{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T17:34:58Z","timestamp":1777656898483,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,4,21]],"date-time":"2015-04-21T00:00:00Z","timestamp":1429574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013151","name":"Scientific Research Foundation for Returned Scholars, Ministry of Education of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013151","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, an improved joint time-frequency (TF) analysis method based on a reassigned smoothed pseudo Wigner\u2013Ville distribution (RSPWVD) has been proposed in interference detection for Global Navigation Satellite System (GNSS) receivers. In the RSPWVD, the two-dimensional low-pass filtering smoothing function is introduced to eliminate the cross-terms present in the quadratic TF distribution, and at the same time, the reassignment method is adopted to improve the TF concentration properties of the auto-terms of the signal components. This proposed interference detection method is evaluated by experiments on GPS L1 signals in the disturbing scenarios compared to the state-of-the-art interference detection approaches. The analysis results show that the proposed interference detection technique effectively overcomes the cross-terms problem and also preserves good TF localization properties, which has been proven to be effective and valid to enhance the interference detection performance of the GNSS receivers, particularly in the jamming environments.<\/jats:p>","DOI":"10.3390\/s150409404","type":"journal-article","created":{"date-parts":[[2015,4,22]],"date-time":"2015-04-22T04:41:53Z","timestamp":1429677713000},"page":"9404-9426","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["An Improved Time-Frequency Analysis Method in Interference Detection for GNSS Receivers"],"prefix":"10.3390","volume":"15","author":[{"given":"Kewen","family":"Sun","sequence":"first","affiliation":[{"name":"School of Computer and Information, Hefei University of Technology, Tunxi Road 193, Hefei 230009, 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, XueYuan Road 37, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongkai","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, XueYuan Road 37, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,21]]},"reference":[{"key":"ref_1","unstructured":"(2010). Galileo OS SIS ICD (Open Service Signal-In-Space Interface Control), European Union. Issue 1.1."},{"key":"ref_2","unstructured":"(2013). Systems Enginneing & Integration Interface Specification IS-GPS-705D, Navstar GPS Space Segment\/User Segment L5 Interface, Global Positioning Systems Directorate."},{"key":"ref_3","unstructured":"(2013). BeiDou Navigation Satellite System Signal in Space Interface Control Document Open Service Signal (Version 2.0), China Satellite Navigation Office. BDS-SIS-ICD-2.0."},{"key":"ref_4","unstructured":"Kaplan, E., and Hegarty, C. (2006). Understanding GPS: Principles and Applications, Artech House Press. [2nd ed.]."},{"key":"ref_5","unstructured":"Bastide, F., Chatre, E., Macabiau, C., and Roturier, B. (2004, January 26\u201328). GPS L5 and Galileo E5a\/E5b signal-to-noise density ratio degradation due to DME\/TACAN signals: Simulations and theoretical derivation. San Diego, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/LSP.2012.2209873","article-title":"Anti-Jamming GPS Receiver With Reduced Phase Distortions","volume":"19","author":"Zhang","year":"2012","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3005","DOI":"10.1109\/78.969509","article-title":"Array Processing for Nonstationary Interference Suppression in DS\/SS Communications Using Subspace Projection Techniques","volume":"49","author":"Zhang","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1109\/TVT.2009.2038391","article-title":"Reduced-Rank Space-Time Adaptive Interference Suppression With Joint Iterative Least Squares Algorithms for Spread-Spectrum Systems","volume":"59","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","unstructured":"Bastide, F., Akos, D., Macabiau, C., and Roturier, B. (2003, January 9\u201312). Automatic Gain Control (AGC) as an Interference Assessment Tool. Portland, OR, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1109\/TCOM.1986.1096517","article-title":"Performance of the Adaptive A\/D Converter in Combined CW and Gaussian Interference","volume":"COM-34","author":"Amoroso","year":"1986","journal-title":"IEEE Trans. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1109\/TCOM.1983.1095753","article-title":"Adaptive A\/D Converter to Suppress CW Interference in DSPN Spread-Spectrum Communications","volume":"31","author":"Amoroso","year":"1983","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/TEMC.2003.811309","article-title":"Investigation of Spurious Emissions From Cellular Phones and the Possible Effect on Aircraft Navigation Equipment","volume":"45","author":"Kuriger","year":"2003","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/JSYST.2007.914914","article-title":"Time-Frequency Excision for GNSS Application","volume":"2","author":"Borio","year":"2008","journal-title":"IEEE Syst. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/78.912929","article-title":"Short-Time Fourier Transform Receiver for Nonstationary Interference Excision in Direct Sequence Spread Spectrum Communications","volume":"49","author":"Ouyang","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1109\/49.761046","article-title":"Broadband Interference Excision for Software-Radio Spread-Spectrum Communications Using Time-Frequency Distribution Synthesis","volume":"17","author":"Lach","year":"1999","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_16","unstructured":"Sun, K., Liu, W., Xu, H., and Yang, D. (2013, January 16\u201320). Interference Detection Based on Time-Frequency Analysis for GNSS Receivers. Nashville, TN, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/79.127284","article-title":"Linear and Quadratic Time-Frequency Signal Representations","volume":"9","author":"Hlawatsch","year":"1992","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1109\/TAES.2013.6404112","article-title":"Interference Mitigation in GNSS Receivers by a Time-Frequency Approach","volume":"49","author":"Savasta","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","unstructured":"Paonni, M., Jang, J., Eissfeller, B., Wallner, S., Avila-Rodriguez, J.A., Samson, J., and Fernandez, F.A. (2011). Wavelets and Notch Filtering: Innovative Digital Processing Techniques for Mitigating RF Interference, Inside, GNSS; Gibbons Media & Research LLC."},{"key":"ref_20","unstructured":"Cohen, L. (1995). Time-Frequency Analysis: Theory and Applications, Prentice-Hall Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1109\/78.388866","article-title":"Analysis of Multicomponent LFM Signals by a Combined Wigner-Hough Transform","volume":"43","author":"Barbarossa","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1996","DOI":"10.1109\/78.215325","article-title":"Kernel Design for Time-Frequency Signal Analysis using the Radon Transform","volume":"41","author":"Ristic","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1109\/78.506622","article-title":"Auto-term Representation by the Reduced Interference Distributions: A Procedure for Kernel Design","volume":"44","author":"Stankovic","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2361","DOI":"10.1109\/78.469854","article-title":"An Adaptive Optimal-Kernel Time-Frequency Representation","volume":"43","author":"Jones","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1109\/78.382394","article-title":"Improving the Readability of Time-Frequency and Time-Scale Representations by the Reassignment Method","volume":"43","author":"Auger","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/S0165-1684(97)80004-7","article-title":"Joint Recursive Implementation of Time-Frequency Representations and Their Modified Version by the Reassignment Method","volume":"60","author":"Richard","year":"1997","journal-title":"Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Grochenig, K. (2001). Foundations of Time-Frequency Analysis, Birkhauser Press.","DOI":"10.1007\/978-1-4612-0003-1"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s10291-012-0290-8","article-title":"Stability Analysis of GPS Carrier Tracking Loops by Phase Margin Approach","volume":"17","author":"Jin","year":"2013","journal-title":"GPS Solut."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/4\/9404\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:04Z","timestamp":1760215504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/4\/9404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,21]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,4]]}},"alternative-id":["s150409404"],"URL":"https:\/\/doi.org\/10.3390\/s150409404","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,21]]}}}