One of the main tasks of deploying sensor networks is determining the coordinates of nodes that are unknown at their initial placement. This problem is known as the localization problem of sensor networks. It can be solved if each node has a GPS receiver in its composition. However, such nodes are more expensive, and for networks of various purposes, for example, environmental monitoring, fixation of moving objects in a certain area, various types of IoT, and others, nodes without GPS can be used. To solve the problem of localization in such networks, so-called anchor nodes are used, the coordinates of which are known. They form a certain percentage of the total number of nodes. They are used to find the coordinates of the remaining nodes that are part of the network. If only anchor nodes are used for the localization problem, then such networks are called non-cooperative networks. If all nodes participate in the positioning of nodes, then such networks are called cooperative. Different methods are used to solve this problem such as the method of trilateration, multilateration, triangulation, random, and others. To apply these methods, it is necessary to know the distances or angles to nodes whose coordinates are determined based on the nodes with known coordinates. At the same time, various methods are used to determine distances, namely: TDOA, DOA, TOA, RTT, RSSI. Corresponding means in modern nodes are present as separate functions. For example, the IEEE 802.15.4 (ZigBee) standard. In this paper, studies of the influence of the multilateration method on the accuracy of determining the coordinates of nodes were carried out. An algorithm was used, according to which the position of the node, for which the coordinates should be determined, was generated, as well as the coordinates of the anchor nodes that take part in the localization of the node. The distance measurement error according to the ZigBee standard with a range of 1000 m was taken as 10 %. The number of anchor nodes was changed throughout the analysis, and the respective positioning error was calculated. For greater statistical significance, the experiments were repeated a certain number of times while changing the initial value of the generator of uniformly distributed random numbers, and at the same time, the average value of the localization error, and the minimum and maximum values were calculated. The obtained statistical data were visualized in the form of relevant graphs. As a result of research, it was determined that six anchor nodes are enough to obtain a positioning accuracy of 10 m.
[1] Akyildiz, W. Su., Sankarasubramaniam, Y., & Cayirci, E. (2002). Wireless sensor networks: A survey, Comput. Networks J., 38(4), 393–422. https://doi.org/10.1016/S1389-1286(01)00302-4
[2] Mohammad, Reza Gholami. (2011). Positioning Algorithms for Wireless Sensor Networks. Department of Signals and Systems Technical Report. No. R001/2011 ISSN 1403-266X
[3] Dhillon, S. S., Chakrabarty, K., & Iyengar, S. S. (2002). Sensor placement for grid coverage under imprecise detections. Proceedings of 5th International Conference on Information Fusion, (Fusion 2002), Vol. 2, Annapolis, M July 2002, IEEE, New York, 1581–1587. https://doi.org/10.1109/ICIF.2002.1021005D
[4] Chakrabarty, K., Iyengar, S. S. Qi., H., & Cho, E. (2002). Grid coverage for surveillance and target location in distributed sensor networks. IEEE Transactions on Computers, 51(12), 1448–1453. https://doi.org/10.1109/TC.2002.1146711
[5] Biagioni, E. S., & Sasaki, G. (2003). Wireless sensor placement for reliable and efficient data collection. Hawaii International Conference on Systems Sciences, (HICSS), Hawaii, January, IEEE, New York, 127–136. https://doi.org/10.1109/HICSS.2003.1174290
[6] Xu, Y., Heidemann, J., & Estrin, D. (2001). Geography-informed energy conservation for ad-hoc routing. Proceedings ACM/IEEE MobiCom01, 16–21 July, Rome. https://doi.org/10.1145/381677.381685
[7] Schurgers, C., Tsiatsis, V., Ganeriwal, S., & Srivastava, M. (2002). Optimizing sensor networks in the energy-latency-density design space. IEEE Transactions on Mobile Computing, 1(1), 70–80. https://doi.org/10.1109/TMC.2002.1011060
[8] Chen, B., Jamieson, K., Balakrishnan, H., & Morris, R. (2002). Span: An energy-efficient coordination algorithm for topology maintenance in ad hoc wireless networks. Wireless Networks, 8(5), 481–494. https://doi.org/10.1023/A:1016542229220
[9] Ye, F., Zhong, G., Cheng, J., Lu, S., & Zhang, L. (2003). PEAS: A robust energy conserving protocol for long-lived sensor networks. Proceedings of the 23rd International Conference on Distributed Computing Systems, Providence, RI, May, IEEE, New York, 28‑37.
[10] Niculescu, D., & Nath, B. (2001). Ad hoc positioning system (APS). 2001 IEEE Global Telecommunications Conference (GLOBECOM '01), Vol. 5, San Antonio, TX, Novermber, IEEE, New York, 2926–2931. https://doi.org/10.1109/GLOCOM.2001.965964
[11] Savarese, C., Rabaey, J. M., & Beutel, J. (2001). Locationing in distributed ad-hoc wireless sensor networks. Proceedings of the IEEE Signal Processing Society International Conference on Acoustics, Speech, and Signal Processing 2001 (ICASSP 01), Vol. 4, Salt Lake City, UT, May, IEEE, New-York, 2037‑2040.
[12] Savvides, A., Park, H., & Srivastava, M. B. (2002). The bits and flops of the n-hop multilateration primitive for node localization problems. Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications (WSNA’02), Atlanta, GA, September, ACM, New-York, 112–121. https://doi.org/10.1145/570738.570755
[13] Savvides, A., Han, C.-C., & Strivastava, M. B. (2003). The n-hop multilateration primitive for node localization. Mobile Networks and Applications, 8(4), 443–451. https://doi.org/10.1023/A:1024544032357
[14] Carter, G. C. (1993). Coherence and Time Delay Estimation. New York: IEEE Press.
[15] Xinwei, W., Ole, B., Rainer, L., Steffen, P. (2009). Localization in Wireless Ad-hoc Sensor Networks using Multilateration with RSSI for Logistic Applications. Proceedings of the Eurosensors XXIII conference. Published by Elsevier B. V. https://doi.org/10.1016/j.proche.2009.07.115
[16] Amanpreet, K., Padam, K., Govind, P. G. (2019). A weighted centroid localization algorithm for randomly deployed wireless sensor networks. Journal of King Saud University – Computer and Information Sciences, 31, 82–91. https://doi.org/10.1016/j.jksuci.2017.01.007
[17] Laaouafy, М., Lakrami, F., Labouidya, О., Elkamoun, N. (2022). An experimental evaluation of localization methods used in wireless sensor networks. Indonesian Journal of Electrical Engineering and Computer Science, Vol. 25, 3, March, 1518–1528. https://doi.org/10.11591/ijeecs.v25.i3.pp1518-1528
[18] Arun, M., Sivasankari, N., Vanathi, Dr. P. T., Manimegalai, Dr. P. (2017). Analysis of Average Weight Based Centroid Localization Algorithm for Mobile Wireless Sensor Networks. Advances in Wireless and Mobile Communications. ISSN 0973-6972, Vol. 10, 4, 757–780.
[19] Pingfang, H., Bo, Z. (2021). Research on Centroid Localization Algorithm in Wireless Sensor Networks. Journal of Physics: Conference Series 1883, 012026. https://doi.org/10.1088/1742-6596/1883/1/012026
[20] Ram, D., Varinderjit, K. (2014). Analysis of Some Localization Algorithm in Wireless Sensor Networks. International Journal of Computer & Organization Trends, 4, July to August, 32–36.
[21] Xin, L. (2020). Research on WSN Node Localization Algorithm Based on RSSI Iterative Centroid Estimation. Technical Gazette, 27, 5, 1544–1550. https://doi.org/10.17559/TV-20190827114252