{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T11:59:19Z","timestamp":1784030359402,"version":"3.55.0"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T00:00:00Z","timestamp":1618185600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2018YFB1702500"],"award-info":[{"award-number":["2018YFB1702500"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In the scenario of high dynamics and low C\/N0, the discriminator output of a GNSS tracking loop is noisy and nonlinear. The traditional method uses a fixed-gain loop filter for error estimation, which is prone to lose lock and causes inaccurate navigation and positioning. This paper proposes a cascaded adaptive vector tracking method based on the KF+EKF architecture through the GNSS Software defined receiver in the signal tracking module and the navigation solution module. The linear relationships between the pseudo-range error and the code phase error, the pseudo-range rate error and the carrier frequency error are obtained as the measurement, and the navigation filter estimation is performed. The signal C\/N0 ratio and innovation sequence are used to adjust the measurement noise covariance matrix and the process noise covariance matrix, respectively. Then, the estimated error value is used to correct the navigation parameters and fed back to the local code\/carrier NCO. The field vehicle test results show that, in the case of sufficient satellite signals, the positioning error of the proposed method has a slight advantage compared with the traditional method. When there is signal occlusion or interference, the traditional method cannot achieve accurate positioning. However, the proposed method can maintain the same accuracy for the positioning results.<\/jats:p>","DOI":"10.3390\/rs13081477","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T11:05:06Z","timestamp":1618225506000},"page":"1477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Performance and Evaluation of GNSS Receiver Vector Tracking Loop Based on Adaptive Cascade Filter"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2682-1806","authenticated-orcid":false,"given":"Haotian","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijng 100084, China"},{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7206-6418","authenticated-orcid":false,"given":"Bin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijng 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lixin","family":"Wang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Research Institute of High Technology, Xi\u2019an 710025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3189-7562","authenticated-orcid":false,"given":"Qi","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijng 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Ji","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijng 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9872-2954","authenticated-orcid":false,"given":"Rong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijng 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-019-0839-x","article-title":"Open-source MATLAB Code for GPS Vector Tracking on a Software-defined Receiver","volume":"23","author":"Xu","year":"2019","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/LCOMM.2013.01113.122503","article-title":"A Tuning Method Based on Signal-to-noise Power Ratio for Adaptive PLL and its Relationship with Equivalent Noise Bandwidth","volume":"17","author":"Won","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10291-015-0510-0","article-title":"Analysis of a Variational Bayesian Adaptive Cubature Kalman Filter Tracking Loop for High Dynamic Conditions","volume":"21","author":"Miao","year":"2017","journal-title":"GPS Solut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1007\/s12555-011-0412-z","article-title":"Adaptive Vector-tracking Loop for Low-quality GPS Signals","volume":"9","author":"Kim","year":"2011","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2903","DOI":"10.1109\/LCOMM.2020.3018742","article-title":"A Carrier Tracking Loop Using Adaptive Strong Tracking Kalman Filter in GNSS Receivers","volume":"24","author":"Cheng","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s10291-016-0546-9","article-title":"Performance Analysis of a Kalman Filter Carrier Phase Tracking Loop","volume":"21","author":"Jiang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s10291-014-0408-2","article-title":"Theoretical Analysis and Tuning Criteria of the Kalman Filter-based Tracking Loop","volume":"19","author":"Tang","year":"2015","journal-title":"GPS Solut."},{"key":"ref_9","unstructured":"Petovello, M.G., and Lachapelle, G. (2006, January 26\u201329). Comparison of Vector-Based Software Receiver Implementations with Application to Ultra-Tight GPS\/INS Integration. Proceedings of the International Technical Meeting of the Satellite Division, Fort Worth, TX, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1002\/j.2161-4296.2010.tb01777.x","article-title":"Performance Comparison of Different Forms of Kalman Filter Approaches for a Vector-Based GNSS Signal Tracking Loop","volume":"57","author":"Won","year":"2010","journal-title":"Navigation"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3671","DOI":"10.1109\/TAES.2012.6324756","article-title":"Characteristics of Kalman Filters for GNSS Signal Tracking Loop","volume":"48","author":"Won","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10291-014-0385-5","article-title":"Improved FLL-assisted PLL with In-phase Pre-filtering to Mitigate Amplitude Scintillation Effects","volume":"19","author":"Xu","year":"2015","journal-title":"GPS Solut."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s10291-016-0558-5","article-title":"Design of an Adaptive GPS Vector Tracking Loop with the Detection and Isolation of Contaminated Channels","volume":"21","author":"Sun","year":"2017","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lashley, M., Bevly, D.M., and Hung, J.Y. (2008, January 5\u20138). Impact of Carrier to Noise Power Density, Platform Dynamics, and IMU Quality on Deeply Integrated Navigation. Proceedings of the ION Position, Location and Navigation Symposium, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2008.4569964"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lashley, M., and Bevly, D. (2008, January 18\u201321). Comparison of Adaptive Estimation Techniques for Vector Delay\/Frequency Tracking. Proceedings of the Guidance, Navigation and Control Conference and Exhibit, Honolulu, HI, USA.","DOI":"10.2514\/6.2008-7474"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"163552","DOI":"10.1016\/j.ijleo.2019.163552","article-title":"Performance Assessment of GNSS Scalar and Vector Frequency Tracking Loops","volume":"202","author":"Dou","year":"2020","journal-title":"Optik"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"164984","DOI":"10.1016\/j.ijleo.2020.164984","article-title":"An Intelligent Joint Filter for Vector Tracking Loop Considering Noise Interference","volume":"219","author":"Dou","year":"2020","journal-title":"Optik"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mar\u00e7al, J., Nunes, F., and Sousa, F.M. (2016, January 14\u201316). Performance of a Scintillation Robust Vector Tracking for GNSS Carrier Phase Signals. Proceedings of the Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing, Noordwijk, The Netherlands.","DOI":"10.1109\/NAVITEC.2016.7849354"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Mar\u00e7al, J., Nunes, F., and Sousa, F.M. (2018, January 5\u20137). Performance of an adaptive Partitioned Vector Tracking Algorithm with Real Scintillation Data. Proceedings of the Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing, Noordwijk, The Netherlands.","DOI":"10.1109\/NAVITEC.2018.8642648"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mar\u00e7al, J., and Nunes, F. (2016, January 28\u201330). Robust Vector Tracking for GNSS Carrier Phase Signals. Proceedings of the International Conference on Localization and GNSS, Barcelona, Spain.","DOI":"10.1109\/ICL-GNSS.2016.7533841"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-017-0679-5","article-title":"Robust Multiple Update-rate Kalman Filter for New Generation Navigation Signals Carrier Tracking","volume":"22","author":"Lin","year":"2018","journal-title":"GPS Solut."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1007\/s10291-016-0557-6","article-title":"Complexity Reduction of the Kalman Filter-based Tracking Loops in GNSS Receivers","volume":"21","author":"Tang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1109\/TAES.2017.2673998","article-title":"Generalized GNSS Signal Carrier Tracking: Part I\u2014Modeling and Analysis","volume":"53","author":"Yang","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","unstructured":"Ziedan, N.I., and Garrison, J.L. (2004, January 21\u201324). Extended Kalman Filter-based Tracking of Weak GPS Signals under High Dynamic Conditions. Proceedings of the International technical meeting of the satellite division of the Institute of Navigation, Long Beach, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1109\/TAES.2013.120679","article-title":"Vector Loop RAIM in Nominal and GNSS-stressed Environments","volume":"50","author":"Bhattacharyya","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. 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