{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T12:41:07Z","timestamp":1780317667026,"version":"3.54.1"},"reference-count":24,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,4,12]],"date-time":"2020-04-12T00:00:00Z","timestamp":1586649600000},"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>This paper considers the coherent integration problem for moving target detection using frequency agile (FA) radar, involving range cell migration (RCM) and the nonuniform phase fluctuations among different pulses caused by range-agile frequency (R-AF) coupling and velocity-time-agile frequency (V-T-AF) coupling. After the analysis of the term corresponding to the phase fluctuation caused by V-T-AF coupling, the term can be regarded as related to an equivalent non-uniform slow time, and nonuniform fast Fourier transform (NUFFT) could be the solution. So a fast coherent integration method combining Radon Fourier transform (RFT) and NUFFT based on low-rank approximation, i.e., Radon-NUFFT, is proposed. In this method, the RCM is solved by Radon algorithm via target trajectory searching, the non-uniform phase fluctuation caused by R-AF coupling is compensated by constructing a compensation item corresponding to the range and agile frequency. In addition, the compensation of the non-uniform phase fluctuation caused by V-T-AF coupling is converted into a problem of spectral analysis of non-uniform sampling complex-valued signal, which is solved by the NUFFT based on low rank approximation. Compared with the existing methods, the proposed method can realize the coherent integration for FA radar accurately and quickly. The effectiveness of the proposed method is verified by simulation experiments.<\/jats:p>","DOI":"10.3390\/s20082176","type":"journal-article","created":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T10:41:52Z","timestamp":1586774512000},"page":"2176","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Coherent Integration Method Based on Radon-NUFFT for Moving Target Detection Using Frequency Agile Radar"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6250-0463","authenticated-orcid":false,"given":"Jiameng","family":"Pan","sequence":"first","affiliation":[{"name":"National Key Laboratory of Science and Technology on ATR, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qian","family":"Zhu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on ATR, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinglong","family":"Bao","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on ATR, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zengping","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2350","DOI":"10.1109\/TAES.2015.140315","article-title":"Novel noncoherent radar pulse integration to combat noise jamming","volume":"51","author":"Ahmed","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1049\/el:20081608","article-title":"Range-velocity estimation of multiple targets in randomised stepped-frequency radar","volume":"44","author":"Liu","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1049\/iet-rsn.2015.0006","article-title":"Efficient architecture and hardware implementation of coherent integration processor for digital video broadcast-based passive bistatic radar","volume":"10","author":"Shan","year":"2016","journal-title":"IET Radar, Sonar Navigation"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1109\/TAES.2011.5751251","article-title":"Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank","volume":"47","author":"Xu","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6582","DOI":"10.1109\/TSP.2014.2366719","article-title":"Sparse Discrete Fractional Fourier Transform and Its Applications","volume":"62","author":"Liu","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JSTARS.2019.2929655","article-title":"Coherent Detection Algorithm for Radar Maneuvering Targets Based on Discrete Polynomial-Phase Transform","volume":"12","author":"Pang","year":"2019","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1109\/LSP.2015.2390777","article-title":"Coherent Integration for Maneuvering Target Detection Based on Radon-Lv\u2019s Distribution","volume":"22","author":"Li","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/LGRS.2010.2045340","article-title":"Compressive Stepped-Frequency Continuous-Wave Ground-Penetrating Radar","volume":"7","author":"Suksmono","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"858","DOI":"10.1109\/TAES.2013.120443","article-title":"Cognitive random stepped frequency radar with sparse recovery","volume":"50","author":"Huang","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","unstructured":"Zhou, R., Xia, G., Zhao, Y., and Liu, H. (2015, January 16\u201318). Coherent signal processing method for frequency-agile radar. Proceedings of the 2015 12th IEEE International Conference on Electronic Measurement Instruments (ICEMI), Qingdao, China."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1049\/el.2016.0821","article-title":"Long-time coherent integration method for high-speed target detection using frequency agile radar","volume":"52","author":"Wang","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"VanderPlas, J. (2017). Understanding the Lomb-Scargle Periodogram. Astrophys. J. Suppl. Ser., 236.","DOI":"10.3847\/1538-4365\/aab766"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1109\/TSP.2008.2008973","article-title":"Spectral Analysis of Nonuniformly Sampled Data: A New Approach Versus the Periodogram","volume":"57","author":"Stoica","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bagchi, S., and Mitra, S. (1999). The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing, Springer.","DOI":"10.1007\/978-1-4615-4925-3"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1137\/0914081","article-title":"Fast Fourier Transforms for Nonequispaced Data","volume":"14","author":"Dutt","year":"1993","journal-title":"SIAM J. Sci. Comput"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/75.650975","article-title":"An accurate algorithm for nonuniform fast Fourier transforms (NUFFT\u2019s)","volume":"8","author":"Liu","year":"1998","journal-title":"IEEE Microw. Guided Wave Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1137\/S003614450343200X","article-title":"Accelerating the Nonuniform Fast Fourier Transform","volume":"46","author":"Greengard","year":"2004","journal-title":"SIAM Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/TSP.2002.807005","article-title":"Nonuniform fast Fourier transforms using min-max interpolation","volume":"51","author":"Fessler","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ruiz-Antol\u00edn, D., and Townsend, A. (2017). A Nonuniform Fast Fourier Transform Based on Low Rank Approximation. SIAM J. Sci. Comput., 40.","DOI":"10.1137\/17M1134822"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","article-title":"An Algorithm for the Machine Calculation of Complex Fourier Series","volume":"19","author":"Cooley","year":"1965","journal-title":"Math. Comput."},{"key":"ref_21","first-page":"23","article-title":"Fast evaluation of real and complex exponential sums","volume":"46","author":"Kunis","year":"2017","journal-title":"Electron. Trans. Numer. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1090\/mcom\/3277","article-title":"Fast polynomial transforms based on Toeplitz and Hankel matrices","volume":"87","author":"Townsend","year":"2018","journal-title":"Math. Comput."},{"key":"ref_23","unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Handbook of Mathematical Functions, Cambridge University Press. [1st ed.]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1109\/TIT.1980.1056127","article-title":"A new method of calculating the generalized Q function (Corresp.)","volume":"26","author":"Parl","year":"1980","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2176\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:21:02Z","timestamp":1760361662000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/8\/2176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,12]]},"references-count":24,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20082176"],"URL":"https:\/\/doi.org\/10.3390\/s20082176","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,12]]}}}