{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T15:48:06Z","timestamp":1787500086144,"version":"build-2736575974"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,25]],"date-time":"2018-08-25T00:00:00Z","timestamp":1535155200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Modern indoor positioning system services are important technologies that play vital roles in modern life, providing many services such as recruiting emergency healthcare providers and for security purposes. Several large companies, such as Microsoft, Apple, Nokia, and Google, have researched location-based services. Wireless indoor localization is key for pervasive computing applications and network optimization. Different approaches have been developed for this technique using WiFi signals. WiFi fingerprinting-based indoor localization has been widely used due to its simplicity, and algorithms that fingerprint WiFi signals at separate locations can achieve accuracy within a few meters. However, a major drawback of WiFi fingerprinting is the variance in received signal strength (RSS), as it fluctuates with time and changing environment. As the signal changes, so does the fingerprint database, which can change the distribution of the RSS (multimodal distribution). Thus, in this paper, we propose that symmetrical H\u00f6lder divergence, which is a statistical model of entropy that encapsulates both the skew Bhattacharyya divergence and Cauchy\u2013Schwarz divergence that are closed-form formulas that can be used to measure the statistical dissimilarities between the same exponential family for the signals that have multivariate distributions. The H\u00f6lder divergence is asymmetric, so we used both left-sided and right-sided data so the centroid can be symmetrized to obtain the minimizer of the proposed algorithm. The experimental results showed that the symmetrized H\u00f6lder divergence consistently outperformed the traditional k nearest neighbor and probability neural network. In addition, with the proposed algorithm, the position error accuracy was about 1 m in buildings.<\/jats:p>","DOI":"10.3390\/e20090639","type":"journal-article","created":{"date-parts":[[2018,8,27]],"date-time":"2018-08-27T10:56:04Z","timestamp":1535367364000},"page":"639","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Convex Optimization via Symmetrical H\u00f6lder Divergence for a WLAN Indoor Positioning System"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-6953-7346","authenticated-orcid":false,"given":"Osamah","family":"Abdullah","sequence":"first","affiliation":[{"name":"Department of Electrical Power Engineering Techniques, Al-Ma\u2019moun University College, Baghdad 00964, Iraq"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,25]]},"reference":[{"key":"ref_1","unstructured":"Markets (2014). Indoor Localization Market by Positioning Systems, Map and Navigation, Location based Analysis, Monitoring and Emergency Services-Worldwide Market Forecasts and Analysis (2014\u20132019), Markets. Technical Report."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9263","DOI":"10.1016\/j.eswa.2015.08.013","article-title":"Comprehensive analysis of distance and similarity measures for Wi-Fi fingerprinting indoor positioning systems","volume":"42","author":"Montoliu","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jiang, P., Zhang, Y., Fu, W., Liu, H., and Su, X. (2015). Indoor Mobile Localization Based on Wi-Fi Fingerprint\u2019s Important Access Point. Int. J. Distrib. Sens. Netw.","DOI":"10.1155\/2015\/429104"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Shchekotov, M. (2015, January 20\u201324). Indoor localization methods based on Wi-Fi lateration and signal strength data collection. Proceedings of the 2015 17th Conference of Open Innovations Association (FRUCT), Yaroslavl, Russia.","DOI":"10.1109\/FRUCT.2015.7117991"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1016\/j.pmcj.2008.04.005","article-title":"An Effective Location Fingerprint Model for Wireless Indoor Localization","volume":"4","author":"Swangmuang","year":"2008","journal-title":"Pervasive Mob. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1109\/TIE.2014.2327595","article-title":"Indoor Localization Based on Curve Fitting and Location Search Using Received Signal Strength","volume":"62","author":"Wang","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Abdullah, O., Abdel-Qader, I., and Bazuin, B. (2016, January 16\u201318). A probability neural network-Jensen-Shannon divergence for a fingerprint based localization. Proceedings of the 2016 Annual Conference on Information Science and Systems (CISS), Princeton, NJ, USA.","DOI":"10.1109\/CISS.2016.7460516"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Abdullah, O., and Abdel-Qader, I. (2016, January 19\u201321). A PNN- Jensen-Bregman Divergence symmetrization for a WLAN Indoor Positioning System. Proceedings of the 2016 IEEE International Conference on Electro Information Technology (EIT), Grand Forks, ND, USA.","DOI":"10.1109\/EIT.2016.7535266"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Abdullah, O., Abdel-Qader, I., and Bazuin, B. (2016, January 20\u201322). Fingerprint-based technique for indoor positioning system via machine learning and convex optimization. Proceedings of the 2016 IEEE 7th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON), New York, NY, USA.","DOI":"10.1109\/UEMCON.2016.7777811"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Abdullah, O., Abdel-Qader, I., and Bazuin, B. (2016, January 20\u201322). K-means-Jensen-Shannon divergence for a WLAN indoor positioning system. Proceedings of the 2016 IEEE 7th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON), New York, NY, USA.","DOI":"10.1109\/UEMCON.2016.7777906"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"29","DOI":"10.4018\/IJHCR.2017010103","article-title":"Convex Optimization via Jensen-Bregman Divergence for WLAN Indoor Positioning System","volume":"8","author":"Abdullah","year":"2017","journal-title":"Int. J. Handheld Comput. Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sharma, P., Chakraborty, D., Banerjee, N., Banerjee, D., Agarwal, S.D., and Mittal, S. (July, January 30). KARMA: Improving WiFi-based indoor localization with dynamic causality calibration. Proceedings of the 2014 Eleventh Annual IEEE International Conference on Sensing, Communication, and Networking (SECON), Singapore.","DOI":"10.1109\/SAHCN.2014.6990331"},{"key":"ref_13","unstructured":"H\u00e4hnel, B., Dirk, B., and Fox, D. (2006, January 18\u201322). Gaussian processes for signal strength-based location estimation. Proceedings of the Robotics: Science and Systems, Ann Arbor, MI, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chan, E.C., Baciu, G., and Mak, S. (2009, January 6\u20138). Using Wi-Fi Signal Strength to Localize in Wireless Sensor Networks. Proceedings of the WRI International Conference on Communications and Mobile Computing, Yunnan, China.","DOI":"10.1109\/CMC.2009.233"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Noh, Y., Yamaguchi, H., Lee, U., Vij, P., Joy, J., and Gerla, M. (2013, January 18\u201322). CLIPS: Infrastructure-free collaborative indoor positioning scheme for time-critical team operations. Proceedings of the IEEE International Conference on Pervasive Computing and Communications (PerCom\u201913), San Diego, CA, USA.","DOI":"10.1109\/PerCom.2013.6526729"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ma, J., Li, X., Tao, X., and Lu, J. (2008, January 23\u201326). Cluster filtered KNN: A WLAN based indoor positioning scheme. Proceedings of the IEEE International Symposium on World of Wireless, Mobile and Multimedia Networks (WoWMoM\u201908), Newport Beach, CA, USA.","DOI":"10.1109\/WOWMOM.2008.4594840"},{"key":"ref_17","unstructured":"Altintas, B., and Serif, T. (2011, January 27\u201329). Improving RSS-based indoor positioning algorithm via K-Means clustering. Proceedings of the 11th European Wireless Conference 2011\u2014Sustainable Wireless Technologies (European Wireless), Vienna, Austria."},{"key":"ref_18","unstructured":"Sun, Y., Xu, Y., Ma, L., and Deng, Z. (2009, January 19\u201320). KNN-FCMhybrid algorithm for indoor location in WLAN. Proceedings of the 2nd International Conference on Power Electronics and Intelligent Transportation System (PEITS\u201909), Shenzhen, China."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1186\/1687-1499-2013-272","article-title":"Fingerprint indoor positioning algorithm based on affinity propagation clustering","volume":"2013","author":"Tian","year":"2013","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Castro, P., Chiu, P., Kremenek, T., and Muntz, R. (October, January 30). A Probabilistic Location Service for Wireless Network Environments. Proceedings of the International Conference on Ubiquitous Computing (Ubicomp\u20192001), Atlanta, GA, USA.","DOI":"10.1007\/3-540-45427-6_3"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chen, C., Chen, Y., Yin, L., and Hwang, R. (2012, January 14\u201316). A Modified Probability Neural Network Indoor Positioning Technique. Proceedings of the 2012 International Conference on Information Security and Intelligent Control, Yunlin, Taiwan.","DOI":"10.1109\/ISIC.2012.6449770"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1023\/A:1016003126882","article-title":"A Probabilistic Approach to WLAN User Location Estimation","volume":"9","author":"Roos","year":"2002","journal-title":"Int. J. Wirel. Inf. Netw."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s11036-008-0139-0","article-title":"Unsupervised Learning for Solving RSS Hardware Variance Problem in WiFi Localization","volume":"14","author":"Tsui","year":"2009","journal-title":"Mob. Netw. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Milioris, D., Kriara, L., Papakonstantinou, A., and Tzagkarakis, G. (2010, January 17\u201321). Empirical Evaluation of Signal-Strength Fingerprint Positioning in Wireless LANs. Proceedings of the 13th ACM International Conference on Modeling, Analysis, and Simulation of Wireless and Mobile Systems, Bodrum, Turkey.","DOI":"10.1145\/1868521.1868525"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mirowski, P., Steck, H., Whiting, P.R., Palaniappan, R., MacDonald, M., and Ho, T.K. (2011, January 21\u201323). KL-Divergence Kernel Regression for Non-Gaussian Fingerprint Based Localization. Proceedings of the 2011 International Conference on Indoor Positioning and Indoor Navigation, Guimaraes, Portugal.","DOI":"10.1109\/IPIN.2011.6071928"},{"key":"ref_26","unstructured":"Bahl, P., and Padmanabhan, V.N. (2000, January 26\u201330). RADAR: An in-building RF-based user location and tracking system. Proceedings of the Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies, IEEE INFOCOM 2000, Tel Aviv, Israel."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Youssef, M., and Agrawala, A. (2005, January 6\u20138). The Horus WLAN Location Determination System. Proceedings of the 3rd International Conference on Mobile Systems, Applications, and Services, Seattle, WA, USA.","DOI":"10.1145\/1067170.1067193"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1109\/TMC.2011.216","article-title":"Received-Signal-Strength-Based Indoor Positioning Using Compressive Sensing","volume":"11","author":"Feng","year":"2012","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Nielsen, F., and Nock, R. (2011). Skew Jensen-Bregman Voronoi Diagrams. Transaction on Computer Science XIV, Springer.","DOI":"10.1007\/978-3-642-25249-5_4"},{"key":"ref_30","unstructured":"Nielsen, F. (arXiv, 2010). A family of statistical symmetric divergences based on Jensen\u2019s inequality, arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/18.61115","article-title":"Divergence measures based on the Shannon entropy","volume":"37","author":"Lin","year":"1991","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","article-title":"Least squares quantization in PCM","volume":"28","author":"Lloyd","year":"1982","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_33","first-page":"1705","article-title":"Clustering with Bregman divergences","volume":"6","author":"Banerjee","year":"2005","journal-title":"J. Mach. Learn. Res."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Nielsen, F., Sun, K., and Marchand-Maillet, S. (2017, January 7\u20139). k-Means Clustering with H\u00f6lder Divergences. Proceedings of the International Conference on Geometric Science of Information, Paris, France.","DOI":"10.1007\/978-3-319-68445-1_98"},{"key":"ref_35","unstructured":"Youssef, M., Agrawala, A., and Udaya Shankar, A. (2003, January 24\u201326). WLAN location determination via clustering and probability distributions. Proceedings of the 1st IEEE International Conference on Pervasive Computing and Communications, Fort Worth, TX, USA."},{"key":"ref_36","unstructured":"Duda, R.O., Hart, P.E., and Stork, D.G. (2000). Pattern Classification, Wiley-InterScience. [2nd ed.]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1099-4300\/20\/9\/639\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:21:07Z","timestamp":1760196067000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1099-4300\/20\/9\/639"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,25]]},"references-count":36,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["e20090639"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/e20090639","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,25]]}}}