<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">gyroscopy</journal-id><journal-title-group><journal-title xml:lang="ru">Гироскопия и навигация</journal-title><trans-title-group xml:lang="en"><trans-title>Giroskopiya i Navigatsiya / Gyroscopy and Navigation</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0869-7035</issn><issn pub-type="epub">2075-0927</issn><publisher><publisher-name>AO «Концерн «ЦНИИ «Электроприбор»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17285/0869-7035.2016.24.1.003-035</article-id><article-id custom-type="elpub" pub-id-type="custom">gyroscopy-334</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Обзор параметрических методов позиционирования на основе концепции отпечатка пальца</article-title><trans-title-group xml:lang="en"><trans-title>A survey of fingerprinting and parametric fingerprint-positioning methods</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мюллер</surname><given-names>Ф.</given-names></name><name name-style="western" xml:lang="en"><surname>Müller</surname><given-names>P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мюллер Филипп, докторант.</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Райтохарью</surname><given-names>M.</given-names></name><name name-style="western" xml:lang="en"><surname>Raitoharju</surname><given-names>M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Райтохарью Mатти, доктор наук, научный сотрудник.</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Али-Лойту</surname><given-names>С.</given-names></name><name name-style="western" xml:lang="en"><surname>Ali-Löytty</surname><given-names>S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Али-Лойту Симо, преподаватель</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Вирола</surname><given-names>Л.</given-names></name><name name-style="western" xml:lang="en"><surname>Wirola</surname><given-names>L.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Вирола Лаура, научный сотрудник.</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Пише</surname><given-names>Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Piché</surname><given-names>R.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Пише Роберт. Доктор наук, профессор.</p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Технологический университет Тампере, факультет автоматизации и проектирования</institution><country>Финляндия</country></aff><aff xml:lang="en"><institution>Tampere University of Technology</institution><country>Finland</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Технологический университет Тампере, факультет математики.</institution><country>Финляндия</country></aff><aff xml:lang="en"><institution>Tampere University of Technology</institution><country>Finland</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Технологический университет Тампере.</institution><country>Финляндия</country></aff><aff xml:lang="en"><institution>Tampere University of Technology</institution><country>Finland</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2016</year></pub-date><pub-date pub-type="epub"><day>01</day><month>12</month><year>2025</year></pub-date><volume>24</volume><issue>1</issue><fpage>36</fpage><lpage>48</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Мюллер Ф., Райтохарью M., Али-Лойту С., Вирола Л., Пише Р., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Мюллер Ф., Райтохарью M., Али-Лойту С., Вирола Л., Пише Р.</copyright-holder><copyright-holder xml:lang="en">Müller P., Raitoharju M., Ali-Löytty S., Wirola L., Piché R.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.gyroscopy.ru/jour/article/view/334">https://www.gyroscopy.ru/jour/article/view/334</self-uri><abstract><p>Под термином «позиционирование на основе отпечатка пальца» (англ. fingerprinting – метод отпечатка пальца, метод фингерпринтинга) понимается большое разнообразие методов определения местоположения приемника с использованием базы данных мощностей радиосигнала, ранее измеренных и привязанных к координатам. Непараметрические методы, напр. метод k взвешенных ближайших соседей (WKNN), невозможно использовать в крупномасштабных службах для мобильных устройств вследствие больших объемов данных и требований к передаче информации. В предлагаемой работе представлен обзор параметрических методов фингерпринтинга, которые используют представления данных на основе моделей. Рассмотрены три различные группы параметрических методов: методы, использующие области покрытия, методы, использующие потери при распространении сигнала, и методы, использующие смесь нормальных распределений. В рамках каждой группы рассматриваются различные подходы, их достоинства и недостатки. Обсуждается качество позиционирования в помещении с использованием некоторых из приведенных подходов в различных сценариях по данным беспроводных локальных сетей (WLAN). Полученные результаты сравниваются с результатами для непараметрического метода WKNN.</p></abstract><trans-abstract xml:lang="en"><p>The term fingerprint-based (FP) positioning includes a wide variety of methods for determining a receiver’s position using a database of radio signal strength measurements that were collected earlier at known locations. Nonparametric methods such as the weighted k-nearest neighbor (WKNN) method are infeasible for largescale mobile device services because of the large data storage and transmission requirements. In this work we present an overview of parametric FP methods that use model-based representations of the survey data. We look at three different groups of parametric methods: methods that use coverage areas, methods that use path loss models, and methods that use Gaussian mixtures. Within each group we study different approaches and discuss their pros and cons. Furthermore, we test the positioning performance of several of the analyzed approaches in different scenarios using real-world WLAN indoor data and compare the results to those of the WKNN method.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Фингерпринтинг</kwd><kwd>параметрические методы позиционирования</kwd><kwd>сравнение.</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Fingerprint-based (FP) positioning</kwd><kwd>parametric FP methods</kwd><kwd>comparison.</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">ЛИТЕРАТУРА</mixed-citation><mixed-citation xml:lang="en">ЛИТЕРАТУРА</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">S. Gezici, Z. Tian, G. B. Biannakis, H. Kobayashi, A. F. Molisch, H. V. Poor, and Z. Sahinoglu, “Localization via ultra-wideband radios: a look at positioning aspects for future sensor networks,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 70–84, July 2005.</mixed-citation><mixed-citation xml:lang="en">S. Gezici, Z. Tian, G. B. Biannakis, H. Kobayashi, A. F. Molisch, H. V. Poor, and Z. Sahinoglu, “Localization via ultra-wideband radios: a look at positioning aspects for future sensor networks,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 70–84, July 2005.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">F. Gustafsson and F. Gunnarsson, “Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 41–53, July 2005.</mixed-citation><mixed-citation xml:lang="en">F. Gustafsson and F. Gunnarsson, “Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 41–53, July 2005.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">E. Trevisani and A. Vitaletti, “Cell-id location technique, limits and benefits: an experimental study,” in Proceedings of Sixth IEEE Workshop on Mobile Computing Systems and Applications (WMCSA 2004). Windermere, Cumbria, United Kingdom, December 2004.</mixed-citation><mixed-citation xml:lang="en">E. Trevisani and A. Vitaletti, “Cell-id location technique, limits and benefits: an experimental study,” in Proceedings of Sixth IEEE Workshop on Mobile Computing Systems and Applications (WMCSA 2004). Windermere, Cumbria, United Kingdom, December 2004.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">L. Wirola, “Studies on location technology standards evolution in wireless networks,” Ph.D. dissertation, Tampere University of Technology, March 2010. [Online]. Available: http://URN.fi/URN:NBN:fi:tty-201002121065</mixed-citation><mixed-citation xml:lang="en">L. Wirola, “Studies on location technology standards evolution in wireless networks,” Ph.D. dissertation, Tampere University of Technology, March 2010. [Online]. Available: http://URN.fi/URN:NBN:fi:tty-201002121065</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">D. Dardari, A. Conti, U. Ferner, A. Giorgetti, and M. Z. Win, “Ranging with ultrawide bandwidth signals in multipath environments,” Proceedings of the IEEE, vol. 97, no. 2, pp. 404–426, February 2009.</mixed-citation><mixed-citation xml:lang="en">D. Dardari, A. Conti, U. Ferner, A. Giorgetti, and M. Z. Win, “Ranging with ultrawide bandwidth signals in multipath environments,” Proceedings of the IEEE, vol. 97, no. 2, pp. 404–426, February 2009.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">R. Mautz, “Indoor positioning technologies,” Habilitation Thesis, http://ecollection.library.ethz.ch/eserv/eth:5659/eth-5659-01.pdf, February 2012.</mixed-citation><mixed-citation xml:lang="en">R. Mautz, “Indoor positioning technologies,” Habilitation Thesis, http://ecollection.library.ethz.ch/eserv/eth:5659/eth-5659-01.pdf, February 2012.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor positioning techniques and systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 37, no. 6, pp. 1067–1080, November 2007.</mixed-citation><mixed-citation xml:lang="en">H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor positioning techniques and systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 37, no. 6, pp. 1067–1080, November 2007.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">M. I. Silventoinen and T. Rantalainen, “Mobile station emergency locating in GSM,” in Proceedings of IEEE International Conference on Personal Wireless Communications. New Delhi, India, February 1996, pp. 232–238.</mixed-citation><mixed-citation xml:lang="en">M. I. Silventoinen and T. Rantalainen, “Mobile station emergency locating in GSM,” in Proceedings of IEEE International Conference on Personal Wireless Communications. New Delhi, India, February 1996, pp. 232–238.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">I. Constandache, S. Gaonkar, M. Sayler, R. R. Choudhury, and L. Cox, “EnLoc: Energyefficient localization for mobile phones,” in 2009 Proceedings IEEE INFOCOM. Rio de Janeiro, Brazil, April 2009, pp. 2716–2720.</mixed-citation><mixed-citation xml:lang="en">I. Constandache, S. Gaonkar, M. Sayler, R. R. Choudhury, and L. Cox, “EnLoc: Energyefficient localization for mobile phones,” in 2009 Proceedings IEEE INFOCOM. Rio de Janeiro, Brazil, April 2009, pp. 2716–2720.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">M. A. Spirito, S. Pöykkö, and O. Knuuttila, “Experimental performance of methods to estimate the location of legacy handsets in GSM,” in IEEE VTS 54th Vehicular Technology Conference (VTC), 2001. Atlantic City, NJ, USA, October 2001, pp. 2716–2720.</mixed-citation><mixed-citation xml:lang="en">M. A. Spirito, S. Pöykkö, and O. Knuuttila, “Experimental performance of methods to estimate the location of legacy handsets in GSM,” in IEEE VTS 54th Vehicular Technology Conference (VTC), 2001. Atlantic City, NJ, USA, October 2001, pp. 2716–2720.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">J. A. del Peral-Rosado, J. A. López-Salcedo, G. Seco-Granados, F. Zanier, and M. Crisci, “Analysis of positioning capabilities of 3GPP LTE,” in Proceeddings of 25th International Technical Meeting of the Satellite Division of ION, Nashville, TN, USA, September 2012.</mixed-citation><mixed-citation xml:lang="en">J. A. del Peral-Rosado, J. A. López-Salcedo, G. Seco-Granados, F. Zanier, and M. Crisci, “Analysis of positioning capabilities of 3GPP LTE,” in Proceeddings of 25th International Technical Meeting of the Satellite Division of ION, Nashville, TN, USA, September 2012.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">L. Wirola, T. A. Laine, and J. Syrjärinne, “Mass-market requirements for indoor positioning and indoor navigation,” in 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Zurich, Switzerland, September 2010.</mixed-citation><mixed-citation xml:lang="en">L. Wirola, T. A. Laine, and J. Syrjärinne, “Mass-market requirements for indoor positioning and indoor navigation,” in 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Zurich, Switzerland, September 2010.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">J. Park, D. Curtis, S. Teller, and J. Ledlie, “Implications of device diversity for organic localization,” in 2011 Proceedings IEEE INFOCOM, April 2011, pp. 3182–3190.</mixed-citation><mixed-citation xml:lang="en">J. Park, D. Curtis, S. Teller, and J. Ledlie, “Implications of device diversity for organic localization,” in 2011 Proceedings IEEE INFOCOM, April 2011, pp. 3182–3190.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">A. F. Molisch, Wireless Communications, 2nd ed. Wiley - IEEE, January 2011.</mixed-citation><mixed-citation xml:lang="en">A. F. Molisch, Wireless Communications, 2nd ed. Wiley - IEEE, January 2011.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">V. Honkavirta, T. Perälä, S. Ali-Löytty, and R. Piché, “A comparative survey of WLAN location fingerprinting methods,” in Proceedings of the 6th Workshop on Positioning, Navigation and Communication 2009 (WPNC’09). Hannover, Germany, March 2009, pp. 243–251.</mixed-citation><mixed-citation xml:lang="en">V. Honkavirta, T. Perälä, S. Ali-Löytty, and R. Piché, “A comparative survey of WLAN location fingerprinting methods,” in Proceedings of the 6th Workshop on Positioning, Navigation and Communication 2009 (WPNC’09). Hannover, Germany, March 2009, pp. 243–251.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">C. Figuera, I. Mora-Jiménez, A. Guerrero-Curieses, J. L. Rojo-Álvarez, E. Everss, M. Wilby, and J. Ramos-López, “Nonparametric model comparison and uncertainty evaluation for signal strength indoor location,” IEEE Transactions on Mobile Computing, vol. 8, no. 9, pp. 1250–1264, September 2009.</mixed-citation><mixed-citation xml:lang="en">C. Figuera, I. Mora-Jiménez, A. Guerrero-Curieses, J. L. Rojo-Álvarez, E. Everss, M. Wilby, and J. Ramos-López, “Nonparametric model comparison and uncertainty evaluation for signal strength indoor location,” IEEE Transactions on Mobile Computing, vol. 8, no. 9, pp. 1250–1264, September 2009.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">P. Müller, M. Raitoharju, and R. Piché, “A field test of parametric WLAN-fingerprintpositioning methods,” in Proceedings of the 17th International Conference on Information Fusion (Fusion 2014). Salamanca, Spain, July 2014, pp. 1–8.</mixed-citation><mixed-citation xml:lang="en">P. Müller, M. Raitoharju, and R. Piché, “A field test of parametric WLAN-fingerprintpositioning methods,” in Proceedings of the 17th International Conference on Information Fusion (Fusion 2014). Salamanca, Spain, July 2014, pp. 1–8.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">S. Han, Z. Gong, W. Meng, and C. Li, “An indoor radio propagation model considering angles for WLAN infrastructures,” Wireless Communications and Mobile Computing, 2015 (in press).</mixed-citation><mixed-citation xml:lang="en">S. Han, Z. Gong, W. Meng, and C. Li, “An indoor radio propagation model considering angles for WLAN infrastructures,” Wireless Communications and Mobile Computing, 2015 (in press).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">S. Shrestha, J. Talvitie, and E. S. Lohan, “Deconvolution-based indoor localization with WLAN signals and unknown access point locations,” in 2013 International Conference on Localization and GNSS (ICL-GNSS). Torino, Italy, June 2013, pp. 1–6.</mixed-citation><mixed-citation xml:lang="en">S. Shrestha, J. Talvitie, and E. S. Lohan, “Deconvolution-based indoor localization with WLAN signals and unknown access point locations,” in 2013 International Conference on Localization and GNSS (ICL-GNSS). Torino, Italy, June 2013, pp. 1–6.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">L. Koski, R. Piché, V. Kaseva, S. Ali-Löytty, and M. Hännikäinen, “Positioning with coverage area estimates generated from location fingerprints,” in Proceedings of the 7th Workshop on Positioning, Navigation and Communication 2010 (WPNC’10). Dresden, Germany, March 2010, pp. 99–106.</mixed-citation><mixed-citation xml:lang="en">L. Koski, R. Piché, V. Kaseva, S. Ali-Löytty, and M. Hännikäinen, “Positioning with coverage area estimates generated from location fingerprints,” in Proceedings of the 7th Workshop on Positioning, Navigation and Communication 2010 (WPNC’10). Dresden, Germany, March 2010, pp. 99–106.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">J. Machaj, R. Piché, and P. Brida, “Rank based fingerprinting algorithm for indoor positioning,” in 2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Guimaraes, Portugal, September 2011, pp. 6–11.</mixed-citation><mixed-citation xml:lang="en">J. Machaj, R. Piché, and P. Brida, “Rank based fingerprinting algorithm for indoor positioning,” in 2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Guimaraes, Portugal, September 2011, pp. 6–11.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">L. Wirola, L. Wirola, and R. Piché, “Bandwidth and storage reduction of radio maps for offline WLAN positioning,” in 2013 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Montbeliard-Belfort, France, October 2013.</mixed-citation><mixed-citation xml:lang="en">L. Wirola, L. Wirola, and R. Piché, “Bandwidth and storage reduction of radio maps for offline WLAN positioning,” in 2013 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Montbeliard-Belfort, France, October 2013.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">S. Eisa, J. Peixoto, F. Meneses, and A. Moreira, “Removing useless APs and fingerprints from WiFi indoor positioning radio maps,” in 2013 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Montbeliard-Belfort, France, 2013, pp. 739–745.</mixed-citation><mixed-citation xml:lang="en">S. Eisa, J. Peixoto, F. Meneses, and A. Moreira, “Removing useless APs and fingerprints from WiFi indoor positioning radio maps,” in 2013 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Montbeliard-Belfort, France, 2013, pp. 739–745.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">M. Raitoharju, T. Fadjukoff, S. Ali-Löytty, and R. Piché, “Using unlocated fingerprints in generation of WLAN maps for indoor positioning,” in Proceedings of PLANS 2012 IEEE/ION Position Location and Navigation Symposium. Myrtle Beach, SC, USA, April 2012, pp. 576–583.</mixed-citation><mixed-citation xml:lang="en">M. Raitoharju, T. Fadjukoff, S. Ali-Löytty, and R. Piché, “Using unlocated fingerprints in generation of WLAN maps for indoor positioning,” in Proceedings of PLANS 2012 IEEE/ION Position Location and Navigation Symposium. Myrtle Beach, SC, USA, April 2012, pp. 576–583.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">L. Wirola, I. Halivaara, and J. Syrjärinne, “Requirements for the next generation standardized location technology protocol for location-based services,” Journal of Global Positioning Systems, vol. 7, no. 2, pp. 91–103, 2008.</mixed-citation><mixed-citation xml:lang="en">L. Wirola, I. Halivaara, and J. Syrjärinne, “Requirements for the next generation standardized location technology protocol for location-based services,” Journal of Global Positioning Systems, vol. 7, no. 2, pp. 91–103, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">K. Kaemarungsi and P. Krishnamurthy, “Properties of indoor received signal strength for WLAN location fingerprinting,” in The First Annual International Conference on Mobile and Ubiquitous Systems: Networking and Services (MOBIQUITIOUS 2004). Boston, MA, USA, August 2004, pp. 14–23.</mixed-citation><mixed-citation xml:lang="en">K. Kaemarungsi and P. Krishnamurthy, “Properties of indoor received signal strength for WLAN location fingerprinting,” in The First Annual International Conference on Mobile and Ubiquitous Systems: Networking and Services (MOBIQUITIOUS 2004). Boston, MA, USA, August 2004, pp. 14–23.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">T. Vaupel, J. Seitz, F. Kiefer, S. Haimerl, and J. Thielecke, “Wi-Fi positioning: System considerations and device calibration,” in 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Zurich, Switzerland, September 2010.</mixed-citation><mixed-citation xml:lang="en">T. Vaupel, J. Seitz, F. Kiefer, S. Haimerl, and J. Thielecke, “Wi-Fi positioning: System considerations and device calibration,” in 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Zurich, Switzerland, September 2010.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">C. Laoudias, R. Piché, and C. G. Panayiotou, “Device signal strength self-calibration using histograms,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation><mixed-citation xml:lang="en">C. Laoudias, R. Piché, and C. G. Panayiotou, “Device signal strength self-calibration using histograms,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">L. Koski, T. Perälä, and R. Piché, “Indoor positioning using WLAN coverage area estimates,” in 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Zurich, Switzerland, September 2010.</mixed-citation><mixed-citation xml:lang="en">L. Koski, T. Perälä, and R. Piché, “Indoor positioning using WLAN coverage area estimates,” in 2010 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Zurich, Switzerland, September 2010.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">A. Haeberlen, E. Flannery, A. M. Ladd, A. Rudys, D. S. Wallach, and L. E. Kavraki, “Practical robust localization over large-scale 802.11 wireless networks,” in MobileCom’04. Philadelphia, PA, USA, September-October 2004.</mixed-citation><mixed-citation xml:lang="en">A. Haeberlen, E. Flannery, A. M. Ladd, A. Rudys, D. S. Wallach, and L. E. Kavraki, “Practical robust localization over large-scale 802.11 wireless networks,” in MobileCom’04. Philadelphia, PA, USA, September-October 2004.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">M. B. Kjaergaard, “Indoor location fingerprinting with heterogeneous clients,” Pervasive and Mobile Computing, vol. 7, no. 1, pp. 31–43, 2011.</mixed-citation><mixed-citation xml:lang="en">M. B. Kjaergaard, “Indoor location fingerprinting with heterogeneous clients,” Pervasive and Mobile Computing, vol. 7, no. 1, pp. 31–43, 2011.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Y.-C. Cheng, Y. Chawathe, A. LaMarca, and J. Krumm, “Accuracy characterization for metropolitan-scale Wi-Fi localization,” in Proceedings of the 3rd International Conference on Mobile Systems, Applications and Services (MobiSys 2005). Seattle, WA, USA, June 2005.</mixed-citation><mixed-citation xml:lang="en">Y.-C. Cheng, Y. Chawathe, A. LaMarca, and J. Krumm, “Accuracy characterization for metropolitan-scale Wi-Fi localization,” in Proceedings of the 3rd International Conference on Mobile Systems, Applications and Services (MobiSys 2005). Seattle, WA, USA, June 2005.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">A. M. Hossain and W.-S. Soh, “Cramér-Rao bound analysis of localization using signal strength difference as location fingerprint,” in 2010 Proceedings IEEE INFOCOM. San Diego, CA, USA, March 2010.</mixed-citation><mixed-citation xml:lang="en">A. M. Hossain and W.-S. Soh, “Cramér-Rao bound analysis of localization using signal strength difference as location fingerprint,” in 2010 Proceedings IEEE INFOCOM. San Diego, CA, USA, March 2010.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">A. H. Jazwinski, Stochastic Processes and Filtering Theory, ser. Mathematics in Science and Engineering. Academic Press, 1970, vol. 64.</mixed-citation><mixed-citation xml:lang="en">A. H. Jazwinski, Stochastic Processes and Filtering Theory, ser. Mathematics in Science and Engineering. Academic Press, 1970, vol. 64.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">S. Särkkä, Bayesian Filtering and Smoothing. Cambridge University Press, 2013.</mixed-citation><mixed-citation xml:lang="en">S. Särkkä, Bayesian Filtering and Smoothing. Cambridge University Press, 2013.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Y. Bar-Shalom, R. X. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, Theory Algorithms and Software. John Wiley &amp; Sons, 2001.</mixed-citation><mixed-citation xml:lang="en">Y. Bar-Shalom, R. X. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, Theory Algorithms and Software. John Wiley &amp; Sons, 2001.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">R. Piché, “Robust estimation of a reception region from location fingerprints,” in 2011 International Conference on Localization and GNSS (ICL-GNSS). Tampere, Finland, June 2011, pp. 31–35.</mixed-citation><mixed-citation xml:lang="en">R. Piché, “Robust estimation of a reception region from location fingerprints,” in 2011 International Conference on Localization and GNSS (ICL-GNSS). Tampere, Finland, June 2011, pp. 31–35.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">L. Koski, “Positioning with Bayesian coverage area estimates and location fingerprints,” Master’s thesis, Tampere University of Technology, http://math.tut.fi/posgroup/koski_mscth.pdf, March 2010.</mixed-citation><mixed-citation xml:lang="en">L. Koski, “Positioning with Bayesian coverage area estimates and location fingerprints,” Master’s thesis, Tampere University of Technology, http://math.tut.fi/posgroup/koski_mscth.pdf, March 2010.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">M. Raitoharju, S. Ali-Löytty, R. Piché, and M. Dashti, “Positioning with multilevel coverage area models,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation><mixed-citation xml:lang="en">M. Raitoharju, S. Ali-Löytty, R. Piché, and M. Dashti, “Positioning with multilevel coverage area models,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-6, no. 6, pp. 721–741, 1984.</mixed-citation><mixed-citation xml:lang="en">S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-6, no. 6, pp. 721–741, 1984.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society. Series B (Methodological), vol. 39, no. 1, pp. 1–38, 1977.</mixed-citation><mixed-citation xml:lang="en">A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society. Series B (Methodological), vol. 39, no. 1, pp. 1–38, 1977.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">V. Honkavirta, “Location fingerprinting methods in wireless local area networks,” Master’s thesis, Tampere University of Technology, http://urn.fi/URN:NBN:fi:tty-200911137109, November 2008.</mixed-citation><mixed-citation xml:lang="en">V. Honkavirta, “Location fingerprinting methods in wireless local area networks,” Master’s thesis, Tampere University of Technology, http://urn.fi/URN:NBN:fi:tty-200911137109, November 2008.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">C. Laoudias, C. G. Panayiotou, and P. Kemppi, “On the RBF-based positioning using WLAN signal strength fingerprints,” in Proceedings of the 7th Workshop on Positioning, Navigation and Communication 2010 (WPNC’10). Dresden, Germany, March 2010, pp. 93–98.</mixed-citation><mixed-citation xml:lang="en">C. Laoudias, C. G. Panayiotou, and P. Kemppi, “On the RBF-based positioning using WLAN signal strength fingerprints,” in Proceedings of the 7th Workshop on Positioning, Navigation and Communication 2010 (WPNC’10). Dresden, Germany, March 2010, pp. 93–98.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">K. Kaji and N. Kawaguchi, “Design and implementation of WiFi indoor localization based on Gaussian mixture model and particle filter,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation><mixed-citation xml:lang="en">K. Kaji and N. Kawaguchi, “Design and implementation of WiFi indoor localization based on Gaussian mixture model and particle filter,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">H. Hashemi, “The indoor radio propagation channel,” Proceedings of the IEEE, vol. 81, no. 7, pp. 943–968, July 1993.</mixed-citation><mixed-citation xml:lang="en">H. Hashemi, “The indoor radio propagation channel,” Proceedings of the IEEE, vol. 81, no. 7, pp. 943–968, July 1993.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">N. Patwari, I. Alfred O. Hero, M. Perkins, N. S. Correal, and R. J. O’Dea, “Relative location estimation in wireless sensor networks,” IEEE Transactions on Signal Processing, vol. 51, no. 8, pp. 2137–2148, August 2003.</mixed-citation><mixed-citation xml:lang="en">N. Patwari, I. Alfred O. Hero, M. Perkins, N. S. Correal, and R. J. O’Dea, “Relative location estimation in wireless sensor networks,” IEEE Transactions on Signal Processing, vol. 51, no. 8, pp. 2137–2148, August 2003.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">X. Li, “RSS-based location estimation with unknown pathloss model,” IEEE Transactions on Wireless Communications, vol. 5, no. 12, pp. 3626–3633, December 2006.</mixed-citation><mixed-citation xml:lang="en">X. Li, “RSS-based location estimation with unknown pathloss model,” IEEE Transactions on Wireless Communications, vol. 5, no. 12, pp. 3626–3633, December 2006.</mixed-citation></citation-alternatives></ref><ref id="cit49"><label>49</label><citation-alternatives><mixed-citation xml:lang="ru">T. Roos, P. Myllymäki, and H. Tirri, “A statistical modeling approach to location estimation,” IEEE Transactions on Mobile Computing, vol. 1, no. 1, pp. 59–69, Jan-Mar 2002.</mixed-citation><mixed-citation xml:lang="en">T. Roos, P. Myllymäki, and H. Tirri, “A statistical modeling approach to location estimation,” IEEE Transactions on Mobile Computing, vol. 1, no. 1, pp. 59–69, Jan-Mar 2002.</mixed-citation></citation-alternatives></ref><ref id="cit50"><label>50</label><citation-alternatives><mixed-citation xml:lang="ru">S. M. Bo-Chieh Liu, K.-H. Lin, and J.-C. Wu, “Analysis of hyperbolic and circular positioning algorithms using stationary signal-strength-difference measurements in wireless communications,” IEEE Transactions on Vehicular Technology, vol. 55, no. 2, pp. 499–509, March 2006.</mixed-citation><mixed-citation xml:lang="en">S. M. Bo-Chieh Liu, K.-H. Lin, and J.-C. Wu, “Analysis of hyperbolic and circular positioning algorithms using stationary signal-strength-difference measurements in wireless communications,” IEEE Transactions on Vehicular Technology, vol. 55, no. 2, pp. 499–509, March 2006.</mixed-citation></citation-alternatives></ref><ref id="cit51"><label>51</label><citation-alternatives><mixed-citation xml:lang="ru">H. Nurminen, J. Talvitie, S. Ali-Löytty, P. Müller, E. S. Lohan, R. Piché, and M. Renfors, “Statistical path loss parameter estimation and positioning using RSS measurements in indoor wireless networks,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation><mixed-citation xml:lang="en">H. Nurminen, J. Talvitie, S. Ali-Löytty, P. Müller, E. S. Lohan, R. Piché, and M. Renfors, “Statistical path loss parameter estimation and positioning using RSS measurements in indoor wireless networks,” in 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN). Sydney, NSW, Australia, November 2012.</mixed-citation></citation-alternatives></ref><ref id="cit52"><label>52</label><citation-alternatives><mixed-citation xml:lang="ru">J. Salo, L. Vuokko, H. M. El-Sallabi, and P. Vainikainen, “An additive model as a physical basis for shadow fading,” IEEE Transactions on Vehicular Technology, vol. 56, no. 1, pp. 13–26, January 2007.</mixed-citation><mixed-citation xml:lang="en">J. Salo, L. Vuokko, H. M. El-Sallabi, and P. Vainikainen, “An additive model as a physical basis for shadow fading,” IEEE Transactions on Vehicular Technology, vol. 56, no. 1, pp. 13–26, January 2007.</mixed-citation></citation-alternatives></ref><ref id="cit53"><label>53</label><citation-alternatives><mixed-citation xml:lang="ru">V. Erceg, L. J. Greenstein, S. Y. Tjandra, S. R. Parkoff, A. Gupta, B. Kulic, A. A. Julius, and R. Bianchi, “An empirically based path loss model for wireless channels in suburban environments,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 7, pp. 1205–1211, 1999.</mixed-citation><mixed-citation xml:lang="en">V. Erceg, L. J. Greenstein, S. Y. Tjandra, S. R. Parkoff, A. Gupta, B. Kulic, A. A. Julius, and R. Bianchi, “An empirically based path loss model for wireless channels in suburban environments,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 7, pp. 1205–1211, 1999.</mixed-citation></citation-alternatives></ref><ref id="cit54"><label>54</label><citation-alternatives><mixed-citation xml:lang="ru">T. S. Rappaport, S. Y. Seidel, and K. Takamizawa, “Statistical channel impulse response models for factory and open plan building radio communication system design,” IEEE Transactions on Communications, vol. 39, no. 5, pp. 794–807, 1991.</mixed-citation><mixed-citation xml:lang="en">T. S. Rappaport, S. Y. Seidel, and K. Takamizawa, “Statistical channel impulse response models for factory and open plan building radio communication system design,” IEEE Transactions on Communications, vol. 39, no. 5, pp. 794–807, 1991.</mixed-citation></citation-alternatives></ref><ref id="cit55"><label>55</label><citation-alternatives><mixed-citation xml:lang="ru">S. S. Ghassenizadeh, R. Jana, C. W. Rice, W. Turin, and V. Tarokh, “A statistical path loss model for in-home UWB channels,” in 2002 IEEE Conference on Ultra Wideband Systems and Technologies. Baltimore, MD, USA, May 2002, pp. 59–64.</mixed-citation><mixed-citation xml:lang="en">S. S. Ghassenizadeh, R. Jana, C. W. Rice, W. Turin, and V. Tarokh, “A statistical path loss model for in-home UWB channels,” in 2002 IEEE Conference on Ultra Wideband Systems and Technologies. Baltimore, MD, USA, May 2002, pp. 59–64.</mixed-citation></citation-alternatives></ref><ref id="cit56"><label>56</label><citation-alternatives><mixed-citation xml:lang="ru">B. Dil and P. Havinga, “RSS-based localization with different antenna orientations,” in 2010 Australasian Telecommunication Networks and Applications Conference (ATNAC). Auckland, New Zealand, 2010, pp. 13–18.</mixed-citation><mixed-citation xml:lang="en">B. Dil and P. Havinga, “RSS-based localization with different antenna orientations,” in 2010 Australasian Telecommunication Networks and Applications Conference (ATNAC). Auckland, New Zealand, 2010, pp. 13–18.</mixed-citation></citation-alternatives></ref><ref id="cit57"><label>57</label><citation-alternatives><mixed-citation xml:lang="ru">S. Shrestha, E. Laitinen, J. Talvitie, and E. S. Lohan, “RSSI channel effects in cellular and WLAN positioning,” in Proceedings of the 9th Workshop on Positioning, Navigation and Communication 2012 (WPNC’12). Dresden, Germany, March 2012, pp. 187–192.</mixed-citation><mixed-citation xml:lang="en">S. Shrestha, E. Laitinen, J. Talvitie, and E. S. Lohan, “RSSI channel effects in cellular and WLAN positioning,” in Proceedings of the 9th Workshop on Positioning, Navigation and Communication 2012 (WPNC’12). Dresden, Germany, March 2012, pp. 187–192.</mixed-citation></citation-alternatives></ref><ref id="cit58"><label>58</label><citation-alternatives><mixed-citation xml:lang="ru">T. S. Rappaport, Wireless Communications - Principles and Practice, 2nd ed. Prentice-Hall, 2010. 58. S. Y. Seidel and T. S. Rappaport, “914 MHz path loss prediction models for indoor wireless communications in multifloored buildings,” IEEE Transactions on Antennas and Propagation, vol. 40, no. 2, pp. 207–217, February 1992.</mixed-citation><mixed-citation xml:lang="en">T. S. Rappaport, Wireless Communications - Principles and Practice, 2nd ed. Prentice-Hall, 2010. 58. S. Y. Seidel and T. S. Rappaport, “914 MHz path loss prediction models for indoor wireless communications in multifloored buildings,” IEEE Transactions on Antennas and Propagation, vol. 40, no. 2, pp. 207–217, February 1992.</mixed-citation></citation-alternatives></ref><ref id="cit59"><label>59</label><citation-alternatives><mixed-citation xml:lang="ru">B. Dil and P. Havinga, “On the calibration and performance of RSS-based localization methods,” in Internet of Things 2010 Conference. Tokyo, Japan, November/December 2010.</mixed-citation><mixed-citation xml:lang="en">B. Dil and P. Havinga, “On the calibration and performance of RSS-based localization methods,” in Internet of Things 2010 Conference. Tokyo, Japan, November/December 2010.</mixed-citation></citation-alternatives></ref><ref id="cit60"><label>60</label><citation-alternatives><mixed-citation xml:lang="ru">M. Hata, “Empirical formula for propagation loss in land mobile radio services,” IEEE Transactions on Vehicular Technology, vol. 29, no. 3, pp. 317–325, August 1980.</mixed-citation><mixed-citation xml:lang="en">M. Hata, “Empirical formula for propagation loss in land mobile radio services,” IEEE Transactions on Vehicular Technology, vol. 29, no. 3, pp. 317–325, August 1980.</mixed-citation></citation-alternatives></ref><ref id="cit61"><label>61</label><citation-alternatives><mixed-citation xml:lang="ru">K. Shujaee, A. Ebaid, R. George, and M. A. Sazegarnejad, “Channel modeling and range extension for UWB communications using directional antenna in LOS and NLOS path loss models,” in World Automation Congress (WAC 2008). Hawaii, HI, USA, September-October 2008.</mixed-citation><mixed-citation xml:lang="en">K. Shujaee, A. Ebaid, R. George, and M. A. Sazegarnejad, “Channel modeling and range extension for UWB communications using directional antenna in LOS and NLOS path loss models,” in World Automation Congress (WAC 2008). Hawaii, HI, USA, September-October 2008.</mixed-citation></citation-alternatives></ref><ref id="cit62"><label>62</label><citation-alternatives><mixed-citation xml:lang="ru">H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica, vol. 7, no. 4, pp. 465–479, July 1971.</mixed-citation><mixed-citation xml:lang="en">H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums,” Automatica, vol. 7, no. 4, pp. 465–479, July 1971.</mixed-citation></citation-alternatives></ref><ref id="cit63"><label>63</label><citation-alternatives><mixed-citation xml:lang="ru">S. Ali-Löytty, “Gaussian mixture filters in hybrid positioning,” Ph.D. dissertation, Tampere University of Technology, August 2009. [Online]. Available: http://URN.fi/URN:NBN:fi:tty200905191055</mixed-citation><mixed-citation xml:lang="en">S. Ali-Löytty, “Gaussian mixture filters in hybrid positioning,” Ph.D. dissertation, Tampere University of Technology, August 2009. [Online]. Available: http://URN.fi/URN:NBN:fi:tty200905191055</mixed-citation></citation-alternatives></ref><ref id="cit64"><label>64</label><citation-alternatives><mixed-citation xml:lang="ru">J. T.-H. Lo, “Finite-dimensional sensor orbits and optimal nonlinear filtering,” IEEE Transactions on Information Theory, vol. 18, no. 5, pp. 583–588, September 1972.</mixed-citation><mixed-citation xml:lang="en">J. T.-H. Lo, “Finite-dimensional sensor orbits and optimal nonlinear filtering,” IEEE Transactions on Information Theory, vol. 18, no. 5, pp. 583–588, September 1972.</mixed-citation></citation-alternatives></ref><ref id="cit65"><label>65</label><citation-alternatives><mixed-citation xml:lang="ru">D. L. Alspach and H. W. Sorenson, “Nonlinear Bayesian estimation using Gaussian sum approximations,” IEEE Transactions on Automatic Control, vol. 17, no. 4, pp. 439–448, August 1972.</mixed-citation><mixed-citation xml:lang="en">D. L. Alspach and H. W. Sorenson, “Nonlinear Bayesian estimation using Gaussian sum approximations,” IEEE Transactions on Automatic Control, vol. 17, no. 4, pp. 439–448, August 1972.</mixed-citation></citation-alternatives></ref><ref id="cit66"><label>66</label><citation-alternatives><mixed-citation xml:lang="ru">T. Koshizen, “The sensor selection task of the Gaussians mixture Bayes’ with regularized EM (GMB-REM) technique in robot position estimation,” in Proceedings of the 1999 IEEE International Conference on Robotics &amp; Automation. Detroit, MI Detroit, MI Detroit, MI, USA, May 1999, pp. 2620–2625.</mixed-citation><mixed-citation xml:lang="en">T. Koshizen, “The sensor selection task of the Gaussians mixture Bayes’ with regularized EM (GMB-REM) technique in robot position estimation,” in Proceedings of the 1999 IEEE International Conference on Robotics &amp; Automation. Detroit, MI Detroit, MI Detroit, MI, USA, May 1999, pp. 2620–2625.</mixed-citation></citation-alternatives></ref><ref id="cit67"><label>67</label><citation-alternatives><mixed-citation xml:lang="ru">T. Koshizen, “The evolved Gaussian mixture Bayes’ technique using sensor selection task integrated with sensor fusion scheme in mobile robot position estimation,” in Proceedings of 1999 IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA’99). Monterey, CA, USA, November 1999, pp. 202–207.</mixed-citation><mixed-citation xml:lang="en">T. Koshizen, “The evolved Gaussian mixture Bayes’ technique using sensor selection task integrated with sensor fusion scheme in mobile robot position estimation,” in Proceedings of 1999 IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA’99). Monterey, CA, USA, November 1999, pp. 202–207.</mixed-citation></citation-alternatives></ref><ref id="cit68"><label>68</label><citation-alternatives><mixed-citation xml:lang="ru">T. Koshizen, P. Bartlett, and A. Zelinsky, “Sensor fusion of odometry and sonar sensors by the Gaussian mixture Bayes’ technique in mobile robot position estimation,” in IEEE SMC ’99 Conference Proceedings, vol. 4. Tokyo, Japan, 1999, pp. 742–747.</mixed-citation><mixed-citation xml:lang="en">T. Koshizen, P. Bartlett, and A. Zelinsky, “Sensor fusion of odometry and sonar sensors by the Gaussian mixture Bayes’ technique in mobile robot position estimation,” in IEEE SMC ’99 Conference Proceedings, vol. 4. Tokyo, Japan, 1999, pp. 742–747.</mixed-citation></citation-alternatives></ref><ref id="cit69"><label>69</label><citation-alternatives><mixed-citation xml:lang="ru">S. Ali-L_ytty and N. Sirola, “Gaussian mixture filter in hybrid navigation,” in Proceedings of The European Navigation Conference GNSS 2007. Geneva, Switzerland, May 2007, pp. 831–837.</mixed-citation><mixed-citation xml:lang="en">S. Ali-L_ytty and N. Sirola, “Gaussian mixture filter in hybrid navigation,” in Proceedings of The European Navigation Conference GNSS 2007. Geneva, Switzerland, May 2007, pp. 831–837.</mixed-citation></citation-alternatives></ref><ref id="cit70"><label>70</label><citation-alternatives><mixed-citation xml:lang="ru">M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174–188, 2002.</mixed-citation><mixed-citation xml:lang="en">M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174–188, 2002.</mixed-citation></citation-alternatives></ref><ref id="cit71"><label>71</label><citation-alternatives><mixed-citation xml:lang="ru">S. Ali-Löytty, “Efficient Gaussian mixture filter for hybrid positioning,” in 2008 IEEE/ION Position Location and Navigation Symposium, Monterey, California, May 2008, pp. 60–66.</mixed-citation><mixed-citation xml:lang="en">S. Ali-Löytty, “Efficient Gaussian mixture filter for hybrid positioning,” in 2008 IEEE/ION Position Location and Navigation Symposium, Monterey, California, May 2008, pp. 60–66.</mixed-citation></citation-alternatives></ref><ref id="cit72"><label>72</label><citation-alternatives><mixed-citation xml:lang="ru">S. Ali-Löytty and N. Sirola, “Gaussian mixture filter and hybrid positioning,” in Proceedings of ION GNSS 2007, Fort Worth, Texas, September 2007, pp. 562–570.</mixed-citation><mixed-citation xml:lang="en">S. Ali-Löytty and N. Sirola, “Gaussian mixture filter and hybrid positioning,” in Proceedings of ION GNSS 2007, Fort Worth, Texas, September 2007, pp. 562–570.</mixed-citation></citation-alternatives></ref><ref id="cit73"><label>73</label><citation-alternatives><mixed-citation xml:lang="ru">M. Raitoharju and S. Ali-Löytty, “An adaptive derivative free method for Bayesian posterior approximation,” IEEE Signal Processing Letters, vol. 19, no. 2, pp. 87–90, February 2012.</mixed-citation><mixed-citation xml:lang="en">M. Raitoharju and S. Ali-Löytty, “An adaptive derivative free method for Bayesian posterior approximation,” IEEE Signal Processing Letters, vol. 19, no. 2, pp. 87–90, February 2012.</mixed-citation></citation-alternatives></ref><ref id="cit74"><label>74</label><citation-alternatives><mixed-citation xml:lang="ru">B. D. O. Anderson and J. B. Moore, Optimal Filtering, ser. Prentice-Hall information and system sciences. Prentice-Hall, 1979.</mixed-citation><mixed-citation xml:lang="en">B. D. O. Anderson and J. B. Moore, Optimal Filtering, ser. Prentice-Hall information and system sciences. Prentice-Hall, 1979.</mixed-citation></citation-alternatives></ref><ref id="cit75"><label>75</label><citation-alternatives><mixed-citation xml:lang="ru">S. Ali-Löytty, “On the convergence of the Gaussian mixture filter,” Tampere University of Technology, Institute of Mathematics, http://urn.fi/URN:NBN:fi:tty-2011041510704, Tech. Rep. Research report 89, 2008.</mixed-citation><mixed-citation xml:lang="en">S. Ali-Löytty, “On the convergence of the Gaussian mixture filter,” Tampere University of Technology, Institute of Mathematics, http://urn.fi/URN:NBN:fi:tty-2011041510704, Tech. Rep. Research report 89, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit76"><label>76</label><citation-alternatives><mixed-citation xml:lang="ru">D. J. Salmond, “Mixture reduction algorithms for target tracking,” in IEE Colloquium on State Estimation in Aerospace and Tracking Applications. London, England, 1989, pp. 7/1–7/4.</mixed-citation><mixed-citation xml:lang="en">D. J. Salmond, “Mixture reduction algorithms for target tracking,” in IEE Colloquium on State Estimation in Aerospace and Tracking Applications. London, England, 1989, pp. 7/1–7/4.</mixed-citation></citation-alternatives></ref><ref id="cit77"><label>77</label><citation-alternatives><mixed-citation xml:lang="ru">D. Schieferdecker and M. F. Huber, “Gaussian mixture reduction via clustering,” in Proceedings of the 12th International Conference on Information Fusion (FUSION ’09). Seattle, WA, USA, 2009, pp. 1536–1543.</mixed-citation><mixed-citation xml:lang="en">D. Schieferdecker and M. F. Huber, “Gaussian mixture reduction via clustering,” in Proceedings of the 12th International Conference on Information Fusion (FUSION ’09). Seattle, WA, USA, 2009, pp. 1536–1543.</mixed-citation></citation-alternatives></ref><ref id="cit78"><label>78</label><citation-alternatives><mixed-citation xml:lang="ru">D. F. Crouse, P. Willett, K. Pattipati, and L. Svensson, “A look at Gaussian mixture reduction algorithms,” in Proceedings of the 14th International Conference on Information Fusion (FUSION’11). Chicago, IL, USA, 2011.</mixed-citation><mixed-citation xml:lang="en">D. F. Crouse, P. Willett, K. Pattipati, and L. Svensson, “A look at Gaussian mixture reduction algorithms,” in Proceedings of the 14th International Conference on Information Fusion (FUSION’11). Chicago, IL, USA, 2011.</mixed-citation></citation-alternatives></ref><ref id="cit79"><label>79</label><citation-alternatives><mixed-citation xml:lang="ru">M. Kristan, D. Skočaj, and A. Leonardis, “Incremental learning with Gaussian mixture models,” in Computer Vision Winter Workshop 2008. Moravske Toplice, Slovenia, February 2008, pp. 25–32.</mixed-citation><mixed-citation xml:lang="en">M. Kristan, D. Skočaj, and A. Leonardis, “Incremental learning with Gaussian mixture models,” in Computer Vision Winter Workshop 2008. Moravske Toplice, Slovenia, February 2008, pp. 25–32.</mixed-citation></citation-alternatives></ref><ref id="cit80"><label>80</label><citation-alternatives><mixed-citation xml:lang="ru">P. Müller, S. Ali-Löytty, M. Dashti, H. Nurminen, and R. Piché, “Gaussian mixture filter allowing negative weights and its application to positioning using signal strength measurements,” in Proceedings of the 9th Workshop on Positioning, Navigation and Communication 2012 (WPNC’12). Dresden, Germany, March 2012, pp. 71–76.</mixed-citation><mixed-citation xml:lang="en">P. Müller, S. Ali-Löytty, M. Dashti, H. Nurminen, and R. Piché, “Gaussian mixture filter allowing negative weights and its application to positioning using signal strength measurements,” in Proceedings of the 9th Workshop on Positioning, Navigation and Communication 2012 (WPNC’12). Dresden, Germany, March 2012, pp. 71–76.</mixed-citation></citation-alternatives></ref><ref id="cit81"><label>81</label><citation-alternatives><mixed-citation xml:lang="ru">P. Müller, H. Wymeersch, and R. Piché, “UWB positioning with generalized Gaussian mixture filters,” IEEE Transactions on Mobile Computing, vol. 13, no. 10, pp. 2406–2414, October 2014.</mixed-citation><mixed-citation xml:lang="en">P. Müller, H. Wymeersch, and R. Piché, “UWB positioning with generalized Gaussian mixture filters,” IEEE Transactions on Mobile Computing, vol. 13, no. 10, pp. 2406–2414, October 2014.</mixed-citation></citation-alternatives></ref><ref id="cit82"><label>82</label><citation-alternatives><mixed-citation xml:lang="ru">C. M. Bishop and M. Svensén, “Robust Bayesian mixture modeling,” in Proceedings of 12th European Symposium on Artificial Neural Networks (ESANN 2004). Bruges, Belgium, April 2004, pp. 69–74.</mixed-citation><mixed-citation xml:lang="en">C. M. Bishop and M. Svensén, “Robust Bayesian mixture modeling,” in Proceedings of 12th European Symposium on Artificial Neural Networks (ESANN 2004). Bruges, Belgium, April 2004, pp. 69–74.</mixed-citation></citation-alternatives></ref><ref id="cit83"><label>83</label><citation-alternatives><mixed-citation xml:lang="ru">G. J. McLachlan and D. Peel, “Robust cluster analysis via mixtures of multivariate tdistributions,” in Advances in Pattern Recognition, ser. Lecture Notes in Computer Science, A. Amin, D. Dori, P. Pudil, and H. Freeman, Eds. Springer Berlin Heidelberg, 1998, vol. 1451, pp. 658–666.</mixed-citation><mixed-citation xml:lang="en">G. J. McLachlan and D. Peel, “Robust cluster analysis via mixtures of multivariate tdistributions,” in Advances in Pattern Recognition, ser. Lecture Notes in Computer Science, A. Amin, D. Dori, P. Pudil, and H. Freeman, Eds. Springer Berlin Heidelberg, 1998, vol. 1451, pp. 658–666.</mixed-citation></citation-alternatives></ref><ref id="cit84"><label>84</label><citation-alternatives><mixed-citation xml:lang="ru">S. Ali-Löytty, N. Sirola, and R. Piché, “Consistency of three Kalman filter extensions in hybrid navigation,” in Proceedings of The European Navigation Conference GNSS 2005. Munich, Germany, Jul. 2005.</mixed-citation><mixed-citation xml:lang="en">S. Ali-Löytty, N. Sirola, and R. Piché, “Consistency of three Kalman filter extensions in hybrid navigation,” in Proceedings of The European Navigation Conference GNSS 2005. Munich, Germany, Jul. 2005.</mixed-citation></citation-alternatives></ref><ref id="cit85"><label>85</label><citation-alternatives><mixed-citation xml:lang="ru">H. Nurminen, A. Ristimäki, S. Ali-Löytty, and R. Piché, “Particle filter and smoother for indoor localization,” in 2013 International Conference on Indoor Positioning and Indoor Navigation (IPIN2013). Montbeliard-Belfort, France, October 2013, pp. 137–146.</mixed-citation><mixed-citation xml:lang="en">H. Nurminen, A. Ristimäki, S. Ali-Löytty, and R. Piché, “Particle filter and smoother for indoor localization,” in 2013 International Conference on Indoor Positioning and Indoor Navigation (IPIN2013). Montbeliard-Belfort, France, October 2013, pp. 137–146.</mixed-citation></citation-alternatives></ref><ref id="cit86"><label>86</label><citation-alternatives><mixed-citation xml:lang="ru">Степанов О. А. Применение теории нелинейной фильтрации в задачах обработки навигационной информации. СПб., 2003.</mixed-citation><mixed-citation xml:lang="en">Степанов О. А. Применение теории нелинейной фильтрации в задачах обработки навигационной информации. СПб., 2003.</mixed-citation></citation-alternatives></ref><ref id="cit87"><label>87</label><citation-alternatives><mixed-citation xml:lang="ru">Степанов О. А., Торопов А. Б. Применение последовательных методов Монте-Карло с использованием процедур аналитического интегрирования при обработке навигационной информации. XII Всероссийское совещание по проблемам управления ВСПУ-2014. Институт проблем управления им. В. А. Трапезникова РАН. М., 2014. С. 3324-3337.</mixed-citation><mixed-citation xml:lang="en">Степанов О. А., Торопов А. Б. Применение последовательных методов Монте-Карло с использованием процедур аналитического интегрирования при обработке навигационной информации. XII Всероссийское совещание по проблемам управления ВСПУ-2014. Институт проблем управления им. В. А. Трапезникова РАН. М., 2014. С. 3324-3337.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
