A Weighted DV-Hop Localization Scheme for Wireless Sensor Networks

8/9/2019 A Weighted DV-Hop Localization Scheme for Wireless Sensor Networks

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A Weighted DV-Hop Localization Scheme for Wireless Sensor Networks

Jian Li, Jianmin ZhangDepart. of Computer Science

Henan Institute of EngineeringZhengzhou 451191, China

{lj2006, zjm1996}@163.com

Liu XiandeDepart. of Optoelectronics Engineering

Huazhong University of Sci. and Tech.Wuhan 430074, China

[email protected]

Abstract Localization is an important problem in wirelesssensor networks (WSNs), since location information is widelyrequested in various location-dependent applications. As one ofthe range-free localization algorithm DV-Hop, a well knownlocalization algorithm, can be simply implement in real WSNs.To improve the accuracy of localization, this paper proposes animproved DV-Hop algorithm. The proposed algorithm isderived from DV-Hop algorithm, and uses weight of anchors toimprove localization accuracy without needing no additional

hardware device. Simulation results show that the improvedDV-Hop algorithm can provide more accurate locationestimation than the DV-Hop algorithm.

Keywords- sensor networks; DV-Hop; node localization

I. I NTRODUCTIONRecent technological advances have enabled the

development of low-cost, low-power and multifunctionalsensor devices. In general, wireless sensor networks intend to

provide information on spatio-temporal characteristics of theobserved physical world. Hence, the determination of the

physical position of sensor nodes is a fundamental issue formany applications of wireless sensor networks. A number ofapplications, such as object tracking, environmentmonitoring, inherently rely on location information. Besides,location information is essential to many location-awaresensor network communication protocols, such as packetrouting and sensing coverage. All these mentioned abovemake localization algorithm become one of the mostimportant issues in WSNs researches. However, it has been achallenging task to design a practical algorithm for nodelocalization given the constraints that are imposed onsensors, including limited power, low cost.[1,2]

In typical WSNs, it is not infeasible that all the sensornodes have the ability to know their location informationinitially. Normally, sensor nodes are intended to be low-costdisposable devices, and currently developed solutions suchas global position system (GPS)[16] are inadequate for thehardware and power-limited sensors. Traditional localizationtechniques are not well suited for these requirements.Including a GSP receiver on each device is cost and energy

prohibitive for many applications, not sufficiently robust to jamming for military applications, and limited to outdoorapplications. In general conditions, it is assumed that only asmall portion of sensor nodes are aware of their positioninformation by GPS or manual configuration in mostlocalization methods. We call these nodes anchor nodes and

other nodes, called unknown nodes, can estimate their position by anchor nodes.

Localization in wireless sensor networks is different fromtraditional wireless communication technology. There has

been an increasing interest in the localization technique forWSNs and many localization algorithms for sensor networkshave been developed to provide sensor nodes locationinformation. Generally, the existing localization algorithms

can further be divided into two categories: ranged-based [3-7]and range-free [8-14]. Range-based algorithms exploit range(distance or angle) information for localization. Although theuse of range measurements results in a fine-grainedlocalization scheme, range-based algorithms require thesensor to contain additional hardware to make rangemeasurements. Range-free algorithms do not need absoluterange information. But the accuracy is less than the range-

based but it can still satisfy many applications requirements.Range-free algorithms do not need any special hardware toacquire radio signal strengths, angle of arrival of signal, sothe range-free algorithms are more economical, cost-effective, and feasible for the large-scale wireless sensornetworks. Typical -range-free algorithms include Centroid

algorithm [8], DV-Hop [9,10], amorphous [11], APIT [12],MDS-MAP[13,14], etc.A feasible distributed localization algorithm should be

easily deploy, have good accuracy, promotes scalability, and be energy efficient. Among many of range-free localizationalgorithms, DV-Hop is a neat scheme which worth furtherinvestigation. Its basic idea realize on transforming thedistance to all anchor nodes from hops to meters by usingcomputer average size of a hop. The advantages of the DV-Hop scheme are its simplicity and the fact that it does notdepend on measurement error. It is complimented by manyresearchers because of its facility, friability and goodcoverage quality. However, the DV-Hop techniqueintroduces errors that propagated to the computation of a

nodes location. Based on the DV-Hop algorithm, manyimprovements are given by following researchers [17,18].To decrease the localization error in DV-Hop algorithm,

in this paper we propose an improved DV-Hop algorithm,which user weight of anchor to increase the accuracy oflocalization.

The remainder of the paper is organized as follows. In thenext section, we introduce the background and related workfor location system. In section , we give the weighted DV-

2009 Eighth IEEE International Conference on Embedded Computing; IEEE International Conference on Scalable Computing and Communications

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Hop algorithm in detail. Simulation and analyses are shownin section . Finally, the conclusions are given in section .

II. DV -HOP ALGORITHM In this section, we review the DV-Hop algorithm

proposed by Niculescu and Nath [9,10]. This scheme

consists three phases. First, it employs a classical distancevector exchange so that all nodes in the network getdistances, in hops, to the anchor nodes. And then, it estimatesan average size for one hop, which is then deployed as acorrection to the entire network. Finally, unknown nodescompute their location by multilateration.

In the first phase, all anchor nodes broadcast itsinformation to its neighbor nodes. The broadcastinginformation packages including minimum hop count peranchor node of all the packages it has received. Eachreceiving node maintains the minimum counter value peranchor of all beacons it receives and ignores those beaconswith higher hop-count values. Beacons are flooded outwardwith hop-count values incremented at every intermediate hop.

Such updates and further broadcast will continue until all theshortest paths are found. Through this mechanism, all nodesin the network get the shortest distance, in hops, to everyanchor.

In the second phase, once an anchor gets hop-count valueto other anchors, it estimates an average size for one hop,which is then flooded to the entire network. After receivinghop-size, all nodes multiply the hop-size by the hop-countvalue to derive the physical distance to the anchor. Theaverage hop-size is then estimated by anchor i as follow:

+

=

i j

ij

i j ji ji

i h

y y x x 22 )()(HopSize (1)

Where ( xi, yi), ( x j, y j) are coordinates of anchor i andanchor j, hij is the hops between anchor i and anchor j.

Once the average hop-size is calculated, each anchornode broadcasts its hop-size to network using controlledflooding. Unknown nodes receive hop-size information, andsave the first one. At the same time, they transmit the hop-size to their neighbor nodes. This scheme could assure thatthe most nodes receive the hop-size from anchor node whichhas the least hops between them. When an unknown nodeaccepts the information from one anchor node, it computesthe distance between its self and the anchor nodes as thefollow formula:

ijiijh HopSized = (2)

Where hij is the monomial hops between anchor i andunknown node j.

In the third step, each unknown node computes itslocation coordinate. Suppose ( x, y) be the unknown node D location and ( xi, yi) the known location of the ith anchornode receiver. Let d i be the ith anchor node distance tounknown nodes D, then we have

22 )()( iii y y x xd += (3)

Let 'id be the estimations distance between the ithanchor node distances to unknown nodes D. Thus thedifference between the measured and actual distance can berepresented as iii d d =

' . Several methods are designed

to deal with the ranging noise. The lease squaresminimization is one of them to determine the value ( x, y) that

minimizes =

n

ii

1

' . This problem can be solved by a

numerical solution to an over-determined linear system [15].We re-write the distance constrains as follows: AX = B,

where,

=

nnnn

nn

nn

y y x x

y y x x

y y x x

A

11

22

11

2MM

++

++

++

=

221

221

221

222

222

222

221

221

221

nnnnnn

nnn

nnn

y y x xd d

y y x xd d y y x xd d

BM

=

y

x X .

Now the least square solution is estimate for P thatminimizes 2|||| B AX , then we can calculate

B A A A X T T 1)( = (4)

III. WEIGHTED DV- HOP ALGORITHM In this section, we will introduce the weighted algorithm

that extends the method in [9 10]. In DV-Hop, it supposesthat the closest anchor can provide the most accuracy hop-size for the unknown nodes, but in reality this supposes isntthat case. In real situation some anchors might be placed tooclose to each other. As anchor nodes add up the number ofhops in all the shortest paths to other anchor nodes, if someanchor nodes are too close to each other, the accuracy ofhop-size will be affected. Also from these, when there aremany anchor nodes, the hop-size messages from someanchor nodes are just wasted. Since each piece ofinformation brings its own knowledge, it would be better ifwe can make full use of it. It is obviously that the hop-size

provided by some anchor nodes has more impact on the position of unknown nodes than others. In order to reflect theaffect of different anchor in the unknown nodes localization,in our algorithm each anchor node is given a weight. Theweight of each anchor node is the production of positionweight and distance weight. Here, the hop-size weightreflects the accuracy of hop-size provided by the anchornodes. The distance weight reflects the distance between theanchor nodes the unknown nodes.

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To introduce the weighted DV-Hop algorithm, we alsodivide the proposed algorithm into three phases: MinimalHop-count Computation, Hop-size and WeightedComputation, Location Estimation. In the following, we will

present the weighted DV-Hop algorithm in details.

A. Hop-count Computation

The goal of this phase is that nodes in the network get theminimal hop-count to every anchor node. As in DV-Hopalgorithm, in this phase anchor nodes flood their locationthroughout the network maintaining a running hop-count ateach node along the way. This phase is similar to the DV-Hop algorithm, so we dont discuss this phase here.

B. Hop-size and Weighted ComputationIn this phase, all nodes get the distance to the anchor

nodes and the weight of anchor nodes. To achieve theregoals, the following three steps are needed.

Step 1: In this step, every node estimates an average sizefor one hop and the hop-size weight of other anchor nodes.

1. ij

ji jiij h

y y x x HopSize22

)()( +

= (5)

Where ( xi, yi), ( x j, y j) are coordinates of anchor i andanchor j, hij is the hops between anchor i and anchor j.

2. 1

=

N

HopSize HopSize i j

ij

i (6)

Where N is the number of anchor nodes3. Then , anchor nodes i computes the hop-size weight

of anchor nodes j as follows:

22 /)(1 r HopL HopLWd iijij

= (7)

Here, if Wsij to all nodes.

Step 2: After the step 1 for broadcast, all of nodes getthe HopSize and Wd of all anchor nodes. Node i calculatesthe HopSize and the hop-size weight Whi of anchor nodes j asfollow:

N

HopSizeSize

N

k k

== 1 Hop (8)

ij j h

Wh 1= (9)

Where N is the number of anchor nodes, HopSize k iscomputer by anchor node k hij is the minimal hops

between unknown node i and the anchor node j. Step 3: At this step, unknown nodes i computes the

distance to the anchor nodes j and weight of the anchor node j as follow:

HopSizehd ijij = (10)

N

Wd WhW

N k

k jk

ijij

=

== 1 (11)

Where, Ws jk is anchor node j computes the hop-sizeweight of anchor nodes k.

C. Location EstimationAn unknown node can calculate its location when it

has get estimate distance to at least three anchors andweights of the three anchors. In DV-Hop algorithm, the

position of unknown nodes is calculated by using leastsquare method. We propose to use weighted lease squaremethod.

( ) +==

n

iiiii d y y x xw y x f

1

2222 )()(min),(

where, wi is the weight of anchor node i.

then we have '' b X A = Where

=

y

x X

=

nnnn

nn

nnnn

nn

y yww

y yww

x xww

x xww

A

122

1

122

1

122

1

122

1'

(2

)(2

)(2

)(2MM

++

++

=

)(

)(

21

2221

221

221

21

2221

221

221

'

nnnnnnnn

nnnn

d d y y x xww

d d y y x xww

b M

Then the position of unknown nodes is

''1'' )( b A A A X T T = (12)

IV. SIMULATION RESULTS AND PERFORMANCE ANALYSIS In this section, simulation results are presented and

analyzed. We compare the DV-Hop and our proposedalgorithm to evaluated location performance. And we offersimulation results under the following simulationcircumstance: All the sensor nodes are random placed in asquare area with the fixed size of 100 m 100m. The radio

range of sensor nodes r is set to 15 meter.In the simulation the localization error is defined as the

ratio of the difference between the estimated localization andreal localization to the communication range of sensor nodes.The localization error reflects the accuracy of localization.The less the localization error is, the more accurate thelocalization performance.

Here two graphs of simulation results are presented tocompare the localization performance of the two localizationschemes. Figure 1 show the localization error vs. ratio of

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anchor nodes when the number of sensor nodes is 200, andthe Figure 2 shows the localization error vs. the number ofnodes when the ratio of anchor nodes is 10%. As can be seenfrom the Figure 1 and Figure 2, the proposed weighted DV-Hop algorithm can provide more accurate location estimationthan the DV-Hop algorithm. As in figure 1, for the sameratio of anchor nodes, the position error in our weighted DV-Hop algorithm is smaller than in DV-Hop algorithm. Forexample, the proposed algorithm has an average localizationerror of about 41% when the anchor nodes ratio is 10%,whereas the DV-Hop has an average localization error ofabout 48.5%. In figure 2, when there are 250 sensor nodes(including anchor nodes and unknown nodes) the averagelocalization error is 36% in the proposed weighted DV-Hopalgorithm, while the average error 42% in the original DV-Hop algorithm.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.3

0.35

0.4

0.45

0.5

0.55

0.6

Ratio of Anchor Nodes

L o c a

l i z a

t i o n

E r r o r

DV-HopWeighted DV-Hop

Figure 1 Localization Error vs. Ratio of Anchor Nodes with 200 sensor

nodes

150 175 200 225 2500.3

0.35

0.4

0.45

0.5

0.550.6

0.65

0.7

Number of Nodes

L o c a

l i z a

t i o n

E r r o DV-Hop

Weighted DV-Hop

Figure 2 Localization Error vs. Number of Nodes Given 10 % of Anchor

nodes

V. CONCLUSION In this paper, we present a weighted DV-Hop algorithm

that improves the original DV-Hop algorithm significantly.The proposed weighted DV-Hop algorithm gives everyanchor a weight which reflects the effects of anchor. In thisalgorithm an unknown node computes the hop-size based allthe hop-size values it receives from the anchors, instead of

just taking the first received hop-size value as in originalDV-Hop algorithm. Using this strategy, the position ofunknown nodes is calculated by using weighted least squaremethod. The simulation results show that the proposed

weighted algorithm can improve location accuracy than theoriginal DV-Hop algorithm.

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A Weighted DV-Hop Localization Scheme for Wireless Sensor Networks

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