Improved three-dimensional localization algorithm based on volume-test scan for wireless sensor networks

The Journal of China Universities of Posts and Telecommunications October 2012, 19(Suppl. 2): 1–6 www.sciencedirect.com/science/journal/10058885

http://jcupt.xsw.bupt.cn

Improved three-dimensional localization algorithm based on volume-test scan for wireless sensor networks SHU Jian, YAN Chuan, LIU Lin-lan( ) School of Software, Nanchang Hangkong University, Nanchang 330063, China

Abstract Aiming at the ‘in-to-out error’ and ‘out-to-in error’ caused by boundary effect in approximate point-in-triangulation test three dimension (APIT-3D) algorithm for wireless sensor networks (WSNs), which leads a bad location precession, this paper proposes an improved APIT-3D scheme based on volume-test, named volume test approximate point-in-triangulation test three-dimension (VT-APIT-3D) algorithm. By adding the advantage of comparing to the volume of the triangular pyramids in process of point-in-triangulation test (PIT) during APIT-3D, the unknown node can be accurately determined whether it is in the testing triangular pyramid or not. This method can remove the probability of the ‘in-to-out error’ and ‘out-to-in error’ in APIT-3D. Finally, the simulation results confirm that the proposed scheme has great advantage in aspects of localization accuracy in comparison with original APIT-3D scheme and relational scheme respectively . Keywords boundary effect, APIT-3D, wireless sensor networks (WSNs), localization accuracy

1

Introduction 

WSNs is a kind of networks with low energy consumption and self-organization, diverse structure and connective, wide collaboration [1–2]. According to whether to measure the distance between the nodes, positional algorithms are divided into two categories–range-based algorithms and range-free algorithms. Range-based algorithms achieve to the unknown node located through the measure of the absolute distance or direction. At the present stage this common methods contain: time of arrive (ToA), time different of arrive (TDoA), angle of arrive (AoA) and received signal strength indicator (RSSI) [3–5], etc.. This type of algorithm has a high relative accuracy but brings a high hardware requirements and serious communication consumption. So they are not suitable for the low energy consumption or low cost applications. Range-free algorithms do not demand to measure the absolute distance or direction, which achieve to locate through the

Received date: 29-05-2012 Corresponding author: LIU Lin-lan, E-mail: [email protected] DOI: 10.1016/S1005-8885(11)60452-4

information of network connectivity or others. The common algorithms contain convex, centroid, distance vector-hop (DV-Hop), amorphous, APIT [6–9], etc.. APIT is a classical positional algorithm by calculating the range approaching of overlap region. This algorithm is little influenced by environmental factors and requires a low hardware, which is a widely accepted positional mechanism for WSNs. However, the practical environment is always a three dimensional situation and APIT has a bad accuracy in this case. Currently, most of the improvements for APIT stay in the two-dimensional space. Ref. [10] proposed an algorithm based on the perpendicular bisector, name PB-APIT. The perpendicular bisector of each side is to divide the triangle into 4 or 6 sub-areas. By detecting the signal strength to ensure the unknown node lying on which sub-areas, the positional accuracy can be improved about 18%. Ref. [11] introduced a novel algorithm, APIT2. It improved the positional accurate by changing the initial value of grid scan algorithm. Ref. [12] used monte carlo (MC) method and RSSI filter sampling method in the APIT and simulation results showed that the minimum positional error of MC-APIT is up to 10%. Ref. [13] elaborated the

2

The Journal of China Universities of Posts and Telecommunications

APIT algorithm applied in three-dimensional space, but the positioning accuracy was above 40%. In addition, there was so much other relative research. Through the deep analysis of these studies, VT-APIT-3D is proposed, which uses the volume-test scan method in process of PIT during APIT-3D to remove the ‘in-to-out error’ and ‘out-to-in error’ to improve the positional accuracy. The rest of this paper is organized as follows: Sect. 2 introduced the idea of APIT and testing error. In Sect. 3, we evaluate our algorithm and give its complete procedure. Sect. 4 is focused on presenting simulations about this algorithm and Sect. 5 highlights the conclusions and further directions of the ongoing research.

2

The idea of APIT and testing error

2.1 APIT scheme In WSNs, nodes are usually stationary. Approximate point-in-triangulation test uses the node in a relatively high density to simulate the movement. The unknown node exchanges RSSI with other nodes to determine position. As shown in Fig. 1(a), when the unknown node N moves to a random direction, the new position is always approaching at least one of four beacons or leaving away. So N is judged in the testing triangular pyramid. In Fig. 1(b), the unknown node N is always approaching to four beacons or leaving away.

2012

So N is judged out of the testing triangular pyramid. Then, ensure the overlap region through the testing triangular pyramids. Finally the unknown node position can be estimated by grid scan algorithm. 2.2 Testing error and analyze In practical environment, the nodes are random deployed in sensor networks. When the unknown node is approaching to the borders of the testing triangular pyramid, it is easy to occur an ‘in-to-out error’ and ‘out-to-in error’ as shown in Fig. 2. Fig. 2(a) shows the node M is the actual out of the triangular pyramid. When it moves to N, it is always approaching to the beacon B, C and away from A, D. It can be judged in triangular pyramid. This error named ‘out-to-in error’. In Fig. 2(b), the node M is in the triangular pyramid. If it moves to N, it will be judged which is out of the triangular pyramid. This error named ‘in-to-out error’. Such errors are due to boundary effect.

(a) ‘Out-to-in error’

(a) Node in the triangular pyramid

Fig. 2

(b) Node out of the triangular pyramid Fig. 1 APIT-3D positional case

(b) ‘In-to-out error’ ‘In-to-out error’ and ‘out-to-in error’ in APIT-3D

In procedure of localization, the probability of ‘in-to-out error’ and ‘out-to-in error’ is always different under the nodes density changing as shown in Fig. 3. The probability of ‘out-to-in error’ is up to about 14% and it can enormously affect the positional accuracy [14].

Supplement 2

SHU Jian, et al. / Improved three-dimensional localization algorithm based on volume-test scan for..

3

compose of the unknown node and the each of the testing triangular pyramid’s three vertices equals the volume of the original testing triangular pyramid. The formula can be described as follows: VABCN  VABND  VANCD  VNBCD =VABCD (1)

Fig. 3 APIT error under varying node densities

In APIT-3D, the unknown node is estimated by the centroid of the testing triangular pyramids’ overlap region. In this procedure, the boundary effect may occur and the positional accuracy will be affected. In Fig. 4, if we put the unknown node in many testing triangular pyramids and a relatively smaller space. Then the unknown node is approaching to the boundary of the testing triangular pyramids, and it will inevitably increase the probability of ‘in-to-out error’ and ‘out-to-in error’. On the contrary, the unknown node is in less testing triangular pyramids and a large space. But the probability of ‘in-to-out error’ and ‘out-to-in error’ is much lower. So it is the key to improve positional accuracy that eliminating the probability of ‘in-to-out error’ and ‘out-to-in error’.

Where, V is the volume, VABCN is the volume of ABCNˈ ABCD is the four vertices of testing triangular pyramid, N is the unknown node. 2) The second situation is shown in Fig. 5(b). If the unknown node is out of the testing triangular pyramids, the result of adding the four sub-triangular pyramids which are compose of the unknown node and the each of the testing triangular pyramid’s three vertices is bigger than the volume of the original testing triangular pyramid. The formula can be described as follows: VABCN  VABND  VANCD  VNBCD >VABCD (2)

(a) The unknown node inside

Fig. 4 Boundary effect as varying space and triangular pyramids

3 3.1

VT-APIT-3D algorithm Volume-test scanning

In WSNs, the unknown nodes are randomly deployed and there are only two kinds of situation. 1) The first situation is shown in Fig. 5(a). If the unknown node is in the testing triangular pyramids, the result of adding the four sub-triangular pyramids which are

(b) The unknown node outside Fig. 5 Volume-test scanning

Where, V is the volume, VABCN is the volume of ABCN, ABCD is the four vertices of testing triangular pyramid, N is the unknown node. The formula of volume is calculated as follow:

4

The Journal of China Universities of Posts and Telecommunications

§ x2  x1 y2  y1 z2  z1 · 1¨ ¸ (3) x3  x2 y3  y2 z3  z2 ¸ 6 ¨¨ ¸ © x4  x3 y4  y3 z4  z3 ¹ Where, (x1,y1,z1), (x2,y2,z2), (x3,y3,z3), (x4,y4,z4) is the four vertices’ coordinate of the triangular pyramid, V is the volume. V

3.2 VT-APIT-3D algorithm flow chart Steps of VT-APIT-3D algorithm are elaborated as follows: Step 1 Initialize the network and randomly deploy the nodes. Step 2 Beacons broadcast their information (id, position, RSSI). Step 3 The unknown nodes record the information. Step 4 Neighbor nodes exchange the information to compare with each other. Step 5 Detect the unknown nodes whether it meets the requirement of APIT-3D or not. Step 6 If the unknown node meets the requirement of APIT-3D, its position is calculated. Otherwise, it will be defined as unable positioned node.

Step 7 Find the located nodes and then use the volume-test scanning method to refine the location. After refinement, these nodes can be used as reference nodes for the unable positional node. If unable positional nodes still cannot be located, this paper gets the centroid of space to implement positioning. When the unable positional node has only three neighbor beacons, we choose the centroid of triangular pyramids as the estimated position which is composed by the three neighbor beacons. When the unable positional node has only two neighbor beacons, we use the middle of line as the estimated position which is composed by the two neighbor beacons. When the unable positional node has only one neighbor beacons, we view the position of this beacon as the estimated position. When the unable positional node has none, we take the centroid of this space as the estimated position. Step 8 Localization is over. 3.3 Analysis of performance and efficiency Compared to the original algorithm, VT-APIT-3D has two advantages: 1) In the process of APIT-3D, eliminate the ‘in-to-out error’ and ‘out-to-in error’, to improve the positional

2012

accuracy. 2) The located nodes are used as reference nodes for the unable positional nodes in order to increase the network coverage and the probability of the unknown nodes which will be located. Suppose we use a grid [10,10] to compare the location efficiency. In Fig. 6, the gird scan algorithm is applied in APIT-3D. The actual position is in grid [4,3] and the estimated position is in grid [3,4].

Fig. 6

The grid scan applied in APIT-3D

As shown in Fig. 7, we also use gird scan algorithm to evaluate the unknown node position. The actual position and the estimated position are both in grid [7,5]. So we can find VT-APIT-3D has great advantage in aspects of localization accuracy.

Fig. 7

The grid scan applied in VT-APIT-3D

Most of algorithms improve the positional accuracy through the cost of increasing the computational complexity, O(m). The computational complexity of this algorithm is shown as follows: The computational complexity of Eq. (1) is O(1); the computational complexity of Eq. (2) is also O(1). Eq. (3) is a fixed 3 u 3 matrix, its is still O(1). So the computational complexity of this algorithm is O(1).

Supplement 2

4

SHU Jian, et al. / Improved three-dimensional localization algorithm based on volume-test scan for..

Evaluation

This section provides detailed analysis and contrast in the performance between VT-APIT-3D and the relational algorithms. In the platform Matlab 7.0, we do the simulation. The positional accuracy is defined as follows: | ActualPosition-EstimatedPosition | Positional Error= Wireless Communication Radius (4)

5

pyramid and the positional accuracy natural improving. In view of this figure from the value of R, we can find APIT2-3D localization accuracy is best when R is small. The other algorithms are very litter different. But as R increasing, VT-APIT-3D localization accuracy is priority to others. What’s more, the positional error of VT-APIT-3D descends about 30% compared to APIT algorithm. Because eliminating the ‘in-to-out error’ and ‘out-to-in error’ in APIT-3D, the positional accuracy will natural be improved.

4.1 Simulation parameter and experimental environment Suppose 150 unknown nodes of sensor and some beacons are randomly scattered in a foursquare region with an area of 50 m u 50 m u 50 m. The number of beacons increase from 4 to 40. Try to do experiment to evaluate the positional performance in aspect of the following parameter: Wireless communication radius(R): the signal transports the maximum distance in any direction. Positional time(T): node localization costs how much time. The number of beacons(N): the number of beacons deployed in the area.

4.2.2 Positional accuracy with the different number of beacons Fig. 9 shows the positional error of four algorithms is always down as the number of beacons increasing. VT-APIT-3D is the best. APIT2-3D is the second best algorithm. Therefore, this algorithm is more suitable for lager-scale and ability sensor networks. There is a small amount fluctuation, which is because in the procedure of localization, positional error doesn’t always reduce as the number of beacons increasing. A small probability event may disappear that the positional error may increase as shown in Fig. 10.

4.2 Experiment conclusion and analysis 4.2.1 Positional accuracy as varying R As shown in Fig. 8, when other conditions are the same, the positional error of four algorithms is always reducing as R increasing. Fig. 9

Fig. 8

Positional errors as varying R (N=30)

Because the unknown node can hear more number of neighbor nodes and neighbor beacons. When the number of neighbor nodes increasing, providing more reference nodes and the probability of ‘in-to-out error’ and ‘out-to-in error’ will decrease. When the number of neighbor beacons increasing, it provides more testing triangular

Positional errors as the different number of beacons (R=18)

Fig. 10 The uncertainty of the error with increased beacons

4.2.3 Positional time under the different number of beacons Fig. 11 shows the time under the different number of beacons. We can see when R=18, the positional time of

6

The Journal of China Universities of Posts and Telecommunications

three improvement algorithms are more than the original algorithm. The more the number of beacons is, the more the positional time it will cost. But the positional time of VT-APIT-3D is little different from other algorithms. The maximum disparity is about 5 s. This indicates that VT-APIT-3D is less impact on the energy consumption of sensor networks.

Fig. 11 Positional time under the different number of beacons (R=18)

5

Conclusions

From the simulation results of the above experiments we can see the VT-APIT-3D algorithm has been improved very well in the precision of localization with low energy consumption. It is a priority positional method in three-dimensional space. The next step is to study how to eliminate APIT-3D algorithm about measurement error and further improve the positional accuracy. Acknowledgements This work was supported by the National Natural Science Foundation of China (61262020,60773055), Jiangxi Key Technology

2012

R&D Program (2009BGA01000).

References 1. Sun L M, Li J Z, Chen Y, et al. Wireless sensor networks. Tsinghua University Press, China, 2005: 135136 2. Wang X. Wireless sensor networks measurement systems. China Machine Press, China ,2005: 326328 3. Zhou Y, Li H C. Space localization algorithm based RSSI in wireless sensor networks. Journal on Communications, 2009(30): 7579 4. Frankie K W, Chan H C. Accurate distributed range-based positional algorithm for wireless sensor networks. IEEE Transaction on Signal Processing, 2009(57): 41004105 5. Fujiwara R, Mizugaki K, Nakagawa T, et al. ToA/TDoA hybrid relative positional system using UWB-IR. IEEE Radio and Wireless Week, 2009: 679682 6. Feng X F, Qi H B. Improvement and simulation for a localization based on APIT. International Conference on Computer Technology and Development, 2009: 6872 7. Liu Y, Yi X, He Y. A novel centroid localization for wireless sensor networks. International Journal of Distributed Sensor Networks, 2012(2012): 18 8. Wang F B, Shi L, Ren F Y. Self–localization systems and algorithms for wireless sensor networks. Journal of Software, 2005(16): 857868 9. Wang J Z, Jin H X. Improvement on APIT localization algorithms for wireless sensor networks. International Conference on Networks Security, Wireless Communications and Trusted Computing, 2009(1): 719723 10. Yang J, Liu F. A modified localization algorithm of APIT based on perpendicular bisector feature for wireless sensor network. Chinese Journal of Sensors and Actuators, 2008(21): 14531457 11. Chiti F, Pierucci L. APIT2: a bit of improvement for applications in critical scenarios. The 6th International Wireless Communications and Mobile Computing Conference, New York, USA, 2010 12. Wang J, Fu J Q. Research on APIT and Monte Carlo Method of localization algorithm for wireless sensor networks. LSMS/ICSEE, Part II, LNCS 6329, 2010: 128137 13. Liu Y H, Pu J H, He Y, et al. Three-dimensional self-localization scheme for wireless sensor networks. Journal of Beijing University of Aeronautics and Astronautics, 2008(34): 647651 14. He T, Huang C, Blum B M, et al. Radio range free localization schemes for large scale sensor networks. 9th Annual Int'l Conf. on Mobile Computing and Networking (Mobi Com), San Diego, CA, 2003: 8195