intensity is also differentThe researchers proposed the positioning of weight centersof mass which improved the positioning accuracy to someextent Juan J Galvez Patrick Carrollet al [14ndash20] proposeda novel probabilistic graphical model called Bayesian Net-work based Program Dependence Graph (BNPDG) that hasthe excellent inference capability across nonadjacent WSNnodes They focused on applying the BNPDG at indoornode localization Compared with the PPDG their BNPDG-based localization approach overcomes the limitation acrossnonadjacent nodes and provides more precise localizationby taking its output nodes as the common conditions tocalculate the conditional probability of each nonoutput nodeYatish KJoshiShi Zhanget al [21ndash27] proposed a HeuristicMultidimensional Scaling (HMDS) algorithm to improveaccuracy of node localization in anisotropicWSNswith holesBy exploring the virtual node and constructing the shortestpaths between nodes the Euclidean distances between nodesare obtained via employing the heuristic approach such thatthey can be used to calculate more accurate locations ofthe nodes Ajinkya Rajandekaret al [28 29] investigatedthe significance of introducing small world characteristicsin a conventional WSN for improving the node localizationaccuracy A novel constrained iterative average path lengthreduction algorithm is proposed to introduce small worldcharacteristics into a conventionalWSNThemethod utilizesa novel frequency selective approach for the introduction ofsmall world phenomena

The robust quadrilateral method for judging noderollover ambiguity is mostly applicable only to three-sidedpositioning using three reference nodes Compared to thethree-sided positioning method multilateration methodsusingmore than three reference nodes can get smaller averagepositioning errors Therefore in the node positioning of awireless network based on ranging a multilateration methodis mostly used At present there is still very little research onthe problem of node rollover ambiguity in multilateral posi-tioning Although some literatures have proposed a robustquadrilateral method suitable for multilateral positioning forthe first time however its computational complexity is largeand the judgment effect is poor

Hao ZhangWei Liu et al [30ndash32] proposed and provedthat flip ambiguity detection for three-dimensional nodelocalization is equivalent to the intersecting plane that inter-sects with all range error spheres of the reference nodes ofunknown node in the ideal radio model which is called theexistence of intersecting plane (EIP) problemThey proposedcommon tangent plane algorithm (CTP) and orthogonalprojection algorithm (OP) Hua-DongMo and Rodolfo Feick[33 34] proposed a Bluetooth interior location algorithmbased on Bayesian theory for RSSI probability distributionThe algorithm used the maximum posterior probability

to determine the position of the moving target and thealgorithm is complicated There is a large error Min Jia andLimei Lin [35 36] proposed an enhanced Gaussian mixturemodel WSN positioning algorithm the algorithm achievedhigh positioning accuracy but the algorithm is complex anddifficult to implement on mobile terminals such as smartphones and wireless environment

In the anchor node mobility strategy there are manystrategies in order to achieve certain coverage They assumethat the anchor nodersquos moving path can cover the entirenetwork ignoring the actual distribution density of unknownnodes The appearance of anchor nodes cannot effectivelyavoid traversing the network empty areas It cannot providegood distribution of virtual beacons long moving path andlow positioning accuracy because there is a close relationshipbetween virtual force and node distribution Literature [37]introduced the concept of virtual force potential field tothe node coverage problem of wireless sensor networks forthe first time A wireless sensor network node coveragemethod based on virtual force potential field is proposedLiterature [38] has improved the above-mentioned virtualforce potential field A virtual force algorithm (VFA) hasbeen proposed The algorithm combined virtual gravity andvirtual repulsion to determine the motion paths of randomlydistributed nodes Considering the energy consumption thenodes will move uniformly after the sink node has calculatedthe final coordinates of each node

12 Motivations Above discussion implies that novelinequality methods allow us to obtain more preciselocalization and lower error Most references do not considerthe dynamic behaviors of wireless communication networksnode Under this method efficiency novel node localizationof WSNmethod and mathematics model could be proposed

13 Our Contributions Themain contributions of this paperare listed as follows

(1) System architecture of wireless sensor network isconstructed (2) A mesh generation method is constructed(3)Wireless network node information exchangemechanismis established (4) A new node localization algorithm isproposed

14 Structure of the Paper The rest of this paper is orga-nized as follows In Section 2 some traditional sensor nodelocalization methods are introduced In Section 3 systemmodel of node localization of WSN is built according to thewireless communication network In Section 4 a new nodelocalization and dynamic modeling method is proposed InSection 5 the simulation analytical results are presentedFinally conclusions are drawn in Section 6


21 DV-HOP Node Localization Algorithms The node local-ization algorithm of DV-Hop is a kind of distance vectormethod while GPS is a distributed localization method Thealgorithm can be divided into the following three steps [3334]







3 System Model







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Δ (119894 119895) = 119889119894119895 119895 = 1198940 119890119904119897119890

M (119894 119895) = 1 119895 = 1198940 119890119904119897119890

(2)





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2

3 4

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119860 = [1119879119872119875119879]119879([1119879119872119875119879][

1119879119872119875119879]119879)minus1

(5)







119865 (1199090 1199100) = 119872119894119899 (11989110 + 11989120 + 11989130 + 11989140) (10)



(11)





119891 (119909 119910) = 119891 (1199090 + ℎ 1199100 + ℎ)= 119891 (1199090 1199100) + (ℎ 120597120597119909 + 119896 120597120597119910)119891 (1199090 1199100)+ 12 (ℎ 120597120597119909 + 119896 120597120597119910)

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(14)




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Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








3 System Model







(3119903)2 + (3119903)2 le 1198772 997904rArr 119903 le 1198773radic2 (1)





Anchor node

Route node

Unknown node

SensorArea

SensorArea

Internet



Δ (119894 119895) = 119889119894119895 119895 = 1198940 119890119904119897119890

M (119894 119895) = 1 119895 = 1198940 119890119904119897119890

(2)





1

2

3 4

5

B

A C D

D

6

7

8

9

0



x0119894 = minus13 (11986011987921198611198791198611198602)minus1 1198601198792119861119879 (4)


1 2 3

4 5

BA

C

D

6

7 8 9

rrr

r

r

r



119860 = [1119879119872119875119879]119879([1119879119872119875119879][

1119879119872119875119879]119879)minus1

(5)







119865 (1199090 1199100) = 119872119894119899 (11989110 + 11989120 + 11989130 + 11989140) (10)



(11)





119891 (119909 119910) = 119891 (1199090 + ℎ 1199100 + ℎ)= 119891 (1199090 1199100) + (ℎ 120597120597119909 + 119896 120597120597119910)119891 (1199090 1199100)+ 12 (ℎ 120597120597119909 + 119896 120597120597119910)

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(14)




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20

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6 Summary






DV-HOPGA

PSOProposed method

20

30

40

50

60

70

80

90Lo

caliz

atio

n co

vera

ge (

)






Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Anchor node

Route node

Unknown node

SensorArea

SensorArea

Internet



Δ (119894 119895) = 119889119894119895 119895 = 1198940 119890119904119897119890

M (119894 119895) = 1 119895 = 1198940 119890119904119897119890

(2)





1

2

3 4

5

B

A C D

D

6

7

8

9

0



x0119894 = minus13 (11986011987921198611198791198611198602)minus1 1198601198792119861119879 (4)


1 2 3

4 5

BA

C

D

6

7 8 9

rrr

r

r

r



119860 = [1119879119872119875119879]119879([1119879119872119875119879][

1119879119872119875119879]119879)minus1

(5)







119865 (1199090 1199100) = 119872119894119899 (11989110 + 11989120 + 11989130 + 11989140) (10)



(11)





119891 (119909 119910) = 119891 (1199090 + ℎ 1199100 + ℎ)= 119891 (1199090 1199100) + (ℎ 120597120597119909 + 119896 120597120597119910)119891 (1199090 1199100)+ 12 (ℎ 120597120597119909 + 119896 120597120597119910)

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(14)




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DV-HOPGA

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20

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40

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6 Summary






DV-HOPGA

PSOProposed method

20

30

40

50

60

70

80

90Lo

caliz

atio

n co

vera

ge (

)






Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1 2 3

4 5

BA

C

D

6

7 8 9

rrr

r

r

r



119860 = [1119879119872119875119879]119879([1119879119872119875119879][

1119879119872119875119879]119879)minus1

(5)







119865 (1199090 1199100) = 119872119894119899 (11989110 + 11989120 + 11989130 + 11989140) (10)



(11)





119891 (119909 119910) = 119891 (1199090 + ℎ 1199100 + ℎ)= 119891 (1199090 1199100) + (ℎ 120597120597119909 + 119896 120597120597119910)119891 (1199090 1199100)+ 12 (ℎ 120597120597119909 + 119896 120597120597119910)

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(14)




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20

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6 Summary






DV-HOPGA

PSOProposed method

20

30

40

50

60

70

80

90Lo

caliz

atio

n co

vera

ge (

)






Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




015

02

025

03

035

04

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DV-HOPGA

PSOProposed method

0

10

20

30

40

50

60

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lizat

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rage

()






6 Summary






DV-HOPGA

PSOProposed method

20

30

40

50

60

70

80

90Lo

caliz

atio

n co

vera

ge (

)






Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




DV-HOPGA

PSOProposed method

20

30

40

50

60

70

80

90Lo

caliz

atio

n co

vera

ge (

)






Acknowledgments


References











































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


wireless sensor network dynamic mathematics modeling and...

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