sensors Article
I-DWRL: Improved Dual Wireless Radio Localization Using Magnetometer Abdul Aziz 1 , Ramesh Kumar 2 and Inwhee Joe 3, * 1 2 3
*
Department of Electronics and Computer Engineering, Hanyang University, Seoul 04763, Korea;
[email protected] Department of Electronic Engineering, Dawood University of Engineering and Technology, Karachi 74800, Pakistan;
[email protected] Division of Computer Science and Engineering, Hanyang University, Seoul 04763, Korea Correspondence:
[email protected]; Tel.: +82-2-2220-1088
Received: 30 August 2017; Accepted: 13 November 2017; Published: 15 November 2017
Abstract: In the dual wireless radio localization (DWRL) technique each sensor node is equipped with two ultra-wide band (UWB) radios; the distance between the two radios is a few tens of centimeters. For localization, the DWRL technique must use at least two pre-localized nodes to fully localize an unlocalized node. Moreover, in the DWRL technique it is also not possible for two sensor nodes to properly communicate location information unless each of the four UWB radios of two communicating sensor nodes cannot approach the remaining three radios. In this paper, we propose an improved DWRL (I-DWRL) algorithm along with mounting a magnetometer sensor on one of the UWB radios of all sensor nodes. This addition of a magnetometer helps to improve DWRL algorithm such that only one localized sensor node is required for the localization of an unlocalized sensor node, and localization can also be achieved even when some of the four radios of two nodes are unable to communicate with the remaining three radios. The results show that with the use of a magnetometer a greater number of nodes can be localized with a smaller transmission range, less energy and a shorter period of time. In comparison with the conventional DWRL algorithm, our I-DWRL not only maintains the localization error but also requires around half of semi-localizations, 60% of the time, 70% of the energy and a shorter communication range to fully localize an entire network. Moreover, I-DWRL can even localize more nodes while transmission range is not sufficient for DWRL algorithm. Keywords: DWRL; I-DWRL; UWB; dual radio; magnetometer; localization; wireless sensor network
1. Introduction Wireless sensor networks have been a vital research area for many years. Nowadays sensor nodes are used widely in variety of applications, devices, buildings, vehicles, and so forth. The first research in this area was motivated by military applications, with defense advanced research projects agency (DARPA) funding a number of prominent research projects such as Smart Dust, and neural engineering science and technology (NEST) [1]. Wireless sensor networks (WSNs) consist of collection of small, low-cost, usually randomly placed heterogeneous sensor nodes connected by wireless media to form a sensor field. Nodes monitor the environment, gather data and send it to the sink node through single or multichip communications. Its many applications include battlefield surveillance, habitat monitoring, environmental monitoring, health applications, target tracking, event detection, vehicle tracking, and forest fire detection [2]. To make the collected information valuable, many applications such as geographical routing and location-based information applications require the exact locations of deployed sensor nodes. Therefore, many location-finding schemes have been proposed for wireless sensor networks.
Sensors 2017, 17, 2630; doi:10.3390/s17112630
www.mdpi.com/journal/sensors
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This paper is organized as follows. Section 2 covers related work and details of the dual wireless radio localization (DWRL) algorithm. An improved dual wireless radio localization (I-DWRL) scheme is presented in Section 3. Section 4 presents the simulation work and results, and then we conclude the paper in Section 5. 2. Related Work Localization in WSN is an active area of research with several surveys [3–11] and more than 50 localization algorithms. Localization techniques can be generally categorized as the following:
• • • •
absolute vs. relative centralized vs. decentralized range free vs. range based anchor vs. anchorless.
Absolute localization is to locate sensor nodes with respect to coordinate system, whereas in relative localization, the location of sensor nodes is found in relation to other sensors. Global positioning system is an example of absolute localization [12]. In centralized localization [13,14], one central base station is present for computation. The disadvantage is the overhead, and the cost also increases. Multidimensional scaling map (MDS-MAP) [14] is a centralized algorithm for computing the coordinates of unknown nodes after approximating the distances between the nodes using the shortest path algorithm. In contrast, decentralized or distributed localization techniques [15,16] depend on each sensor node being able to determine its location with only limited communication with nearby nodes. Range-free [17] techniques depend upon factors such as the number of hop counts and connectivity, whereas range-based techniques include received signal strength indication (RSSI) [18], time of arrival (ToA) [19], angle of arrival (AoA) [20], time difference of arrival (TDoA), lateration and angulation, and so forth [10]. There is wide range of radio signals but ultrawide band (UWB) signals are particularly well suited for range-based localization, since they can provide accurate and reliable range measurements due to their fine delay resolution and robustness in harsh environments [21–24]. The anchor-based algorithms provide a starting point for an algorithm by using the position of anchor nodes. In contrast, anchorless schemes measure the distance between nodes for creating a local map of the nodes. The local map created is not a unique one and can be stitched to any coordinate system with the help of translation, rotation or flipping. DWRL and I-DWRL algorithms fall into the category of range-based localization where an anchor node is also used to start the localization process. Both algorithms are designed for coplanar static wireless sensor and ad hoc networks. 2.1. Dual Wireless Radio Localization The dual wireless radio localization (DWRL) algorithm [25] is a Global Positioning System (GPS) free-range based dual radio wireless localization algorithm for static wireless networks, where each node nx has two UWB wireless radios named Radio1 (Rn1 x ) and Radio2 (Rn2 x ) that are attached to an a priori known positions on board, as shown in Figure 1. The straight line joining Rn1 x and Rn2 x is considered as the axis of node. In this technique one of the nodes is designated as sink node whose Rn1 x is set at origin (x nRx1 , ynRx ) = (0, 0) and Rn2 x in the direction of positive x-axis (x nRx2 , ynRx2 ) = (d x , 0), 1 which means the angle θx between the x-axis and the axis of the node is zero and, here, dx is the distance between Rn1 x and Rn2 x . Two nodes are said to be collinear if there is a straight line passing through all four radios of the nodes. The authors of the DWRL algorithm have experimentally shown in their paper and suggested that, for a typical wireless sensor node, the inter-radio distance of 60 cm is sufficient for successful localization [25]. While an increased inter-radio distance improves localization accuracy, in all of our
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R 1n1 Sensors 2017, 17, 2630
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R n21
n1 d1 θ x =0
n1 R1
(x ,y )=(0,0)
(x nR12 ,y Rn12 )=(d1 ,0)
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Figure 1. Dualinter-radio wireless radio node. of 60 cm to avoid a greater size of simulation scenarios we consider the minimum distance sensor nodes for practical scenarios. Two nodes are said to be collinear if there is awhich straight passingbelow. through all four radios of the is presented in three steps, areline presented SensorsDWRL 2017, 17,algorithm 2630 3 of 16 nodes. The authors of the DWRL algorithm have experimentally shown in their paper and suggested that, for a typical wireless sensor node,n1the inter-radio distance of 60 cm is sufficient for successful R n21 n1 R1 localization [25]. While an increased inter-radio distance improves localization accuracy, in all of our n1 (x n11 ,y R1 )=(0,0) (x nR12 ,y Rn12 )=(d1 ,0) d1 simulation scenarios we Rconsider the minimum inter-radio distance of 60 cm to avoid a greater size θ x =0 of sensor nodes for practical scenarios. DWRL algorithm is presentedFigure in three steps, whichradio are presented below. 1. Dual wireless node. Figure 1. Dual wireless radio node.
2.1.1.Two Semi-Localization nodes are said to be collinear if there is a straight line passing through all four radios of the 2.1.1. Semi-Localization nodes. The authors of the DWRL algorithm have experimentally shown in their paper and suggested The first step towards the localization of any unlocalized node with the help of a sink node or step wireless towardssensor the localization any unlocalized thesufficient help of afor sink node or that, The for afirst typical node, the of inter-radio distancenode of 60with cm is successful some other already localized node is semi-localization. For localization only, UWB radio ranging is some other [25]. already localized node is semi-localization. For localization only,accuracy, UWB radio ranging localization While an increased inter-radio distance improves localization in all of our used to measure four distances— r1 , r2 , r3 and r4 —between the radios of the two nodes that are is used to measure , r2 , r3 andinter-radio r4 —between the radios of the two nodes thatsize are simulation scenariosfour we distances—r consider the 1minimum distance of 60 cm to avoid a greater within range range of other, shown an unlocalized unlocalized within of each each other, as asscenarios. shown in inFigure Figure2.2.Here Here nn11 is is the the sink sink node, node, and and nn 22 isisan of sensor nodes for practical node,DWRL wherealgorithm andd2dis2are arealready already known radioseparation separation distances. By using using the the law law of of cosines cosines node, where dd11 and known radio distances. By presented in three steps, which are presented below. n as given in Equations (1)–(8), two solutions are obtained for the location of node . Figure 2 shows location of node n22 . Figure 2 shows 2.1.1. Semi-Localization semi-localization between semi-localization between node node nn11 and andn2n. 2 . The first step towards the localization of any unlocalized node with the help of a sink node or n2 n2 2 some other already localized node is semi-localization. ForRlocalization n 2 ,y R ) only, UWB radio ranging is 2 x ( R2 n 2 r r r r used to measure four distances— 1 , 2 , n32 and 4 —between the radios of the two nodes that are
R1 ) n2 node, where d1 and d 2 are already distances. By using the law of cosines (x R 1,yknown radio separation r3
d 2 n is the sink node, and n is an unlocalized within range of each other, as shown in Figure 2. Here 1 2 n2 R1
as given in Equations (1)–(8), two solutions are obtained forr2 the location of node n 2 . Figure 2 shows r1
r4
semi-localization between node n1 and n 2 . θ2
n1 n1 n(x 2 ,y n1 ) d1 R 2 R 2 n 2R 2 n 2 ) y θ x =0n 2 R 1n1 R n21 (x R 2 , R 2 n2 R1 d2 Figure 2. Semi Localization between node n and n . n Figure 2.nSemi2 )Localization between node n11 and n2 .2 2 ,y R 1 (x R 1 r3 θ1
(x nR11 ,y Rn11 )
2
r1r2
r2 = d12 +r32 2d1r3cosθ 1 r4
r22 = d21 +r23 − 2d1 r3 cos θ1 θ 22 n12 2d1r1cosθ2 r =θ1d 2 +r 2 4 2 1 21 n1 n1 = d + r r 1 (x2 nR12 ,y nR12 ) (x R1 ,y R1 ) 4 d1 1− 2d1 r1 cos θ
(1) (1) (2) (2)
n θ x =0 dd22+r R 1n1 − r221 r2 +2r2R θ1 =±cos cos−11(( 11 3 3 2 )2 ) θ1 =
(3)(3)
d2 +r2 − r2 θ2 = ± cos−11 ( d121+r12 1 r42 4 ) 2 2 ( 2d1 r1 ) θr222==dcos 1 +r3 2d1r3 cosθ1 2d1r1 n2 xR1 = r1 cos θ2 2 r42 =nd12 n+r 2d1r1cosθ2 2 1 yR2x= ±rr11cosθ sin θ2 2 R1 =
(4) (4) (1) (5) (2) (5)(6)
2d 2d1r13r3node n and n . Figure 2. Semi Localization between 1 2
1
θ1
2 2 2 n2 =1r(3dcos 1 +rθ 3 1 r2 = xRcos 2n 2
yR1 = r1sinθ 2d12r3 n2 yR2 = ±r3 sin θ1
)
(7) (3) (6) (8)
+r n r42 : one is the actual position and the other Figure 3 shows two solutions for the position ofd node θ 2 = cos 1 ( 1 1 ) (4) 2d1rof position is located symmetrically on a flip around the axis 1 node n1 . There will be only one solution if and only if the axes of n1 and n2 lie on a same straight line or, in other words, both nodes are collinear. x nR21 = r1cosθ2 (5) 2
2
ynR21 = r1sinθ2
2
(6)
ynR22 = r3sinθ1
(8)
Figure 3 shows two solutions for the position of node n 2 : one is the actual position and the other position is located symmetrically on a flip around the axis of node n1 . There will be only one solution if and if the axes of n1 and n 2 lie on a same straight line or, in other words, both nodes 4are Sensors 2017,only 17, 2630 of 15 collinear. n2
R2 n2 d2
n2
R1 n2 ) n2 (x R 1,y R 1
θ2
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θ1
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(xRn2 , 1
y n2 R1
)
R1n2'
r2 r3
d2 n2'
R2n2'
(xRn2 , 2
y n2 R2
)
Figure 3. Two possible positions of node n 2 (i.e., n 2 and n0 '2 ). Figure 3. Two possible positions of node n2 (i.e., n2 and n2 ).
2.1.2. Rigid Localization 2.1.2. Rigid Localization As in semi-localization, if the two nodes n1 and n 2 are collinear, then both the location As in semi-localization, if the two nodes n1 and n2 are collinear, then both the location solutions solutions will be same, and will indicate actual position of node n 2 . If both the nodes are not collinear will be same, and will indicate actual position of node n2 . If both the nodes are not collinear then there then there is a need of the rigid localization. Rigid localization makes use of an additional node with is a need of the rigid localization. Rigid localization makes use of an additional node with additional additional semi-localization for selecting the correct solution for node n 2 by matching the location semi-localization for selecting the correct solution for node n2 by matching the location that is the best that is the best overlapped from the n1 − n 2 and n 3 − n 2 semi-localization steps, where nodes n1 overlapped from the n1 − n2 and n3 − n2 semi-localization steps, where nodes n1 and n3 are already n 2 is rigid n1 somehow and n 3 In areFigure already localized. Figure 4 node with localized with help node are and n 3 localized. 4 node n2 isIn rigid localized the help of node n1the and n3 , of which ' ' 00 ' 0 , which arelocalized. somehowHere, already rigid Here, and n 2 of aren2not n 2 positions already rigid n and n localized. are not the actual . the actual positions of 2
2
n2 .
Figure 4. Rigid localization of node n2 using localized nodes n1 and n3 .
2.1.3. DWRL Algorithm The sink node initializes the localization process. Firstly, one of the neighbor nodes is semi-localized and declared to be rigid localized even without performing rigid localization, because the sink is the
R2n2 Figure 4. Rigid localization of node n 2 using localized nodes n1 and n 3 .
2.1.3. DWRL Algorithm Sensors 2017, 17, 2630
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The sink node initializes the localization process. Firstly, one of the neighbor nodes is semilocalized and declared to be rigid localized even without performing rigid localization, because the sink is the only localized node therelocalized is no other localized node to perform rigid localization. only localized node and there is and no other node to perform rigid localization. The initialThe guess initial guess of the actual position of the first node is left to be verified by a third party of the of the actual position of the first node is left to be verified by a third party outside outside of the network network such asoperator, networkand operator, and be it should beatverified atwhen the end thenetwork whole network is such as network it should verified the end thewhen whole is localized. localized. Later, the sink and the first localized node will rigid localize their neighbor nodes and the Later, the sink and the first localized node will rigid localize their neighbor nodes and the process process continues. During the localization process, all unlocalized nodes keep listening unless they continues. During the localization process, all unlocalized nodes keep listening unless they receive receive message from two localized neighboring nodes. Finally, a third party should check whether message from two localized neighboring nodes. Finally, a third party should check whether the initial the initial guess of the location of the first node was not correct. In this case, the locations of all nodes guess of the location of the first node was not correct. In this case, the locations of all nodes should be should be symmetrically flipped around the axis of the sink node. Figure 5 shows flowchart of DWRL symmetrically flipped around the axis of the sink node. Figure 5 shows flowchart of DWRL algorithm. algorithm. Start
Sink node initializes localization process so that all reachable unlocalized nodes should keep listening unless they receive message from two localized neighbors.
Sink semi localizes one of it’s neighboring node “n” and declares it as a rigid localized node with initial guess of one of it’s two possible locations.
Sink and node “n” carryout further rigid localization for neighboring nodes and process continues hop to hop till all nodes are localized
Was the initial guess of location of node “n” right?
No
Symmetrically flip locations of all nodes around the axis of sink node
Yes
End
Figure 5. Flowchart of dual wireless radio localization (DWRL) algorithm. Figure 5. Flowchart of dual wireless radio localization (DWRL) algorithm.
2.1.4. DWRL Algorithm Drawbacks Although dual radios on a single node for localization is effective, the DWRL algorithm has the following drawbacks: a.
b.
If the initial location of the sink node is not known, then the DWRL algorithm considers that k k Radio1 (Rsin ) of the sink node has been assigned a specific location (0,0), and Radio2 (Rsin ) of 2 1 sink node is considered in the direction of positive x-axis, which points to local east direction. If nodes are randomly deployed, how then can we suppose the Radio2 of the sink node is in the direction of local east? The wrong angle of axis of the sink node can lead to the wrong location k of the rest of the network nodes. Therefore, we need to find actual direction of Rsin . 2 The DWRL algorithm needs at least two localized nodes to fully localize and unlocalized the node. For this reason, the DWRL algorithm cannot rigid localize first node with one sink node. First, the semi-localized node is declared as rigid localized on the basis of one randomly chosen location solution of the two possible location solutions of the first node. This can lead to serious localization problems if rest of the network continues to localize with the help of the wrong location of first node. What if the applications scenario is critical, and we have to use the location of some nodes before the whole network localization process is completed, and then the third party finds out that location of first node was not right and location of all nodes need to be flipped around the axis of the sink node? Therefore, we need to find the exact location of the first node.
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d.
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To rigid localize a node, a minimum of two semi-localizations are required. If an unlocalized node cannot listen from at least two localized nodes then it cannot be localized and it has to wait, unless somehow two localized signals are received. If some node cannot receive two localized signals then it cannot be localized at all. This requires the DWRL algorithm to perform at least (2n − 3) semi-localizations [25] to localize the entire network. Here, (2n − 3) is the number of semi-localizations required for network with n number of nodes, which is equal to twice the number of nodes n and three less, where three indicates that there are no semi-localizations performed for a sink node and only one semi-localization is performed for the node that will be localized first. Since (2n − 3) semi-localizations can be carried out with each choice of a different edge, the total number of semi-localizations can be, at most, Pn2 × (2n − 3). A higher number of semi-localizations uses more energy and time, therefore we need to minimize the total number of semi-localizations as well as increase number of fully localized nodes even with single semi-localization step. For successful semi-localization, each of four radios of two nodes must be in communication range with rest of the three radios. This requires either high node density or high transmission power, where high node density costs more nodes and high transmission power reduces the life of sensor nodes. We need to develop a way for nodes to be localized even if few of the four radios of the two communicating nodes can reach each other.
3. Improved DWRL (I-DWRL) Algorithm To present the I-DWRL algorithm, we intend to improve the drawbacks of the DWRL algorithm, as mentioned earlier. To achieve such improvements, we use a magnetometer, which is affixed on Radio1 of every single node, as shown in Figure 6. θc is the angle measured with magnetometer and (θ x = 360 − θc ) is the angle which roughly indicates the slope of the axis of node; it will be used in the localization Sensors 2017,process. 17, 2630 7 of 16 sin
k sin R2
n1 sink (x nR11 ,y R1 )=(x sink R1 ,y R1 ) n1 R1
R n21
W
k sin R1
(a)
0 N
E
k s i n ,y x R1 1 ( = n n1 ) R1 ,y R 1
n1 d1 30 θ x=
)
(x
(b)
θ c 330
n1 R1
0
N
27
0
S 180
)
n1 R2
sink (x nR12 ,y Rn12 )=(x sink R 2 ,y R 2 )
n1 d1 θ x =0
90
270
θc 0
(x n 1 )= ,y R 2 n 1 (x R2
k
,y R 2
W
S 0
90
E 18
Figure 6. Node n1 with Magnetometer showing different angles of magnetometer θ c and θ x of Figure 6. Node n1 with Magnetometer showing different angles of magnetometer θc and θx of node node in (a,b). in (a,b).
In I-DWRL, which is distinct from original DWRL, we have added the initial location of Radio1 sink which distinct from original DWRL, we have added the initial location of Radio1 of of In theI-DWRL, sink node ( R1sink is ) as (x sink R , y R ) , which is fed the exact location using GPS or any other means of sin k sin k sin k thelocation sink node (R ) as , y ) , which is fed the location using GPS or any other means x ( source, of exact sink node ( R sink ) is measured using simple 1 and the Rinitial R location of Radio2 2 1 1
1
1
k of location source,asandgiven the initial location of(9). Radio2 of sink node (Rsin ) is measured using simple trigonometry, in Equation Further Equations are modified into 2 (5)–(8) trigonometry, as given in Equation (9). Further Equations (5)–(8) are modified into Equations Equations (10)–(13) to accommodate any initial position and angle of axis of sink node. The (10)–(13) initial to accommodate any node initialcan position and angle of axis of sink position a sink node position of a sink help to locate other nodes withnode. their The real initial positions in theofcoordinate the actual location of a sink solvesinthe first drawbacksystem. of the DWRL algorithm. cansystem. help toAdding locate other nodes with their realnode positions the coordinate Adding the actual location of a sink node solves the first drawback algorithm. sink sink of the DWRL sink (xsink (9) R 2 ,yR 2 ) = (x R1 +d1cosθ x ,yR1 +d1sinθ x )
x nR21 = r1cos(θ2 +θx )+x Rn11
(10a)
x nR21 = r1cos( θ2 +θ x )+x Rn11
(10b)
'
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sin k k sin k sin k (x sin R2 , yR2 ) = (x R1 +d1 cos θx , yR1 +d1 sin θx ) n
xnR21 = r1 cos(θ 2 +θx ) + xR11 n0
(10a)
n
xR2 = r1 cos(−θ2 +θx ) + xR1 1
(10b)
1
n
ynR21 = r1 sin(θ 2 +θx ) + yR11 n0
(11a)
n
yR2 = r1 sin(−θ2 +θx ) + yR1 1
(11b)
1
n
xnR22 = r3 cos(θ 1 +θx ) + xR1
(12a)
1
n0
(9)
n
(12b)
ynR22 = r3 sin(θ 1 +θx ) + yR1
(13a)
xR22 = r3 cos(−θ1 +θx ) + xR11 n
1
n0
n
yR22 = r3 sin(−θ1 +θx ) + yR11
(13b)
A magnetometer is cheap but susceptible to environmental noise, and it may require calibration from time to time. To deal with the problem of magnetometer calibration, we consider that all magnetometers are calibrated well before the localization process starts, and magnetometers should be calibrated whenever required and feasible. To deal with the problem of angle errors due to environmental noise, we consider that we have knowledge of environmental noise and we know the Sensors 2017, 17, 2630 on magnetometer angle deflection. With this knowledge, it appears that 8we of 16 effect of such noise can calculate, in advance, the maximum possible magnetometer angle errors due to environmental noise. n anangle angleobtained obtained from from magnetometer magnetometer at and±θθd_max Rn1n2 and d_max is If θθnxx2 isisan at R isthe themaximum maximumpossible possibleangle angle 1 deflection causeddue duetotoenvironmental environmental noise, noise, then we deflection caused we compare comparewhich whichofofthe theslope slopeofoftwo twopossible possible n2 n positions ofof unlocalized range θθrange θ ± θ is considered as an θ= θ positions unlocalizednode node nn22 falls fallswithin within angle angle range is considered as an actual range x d_max x d_max actual location of n without performing rigid localization. Figure 7 depicts such a scenario, where 2 location of n 2 without performing rigid localization. Figure 7 depicts such a scenario, where slope S1 slope S and S can be found using Equation 2 1 and S can be found using Equation (14). (14). 2
2
2
2
θ range θ nx 2 θ d_max 5 n2 θ x =1 n2
R1
15 10
n2
R2
n2 d2 5 S 1 =1 Magnetometer
θ nx1 =0
R
n1 1
n1 d1 S0 =0
R n21 θ range θ nx 2 θ d_max 15 10
' 5 R1n2 θ =1
n2 x
n2' d S2 = 2 15
R2n2'
Figure 7. The magnetometer sensor helps to distinguish between actual and another possible location Figure 7. The magnetometer sensor helps to distinguish between actual and another possible location of node n 2 . of node n2 .
S1 = tan 1 (
S2 = tan 1 (
y nR22 y nR21 x nR22 x nR21
)
( y nR22 ) ( y Rn21 ) x nR22 x nR21
(14a)
)
(14b)
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S1 = tan
−1
(
ynR22 − ynR2
1
)
xnR22 − xnR2
(14a)
1
S2 = tan−1 (
(−ynR22 ) − (− ynR21 ) xnR22 − xnR2
)
(14b)
1
For such semi-localization to produce accurate results of rigid localization without performing rigid localization, the minimum difference between the angle of slope of a localized node and the angle of the magnetometer of an unlocalized node must be greater than θd_max . As with the use of a magnetometer, we can use only one semi-localization to rigid localize an unlocalized node, therefore, it solves the second and third drawbacks of the DWRL algorithm. To overcome the connectivity problem of the DWRL algorithm, we have considered six cases, four of which are shown in Figure 8. Sensors 2017, 17, 2630 9 of 16 n2
R1
n 2
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) n1
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'
n2
y ) (x , Rn 12 R2 n1 R2
r4
(x
=4
n
5
2
,y
(x
R
R
1
n
2
,y
n2
2
R
1
n
2
)
d2
25
2
n
1
R1
R
2
2
(x
n
2
n2
2
,y
2
R
(x R
)
)
n2
,y R
n2
d2
θ nx 2 =180 '
R 1n 2 ' (x R1 ,y Rn 21 ) n '2
(d)
Figure 8. Various cases of connectivity problem. (a) Case a. Two radios of a localized node can reach Figure 8. Various cases of connectivity problem. (a) Case a. Two radios of a localized node can reach only Radio1 of unlocalized node. (b) Case b. Two radios of a localized node can reach only Radio2 of only Radio1 of unlocalized node. (b) Case b. Two radios of a localized node can reach only Radio2 of an unlocalized node. (c) Case c. Radio1 of a localized node can reach only Radio1 of an unlocalized an unlocalized node. (c) Case c. Radio1 of a localized node can reach only Radio1 of an unlocalized node, whereas Radio2 of a localized node can reach both radios of an unlocalized node. (d) Case d. node, whereas Radio2 of a localized node can reach both radios of an unlocalized node. (d) Case d. Radio1 of a localized node can only reach Radio2 of an unlocalized node, whereas Radio2 of a Radio1 of a localized node can only reach Radio2 of an unlocalized node, whereas Radio2 of a localized localized node can reach both radios of an unlocalized node. node can reach both radios of an unlocalized node.
For Case a, the actual and other possible position of R1n
2
of an unlocalized node can be found
with the help of a localized node n1 using Equations (4), (10) and (11), whereas the actual and other possible location of R n2 of an unlocalized n 2 can be found using angle θ nx in Equations (15) and 2
2
(16).
x nR22 = x nR21 +d 2cosθnx2
(15a)
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For Case a, the actual and other possible position of Rn1 2 of an unlocalized node can be found with the help of a localized node n1 using Equations (4), (10) and (11), whereas the actual and other possible location of Rn2 2 of an unlocalized n2 can be found using angle θnx 2 in Equations (15) and (16). xnR22 = xnR2 +d2 cos θnx 2
(15a)
1
n0
n0
xR22 = xR2 +d2 cos θnx 2
(15b)
ynR22 = ynR2 +d2 sin θnx 2
(16a)
1
1
n0
n0
yR22 = yR2 +d2 sin θnx 2
(16b)
1
The decision regarding the choosing of the actual location of n2 out of two obtained locations is made on the basis that Radio1 and Radio2 of node n1 cannot reach Radio2 of node n2 , but in obtained location n20 Radio2 of node n20 lies within the communication range of Radio2 of node n1 . Mathematically, the actual location of node n2 can be confirmed using Equation (17). In Equation (17), if the condition is true then n2 is the actual location else n20 . n
n
n
n0
n
n0
R1 1 Rn2 2 + R2 1 Rn2 2 > R1 1 R2 2 + R2 1 R2 2
(17)
For Case b, the actual and other possible location of Rn1 2 and Rn2 2 of node n2 can be found using Equations (4) and (18)–(21). Moreover, we can decide actual position of node n2 using Equation (22). In Equation (22) if the condition is true then n2 is the actual location else n20 . n
xnR22 = r1 cos(θ 2 +θx ) + xR1
(18a)
1
n0
n
xR22 = r1 cos(−θ2 +θx ) + xR1
(18b)
1
n
ynR22 = r1 sin(θ 2 +θx ) + yR11 n0
(19a)
n
yR22 = r1 sin(−θ2 +θx ) + yR1
(19b)
xnR2 = xnR22 +d2 cos(θ nx 2 − 180)
(20a)
1
1
n0
n0
xR2 = xR22 +d2 cos(θ nx 2 − 180)
(20b)
ynR2 = ynR22 +d2 sin(θ nx 2 − 180)
(21a)
1
1
n0
n0
yR2 = yR22 +d2 sin(θ nx 2 − 180)
(21b)
1
n
n
n
n0
n
n0
R1 1 Rn1 2 + R2 1 Rn1 2 > R1 1 R1 2 + R2 1 R1 2
(22)
For Case c, the actual and another possible location of node n2 is found using Equations (4), (10), (11), (15) and (16), where Equation (23) helps to decide actual position of node n2 . In Equation (23) if the condition is true then n2 is the actual location, otherwise n20 . n
n
n
n0
n
n0
R1 1 Rn2 2 + R2 1 Rn2 2 < R1 1 R2 2 + R2 1 R2 2
(23)
For Case d, Equations (4), and (18)–(21) are used to find the actual and other possible locations, where Equation (24) is used to decide actual position of node n2 . In Equation (24), if the condition is true then n2 is the actual location else n20 . n
n
n
n0
n
n0
R1 1 Rn1 2 + R2 1 Rn1 2 < R1 1 R1 2 + R2 1 R1 2
(24)
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Case e and f can also be considered with little variation to Case c and d, where Radio1 of a localized node can reach both radios of an unlocalized node, and Radio2 of a localized node can reach either Radio1 or Radio2 of unlocalized node, respectively. Same equations will be used for Case e and f, as in Case c and d. All six of these cases are used to solve the connectivity issue of DWRL algorithms in situations where node density or transmission range is not enough. A detailed flowchart of the DWRL algorithm is shown in Figure 9.
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Start
All the nodes keep listening for localization messages unless they are localized.
Sink / localized node initiates localization process by sending its location information and maximum possible angle of magnetometer deflection . d_max
θ
No
Does situation match any of 06 cases that solve connectivity problem ?
No
Receiving node checks if all four radios can communicate?
Yes
End
Forward location message to localize further nodes
Yes
Localize, an unlocalized node
and, is this first localization message?
listen for another better localization message to reduce location error
No
Yes
and, is angle between two nodes
Rigid localize
Wait for other localization message No
> θ d_max ? End
Yes
Message receiving node performs semi localization Localized node act like sink to carry on further localization process
Un localized node is now localized
Yes
Slope Of any of two possible locations falls with in ? range
No
θ
Figure 9. Flow chart of the improved (I)-DWRL algorithm. Figure 9. Flow chart of the improved (I)-DWRL algorithm.
4. Simulation Scenario, Parameters and Results 4. Simulation Scenario, Parameters and Results In this section, we simulate the DWRL and I-DWRL algorithms and analyze the effects of In thissuch section, we simulate the DWRL I-DWRL algorithms and analyze theand effects of parameters as range measurement errors, and magnetometer errors, transmission range, so on, parameters such as range measurement errors, magnetometer errors, transmission range, and so where NS-2 [26] is used as a simulation tool. We compare DWRL and I-DWRL in terms of the number on,semi-localizations where NS-2 [26] is used asthe a simulation We compare andand I-DWRL in terms of the of required, percentagetool. of network nodesDWRL localized, the time and energy number of semi-localizations required, the percentage of network nodes localized, and the time and required to finish localization process. To accommodate range measurement errors, real-world noise energy required to finish localization process. To accommodate range errors, real-world is considered as the summation of high probability small noise and lowmeasurement probability large noise [27,28]. Small noise is modeled as a Gaussian random process as a function of “R”, which is the wireless range of nodes, which is given in Equation (25).
NS R = 0.022 ln 1+R -0.038
(25)
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noise is considered as the summation of high probability small noise and low probability large noise [27,28]. Small noise is modeled as a Gaussian random process as a function of “R”, which is the wireless range of nodes, which is given in Equation (25). NS (R) = 0.022 ln(1 + R) − 0.038
(25)
The low probability large noise value is selected as a function of “R” with probability less than 0.025, which is given in Equation (26). Sensors 2017, 17, 2630
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NL (R) = 0.025 × R
Further Further magnetometer magnetometer maximum possible deflection from its accurate angle is a joint joint effect effect of of both of of both noises θd_max NLL) ). .The Theeffect effect of of both noises is θd_max(N (NSS,,N both noises, noises,and andititisismodeled modeledasasa function a function both noises is considered in such a way that 0 < θ ≤ 45. d_max 45 . considered in such a way that 0 θd_max Figure 10 and Table 1 shows simulation scenario and parameters, respectively. Figure 10 and Table 1 shows simulation scenario and parameters, respectively.
Figure 10. Network simulation scenario. Figure 10. Network simulation scenario. Table 1. Network simulation parameters. Ultra-wide band (UWB). Table 1. Network simulation parameters. Ultra-wide band (UWB).
Simulations Parameter SimulationsArea Parameter
Value Value 50 × 50 m2
Unlocalized nodes Area 50 × 5032m2 Unlocalized nodes 32 1 Localized nodes/sink Localized nodes/sink 1 Node distribution Uniform random distribution Node distribution Uniform random distribution Angle of axis of nodes random Angle of axis of nodes random Different transmission ranges 8,10, 10,12.5, 12.5,13.5, 13.5, 14.5, Different transmission ranges 8, 14.5, 15.515.5 m m Inter-radio distance 6060 cmcm Inter-radio distance Radio UWB Radio UWB UWB Range error without environmental noise 1% of transmission range UWB Range error without environmental noise 1% of transmission range Figure Figure 11 11 shows shows that that with with lower lower transmission transmission range range connectivity connectivity problems can occur, occur, and and aa smaller number of nodes will be localized with the DWRL algorithm, whereas the I-DWRL algorithm smaller number of nodes will be localized with the DWRL algorithm, whereas the I-DWRL algorithm performs transmission range of nodes. With the transmission rangerange of 8 m, performswell welleven evenwith withthe thesmaller smaller transmission range of nodes. With the transmission of 8 m, the DWRL algorithm cannot even localize more than 5% of network nodes, whereas our I-DWRL can localize around 80% of network nodes.
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the DWRL algorithm cannot even localize more than 5% of network nodes, whereas our I-DWRL can localize around 80% of network nodes. Sensors 2017, 17, 2630 13 of 16 Sensors 2017, 17, 2630
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Figure 11. 11. Transmission range versus versus total total percentage percentage of of localized localized nodes. nodes. Figure Transmission range Figure 11. Transmission range versus total percentage of localized nodes.
As we have improved the DWRL algorithm in terms of having a smaller number of semiAs improved the the DWRL algorithm in terms having smaller anumber of semi-localizations Aswe wehave have improved DWRL algorithm in of terms of ahaving smaller number of semilocalizations required for the full localization of unlocalized nodes, therefore, Figure 12 shows that required for the full localization unlocalizedofnodes, therefore, Figure 12 shows that12the I-DWRL localizations required for the fulloflocalization unlocalized nodes, therefore, Figure shows that the I-DWRL algorithm can localize higher percentage of nodes with a lower number of semialgorithm canalgorithm localize higher percentage of nodes with a of lower number even the I-DWRL can localize higher percentage nodes with of a semi-localizations, lower number of semilocalizations, even in noisy environments. In an ideal case where the transmission range is 15 m and in noisy environments. In an ideal case where transmission is 15 m andrange there is 15 no m noise, localizations, even in noisy environments. In anthe ideal case whererange the transmission and there is no noise, the I-DWRL algorithm can save around 50% of semi-localizations. In the worst case, the I-DWRL algorithm can save aroundcan 50% ofaround semi-localizations. In the worstIn case, wherecase, the there is no noise, the I-DWRL algorithm save 50% of semi-localizations. the worst where the transmission range is 10 m, the DWRL algorithm can reach only 9% of network nodes; transmission range is 10range m, theis DWRL algorithm reach only 9% ofonly network therefore, where the transmission 10 m, the DWRL can algorithm can reach 9% ofnodes; network nodes; therefore, it performs a smaller number of semi-localizations, while I-DWRL can reach 100% of ittherefore, performsita performs smaller number of semi-localizations, while I-DWRLwhile can reach 100%can of network nodes a smaller number of semi-localizations, I-DWRL reach 100% of network nodes and performs a greater number of semi-localizations. If the angle of deflection of the and performs a greater numbera of semi-localizations. If the angle of deflection of the is network nodes and performs greater number of semi-localizations. If the angle ofmagnetometer deflection of the magnetometer is increased, then the performance of the I-DWRL algorithm degrades and requires a increased, then the performance of the I-DWRL algorithm degrades and requires a greater number magnetometer is increased, then the performance of the I-DWRL algorithm degrades and requires a greater number of semi-localizations. of semi-localizations. greater number of semi-localizations.
Figure 12. Transmission range versus number of semi-localizations in noiseless and noisy environment. Figure 12. Transmission range versus number of semi-localizations in noiseless and noisy environment. Figure 12. Transmission range versus number of semi-localizations in noiseless and noisy environment.
For a transmission range of 15.5 m, Figure 13 shows that the I-DWRL algorithm requires less For a transmission range of 15.5 m, Figure 13 shows that the I-DWRL algorithm requires less than For 60% of network localization timem, and takes 13 around 70% ofthe the energy toalgorithm fully localize the same transmission range of 15.5 shows that requires less than 60%aof network localization time andFigure takes around 70% of theI-DWRL energy to fully localize the same network as with the DWRL algorithm. than 60%as of with network localization time and takes around 70% of the energy to fully localize the same network the DWRL algorithm. For as thewith simulation results of localization error, we have considered two transmission ranges, network the DWRL algorithm. For the simulation results of localization error, we have considered two transmission ranges, namely, 15.5simulation m and 14.5 m. The of magnetometer deflection due to environmental is For the of angle localization error, we have considered two transmission noise ranges, namely, 15.5 m and 14.5results m. The angle of magnetometer deflection due to environmental noise is considered asm±20 degrees. Figure 14a shows that as the deflection distance between sensor nodes and sink namely, 15.5 and 14.5 m. The angle of magnetometer due to environmental noise is considered as ±20 degrees. Figure 14a shows that as the distance between sensor nodes and sink nodes is increasing due to multi-hop communication and is the error, but both the algorithms considered as ±20 degrees. Figure 14a shows that as theso between sensor nodes and have sink nodes is increasing due to multi-hop communication and sodistance is the error, but both the algorithms have same the performance. Figure 14b shows that, due to limited wireless range, the DWRL algorithm nodes is increasing due to multi-hop communication and so is the error, but both the algorithms have same the performance. Figure 14b shows that, due to limited wireless range, the DWRL algorithm cannotthe reach all networkFigure nodes and,shows for the considered parameters, three nodes cannot bealgorithm localized. same performance. that, due to limited wireless range, the DWRL cannot reach all network nodes14b and, for the considered parameters, three nodes cannot be localized. So, for these three nodes the localization error is infinite. Figure 14b shows that the I-DWRL So, for these three nodes the localization error is infinite. Figure 14b shows that the I-DWRL algorithms can reach these three nodes and localize them well. algorithms can reach these three nodes and localize them well.
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cannot reach all network nodes and, for the considered parameters, three nodes cannot be localized. So, for these three nodes the localization error is infinite. Figure 14b shows that the I-DWRL algorithms Sensors 2017,these 17, 2630 14 of 16 can reach three nodes and localize them well. Sensors 2017, 17, 2630
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Figure 13. Time and energy graph for full network localization. localization. Figure 13. Time and energy graph for full network localization.
Figure 14. Localization error. (a) Without connectivity problem, (b) With some connectivity problem Figure14. 14.Localization Localizationerror. error.(a) (a)Without Withoutconnectivity connectivityproblem, problem,(b) (b)With Withsome someconnectivity connectivityproblem. problem Figure
5. Conclusions
5. Conclusions Conclusions The DWRL algorithm uses two UWB radios with each node and requires a minimum of two 5. localized nodes algorithm for the localization of an unlocalized where all four radios ofof two The DWRL DWRL uses two two UWB UWB radios with each eachnode, node and and requires requires minimum two The algorithm uses radios with node aa minimum of two communicating nodes should be able to communicate with the remaining three radios. We have localizednodes nodes the localization of an unlocalized node, where alloffour radios of two localized for for the localization of an unlocalized node, where all four radios two communicating improved the DWRL algorithm by using a magnetometer on one ofremaining the radios of eachradios. node, such that communicating nodes should be able to communicate with the three We have nodes should be able to communicate with the remaining three radios. We have improved the the I-DWRL algorithm requires only one node to fully localize an unlocalized nodes without the strict improved the DWRL algorithm by using a magnetometer on oneof ofeach the radios each node, that DWRL algorithm by using a magnetometer on one of the radios node, of such that the such I-DWRL requirement of connectivity among all four radios of the two communicating nodes.without Our results also the I-DWRL algorithm requires only one node to fully localize annodes unlocalized nodes the strict algorithm requires only one node to fully localize an unlocalized without the strict requirement verify the fact that I-DWRL outperforms in terms of time, energy, number of localized nodes, requirement of among connectivity among allof four radios of the two communicating Our results also of connectivity allon. four radios thewith two the communicating nodes. Our nodes. results alsoalmost verifyhalf the localization error, and so In comparison DWRL algorithm, I-DWRL requires verify the fact that I-DWRL outperforms in terms of time, energy, number of localized nodes, fact that I-DWRL outperforms in terms of time, energy, number of localized nodes, localization error, the number of semi-localizations in a low-noise environment, 60% of I-DWRL whole network localization localization error, and so on. In comparison with the DWRL algorithm, requires almost half and so on. In comparison with the DWRL algorithm, I-DWRL requires almost half the number of time, 70% ofofthe energy, and caninlocalize moreenvironment, number of network nodes network with a maintained the number semi-localizations a low-noise 60% oflocalization whole localization semi-localizations in a low-noise environment, 60% of whole network time, 70% of the localization error inenergy, cases when DWRL algorithm cannot reach all networknodes nodes.with a maintained time, 70% and can localize more number network energy, and of canthe localize more number of network nodes with aofmaintained localization error in cases localization error in cases whenreach DWRL algorithmnodes. cannot reach all network nodes. when DWRL algorithm cannot all network Author Contributions: Abdul Aziz developed this idea, Ramesh Kumar helped in simulation work and Inwhee Joe guided and supported well at every stage. Author Contributions: Contributions: Abdul Abdul Aziz Aziz developed developed this this idea, idea, Ramesh Ramesh Kumar Kumar helped helped in in simulation simulation work work and and Author Inwhee and supported well stage. InwheeJoe Joe guided and supported wellatatevery every stage. Conflicts ofguided Interest: The authors declare no conflict of interest. Conflicts Conflictsof ofInterest: Interest:The Theauthors authorsdeclare declareno noconflict conflictofofinterest. interest.
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