{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T07:12:24Z","timestamp":1766733144421,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,1,23]],"date-time":"2016-01-23T00:00:00Z","timestamp":1453507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As the weak link in global navigation satellite system (GNSS) signal processing, the phase-locked loop (PLL) is easily influenced with frequent cycle slips and loss of lock as a result of higher vehicle dynamics and lower signal-to-noise ratios. With inertial navigation system (INS) aid, PLLs\u2019 tracking performance can be improved. However, for harsh environments with high dynamics and signal attenuation, the traditional INS-aided PLL with fixed loop parameters has some limitations to improve the tracking adaptability. In this paper, an adaptive INS-aided PLL capable of adjusting its noise bandwidth and coherent integration time has been proposed. Through theoretical analysis, the relation between INS-aided PLL phase tracking error and carrier to noise density ratio (C\/N0), vehicle dynamics, aiding information update time, noise bandwidth, and coherent integration time has been built. The relation formulae are used to choose the optimal integration time and bandwidth for a given application under the minimum tracking error criterion. Software and hardware simulation results verify the correctness of the theoretical analysis, and demonstrate that the adaptive tracking method can effectively improve the PLL tracking ability and integrated GNSS\/INS navigation performance. For harsh environments, the tracking sensitivity is increased by 3 to 5 dB, velocity errors are decreased by 36% to 50% and position errors are decreased by 6% to 24% when compared with other INS-aided PLL methods.<\/jats:p>","DOI":"10.3390\/s16020146","type":"journal-article","created":{"date-parts":[[2016,1,25]],"date-time":"2016-01-25T10:03:06Z","timestamp":1453716186000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["An Adaptive INS-Aided PLL Tracking Method for GNSS Receivers in Harsh Environments"],"prefix":"10.3390","volume":"16","author":[{"given":"Li","family":"Cong","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3685-2435","authenticated-orcid":false,"given":"Tian","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Song","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,1,23]]},"reference":[{"key":"ref_1","unstructured":"El-Rabbany, A. (2002). Introduction to GPS: The Global Positioning System, Artech House."},{"key":"ref_2","unstructured":"Kaplan, E., and Hegarty, C. (2005). Understanding GPS: Principles and Applications, Artech House."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s10291-014-0382-8","article-title":"A high-sensitivity GPS receiver carrier-tracking loop design for high-dynamic applications","volume":"19","author":"Wang","year":"2015","journal-title":"GPS Solut."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Li, W., Liu, S., Zhou, C., Zhou, S., and Wang, T. (2007, January 21\u201325). High Dynamic Carrier Tracking Using Kalman Filter Aided Phase-Lock Loop. Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing (WiCom 2007), Shanghai, China.","DOI":"10.1109\/WICOM.2007.174"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"8685","DOI":"10.3390\/s150408685","article-title":"Performance Analysis on Carrier Phase-Based Tightly-Coupled GPS\/BDS\/INS Integration in GNSS Degraded and Denied Environments","volume":"15","author":"Han","year":"2015","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s10291-010-0194-4","article-title":"Choosing the coherent integration time for Kalman filter-based carrier-phase tracking of GNSS signals","volume":"15","author":"Petovello","year":"2011","journal-title":"GPS Solut."},{"key":"ref_7","unstructured":"Petovello, M., Sun, D., Lachapelle, G., and Cannon, M. (2007, January 25\u201328). Performance analysis of an ultra-tightly integrated GPS and reduced IMU system. Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation ION GNSS, Fort Worth, TX, USA."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Qin, H., Sun, X., and Cong, L. (2013). Using fuzzy logic control for the robust carrier tracking loop in a Global Positioning System\/Inertial Navigation System tightly integrated system. Trans. Inst. Meas. Control, 36.","DOI":"10.1177\/0142331213503863"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"16406","DOI":"10.3390\/s131216406","article-title":"Performance Improvement of Receivers Based on Ultra-Tight Integration in GNSS-Challenged Environments","volume":"13","author":"Qin","year":"2013","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1109\/TAES.2008.4560215","article-title":"Carrier loop architectures for tracking weak GPS signals","volume":"44","author":"Razavi","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","unstructured":"Alban, S., Akos, D., Rock, S.M., and Gebre-Egziabher, D. (2003, January 22\u201324). Performance analysis and architectures for INS-Aided GPS tracking loops. Proceedings of the 2003 National Technical Meeting of The Institute of Navigation 2003, Anaheim, CA, USA."},{"key":"ref_12","unstructured":"Gao, G., and Lachapelle, G. (2006, January 26\u201329). INS-assisted high sensitivity GPS receivers for degraded signal navigation. Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, TX, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1002\/j.2161-4296.2005.tb01731.x","article-title":"Sensitivity and Performance Analysis of Doppler-Aided GPS Carrier-Tracking loops","volume":"52","author":"Razavi","year":"2005","journal-title":"Navigation"},{"key":"ref_14","unstructured":"Lian, P. (2004). Improving Tracking Performance of PLL in High Dynamic Applications. [Master Thesis, University of Calgary]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10291-009-0159-7","article-title":"Use of a reduced IMU to aid a GPS receiver with adaptive tracking loops for land vehicle navigation","volume":"14","author":"Sun","year":"2010","journal-title":"GPS Solut."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1109\/26.768758","article-title":"On phase-locked loops and Kalman filters","volume":"47","author":"Patapoutian","year":"1999","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","first-page":"52","article-title":"Coherent integration time: The longer, the better","volume":"4","author":"Pany","year":"2009","journal-title":"Inside GNSS"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"15","DOI":"10.9746\/jcmsi.4.15","article-title":"Development of Ins-aided GPS tracking loop and flight test evaluation","volume":"4","author":"Tsujii","year":"2011","journal-title":"SICE J. Control Meas. Syst. Integr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3768","DOI":"10.3390\/s140203768","article-title":"Implementation and performance of a GPS\/INS tightly coupled assisted pll architecture using MEMS inertial sensors","volume":"14","author":"Tawk","year":"2014","journal-title":"Sensors"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1109\/7.489518","article-title":"Performance analysis of GPS carrier phase observable","volume":"32","author":"Zhuang","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/7.366295","article-title":"Controlled-root formulation for digital phase-locked loops","volume":"31","author":"Stephens","year":"1995","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/PL00012911","article-title":"PLL tracking performance in the presence of oscillator phase noise","volume":"5","author":"Irsigler","year":"2002","journal-title":"GPS Solut."},{"key":"ref_23","unstructured":"Bhaskar, S. (2014, January 8\u201312). Exploiting quasi-periodicity in receiver dynamics to enhance GNSS carrier phase tracking. Proceedings of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation 2014, Tampa, FL, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jovanovic, A., Tawk, Y., Botteron, C., and Farine, P.-A. (2010, January 4\u20136). Multipath mitigation techniques for CBOC, TMBOC and ALTBOC signals using advanced correlators architectures. Proceedings of the 2010 IEEE\/ION Position Location and Navigation Symposium (PLANS), Indian Wells, CA, USA.","DOI":"10.1109\/PLANS.2010.5507231"},{"key":"ref_25","unstructured":"GSS8000 Multi-GNSS Constellation Simulator. Available online: http:\/\/www.spirent.com\/Solutions-Directory\/GSS8000."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/146\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:18:12Z","timestamp":1760210292000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/2\/146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,23]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2]]}},"alternative-id":["s16020146"],"URL":"https:\/\/doi.org\/10.3390\/s16020146","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,1,23]]}}}