{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:21:39Z","timestamp":1765808499638,"version":"3.41.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"the Fundamental Research Funds for the Central Universities","award":["2412023QD033"],"award-info":[{"award-number":["2412023QD033"]}]},{"name":"Major Program of National Natural Science Foundation of China","award":["12292980, 12292984"],"award-info":[{"award-number":["12292980, 12292984"]}]},{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2020YFA0712203, 2020YFA0712201, 2023YFA1009000, 2023YFA1009004"],"award-info":[{"award-number":["2020YFA0712203, 2020YFA0712201, 2023YFA1009000, 2023YFA1009004"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Key project of National Natural Science Foundation of China","award":["NSFC12031016"],"award-info":[{"award-number":["NSFC12031016"]}]},{"name":"Beijing Natural Science Foundation","award":["BNSF-Z210003"],"award-info":[{"award-number":["BNSF-Z210003"]}]},{"name":"the Department of Science, Technology and Information of the Ministry of Education","award":["8091B042240"],"award-info":[{"award-number":["8091B042240"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Detecting weak radar targets in complex cluttered environments remains a significant challenge, particularly when attempting to effectively detect low signal-to-clutter ratio (SCR) targets while maintaining a constant false alarm rate (CFAR). We propose novel CFAR detectors based on time series analysis and statistical foundations. We model radar echo data within a coherent processing interval as stationary time series governed by linear random processes, enabling the application of a time series resampling approach to establish the autoregressive sieve bootstrap consistency of the banded sample autocovariance matrix (SACM) in the spectral norm. Leveraging this, we derive the numerical distribution of statistics related to the largest eigenvalue of the banded SACM. We introduce two improved CFAR detectors: one based on the banded SACM spectral norm (BSN detector) and another based on the likelihood ratio test in banded SACM eigenvalues (BLR detector). Additionally, we propose an adaptive CFAR detector, the maximum eigenvalue trimmed (MET) detector, developed using single-sample hypothesis testing. Our analysis demonstrates that detection probabilities stabilize as the number of bands exceeds a certain threshold, with robust performance under varying SCRs and false alarm probabilities. Simulations and real data experiments validate that all three detectors significantly outperform traditional radar target detection methods in terms of both detection performance and computational efficiency. Notably, the MET detector offers unique advantages by eliminating the need for non-target reference data and exhibiting strong adaptive characteristics. Experimental results confirm its remarkable robustness in scenarios with other targets present in reference cells, achieving over 80% detection probability when the SCR is set to -5 dB with appropriate parameter adjustments. This work provides a comprehensive framework for enhancing radar target detection performance through advanced statistical methods and innovative detector designs.<\/jats:p>","DOI":"10.1186\/s13634-025-01232-9","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T19:03:14Z","timestamp":1750446194000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Radar target detector based on banded sample autocovariance matrices"],"prefix":"10.1186","volume":"2025","author":[{"given":"Chang","family":"Qu","sequence":"first","affiliation":[]},{"given":"Xiaoying","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Jing","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Junping","family":"Yin","sequence":"additional","affiliation":[]},{"given":"Jiang","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Zhigen","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"1232_CR1","volume-title":"Time Series: Theory and Methods","author":"PJ Brockwell","year":"2009","unstructured":"P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, 2nd edn. (Springer, New York, 2009)","edition":"2"},{"key":"1232_CR2","volume-title":"The Statistical Analysis of Time Series","author":"TW Anderson","year":"2011","unstructured":"T.W. Anderson, The Statistical Analysis of Time Series (John Wiley & Sons, New York, 2011)"},{"key":"1232_CR3","volume-title":"Time Series Analysis: Methods and Applications","author":"TS Rao","year":"2012","unstructured":"T.S. Rao, S.S. Rao, C.R. Rao, Time Series Analysis: Methods and Applications, 1st edn. (Elsevier, North Holland, 2012)","edition":"1"},{"key":"1232_CR4","doi-asserted-by":"crossref","unstructured":"J. Lapuyade-Lahorgue, F. Barbaresco, Radar detection using siegel distance between autoregressive processes, application to HF and X-band radar. In: 2008 IEEE Radar Conference, pp. 1\u20136. IEEE (2008)","DOI":"10.1109\/RADAR.2008.4721049"},{"key":"1232_CR5","unstructured":"H. Sun, Z. Zhang, l. Peng, X. Duan, Information Geometry Guidance. Science Press, Beijing (2016)"},{"key":"1232_CR6","doi-asserted-by":"crossref","unstructured":"Z. Liu, F. Barbaresco, Doppler information geometry for wake turbulence monitoring. In: Matrix Information Geometry, pp. 277\u2013290. Springer (2012)","DOI":"10.1007\/978-3-642-30232-9_11"},{"key":"1232_CR7","first-page":"466","volume":"40","author":"H Xiao","year":"2011","unstructured":"H. Xiao, W. Wu, Covariance matrix estimation for stationary time series. Ann. Stat. 40, 466\u2013493 (2011)","journal-title":"Ann. Stat."},{"key":"1232_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0661-8","volume-title":"Spectral Analysis of Large Dimensional Random Matrices","author":"Z Bai","year":"2010","unstructured":"Z. Bai, J.W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices, vol. 20 (Springer, New York, 2010)"},{"issue":"4","key":"1232_CR9","first-page":"507","volume":"114","author":"VA Marchenko","year":"1967","unstructured":"V.A. Marchenko, L.A. Pastur, Distribution of eigenvalues for some sets of random matrices. Matematicheskii Sbornik 114(4), 507\u2013536 (1967)","journal-title":"Matematicheskii Sbornik"},{"issue":"2","key":"1232_CR10","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1214\/aos\/1009210544","volume":"29","author":"IM Johnstone","year":"2001","unstructured":"I.M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis. Ann. Stat. 29(2), 295\u2013327 (2001)","journal-title":"Ann. Stat."},{"key":"1232_CR11","unstructured":"Z. Bai, W. Zhou, Large sample covariance matrices without independence structures in columns. Statistica Sinica, 425\u2013442 (2008)"},{"key":"1232_CR12","doi-asserted-by":"publisher","first-page":"104623","DOI":"10.1016\/j.jmva.2020.104623","volume":"178","author":"A Bose","year":"2020","unstructured":"A. Bose, W. Hachem, Smallest singular value and limit eigenvalue distribution of a class of non-hermitian random matrices with statistical application. J. Multivar. Anal. 178, 104623 (2020)","journal-title":"J. Multivar. Anal."},{"key":"1232_CR13","unstructured":"D. Bi, X. Han, A. Nie, Y. Yang, Spiked eigenvalues of high-dimensional sample autocovariance matrices: CLT and applications. arXiv:abs\/2201.03181 (2022)"},{"key":"1232_CR14","doi-asserted-by":"crossref","unstructured":"A. Basak, A. Bose, S. Sen, Limiting spectral distribution of sample autocovariance matrices (2014)","DOI":"10.3150\/13-BEJ520"},{"key":"1232_CR15","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972191","volume-title":"The Statistical Theory of Linear Systems","author":"EJ Hannan","year":"2012","unstructured":"E.J. Hannan, M. Deistler, The Statistical Theory of Linear Systems (SIAM, Philadelphia, 2012)"},{"key":"1232_CR16","unstructured":"W.B. Wu, M. Pourahmadi, Banding sample autocovariance matrices of stationary processes. Statistica Sinica, 1755\u20131768 (2009)"},{"issue":"1","key":"1232_CR17","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.crhy.2010.01.001","volume":"11","author":"F Barbaresco","year":"2010","unstructured":"F. Barbaresco, U. Meier, Radar monitoring of a wake vortex: electromagnetic reflection of wake turbulence in clear air. C R Phys. 11(1), 54\u201367 (2010)","journal-title":"C R Phys."},{"issue":"11","key":"1232_CR18","doi-asserted-by":"publisher","first-page":"381","DOI":"10.3390\/e18110381","volume":"18","author":"Y Cheng","year":"2016","unstructured":"Y. Cheng, X. Hua, H. Wang, Y. Qin, X. Li, The geometry of signal detection with applications to radar signal processing. Entropy 18(11), 381 (2016)","journal-title":"Entropy"},{"issue":"6","key":"1232_CR19","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1049\/iet-spr.2016.0547","volume":"11","author":"X Hua","year":"2017","unstructured":"X. Hua, Y. Cheng, H. Wang, Y. Qin, Y. Li, Geometric means and medians with applications to target detection. IET Signal Proc. 11(6), 711\u2013720 (2017)","journal-title":"IET Signal Proc."},{"key":"1232_CR20","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.dsp.2017.06.019","volume":"69","author":"X Hua","year":"2017","unstructured":"X. Hua, Y. Cheng, H. Wang, Y. Qin, Y. Li, W. Zhang, Matrix CFAR detectors based on symmetrized Kullback-Leibler and total Kullback-Leibler divergences. Digital Signal Process. 69, 106\u2013116 (2017)","journal-title":"Digital Signal Process."},{"issue":"4","key":"1232_CR21","doi-asserted-by":"publisher","first-page":"256","DOI":"10.3390\/e20040256","volume":"20","author":"X Hua","year":"2018","unstructured":"X. Hua, H. Fan, Y. Cheng, H. Wang, Y. Qin, Information geometry for radar target detection with total Jensen-Bregman divergence. Entropy 20(4), 256 (2018)","journal-title":"Entropy"},{"key":"1232_CR22","doi-asserted-by":"publisher","first-page":"4326","DOI":"10.1109\/TSP.2021.3095725","volume":"69","author":"X Hua","year":"2021","unstructured":"X. Hua, Y. Ono, L. Peng, Y. Cheng, H. Wang, Target detection within nonhomogeneous clutter via total bregman divergence-based matrix information geometry detectors. IEEE Trans. Signal Process. 69, 4326\u20134340 (2021)","journal-title":"IEEE Trans. Signal Process."},{"key":"1232_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TGRS.2023.3283135","volume":"61","author":"X Hua","year":"2023","unstructured":"X. Hua, L. Peng, W. Liu, Y. Cheng, H. Wang, H. Sun, Z. Wang, LDA-MIG detectors for maritime targets in nonhomogeneous sea clutter. IEEE Trans. Geosci. Remote Sens. 61, 1\u201315 (2023)","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"11","key":"1232_CR24","doi-asserted-by":"publisher","first-page":"1294","DOI":"10.1049\/iet-rsn.2018.5229","volume":"12","author":"W Zhao","year":"2018","unstructured":"W. Zhao, C. Liu, W. Liu, M. Jin, Maximum eigenvalue-based target detection for the k-distributed clutter environment. IET Radar Sonar Navigation 12(11), 1294\u20131306 (2018)","journal-title":"IET Radar Sonar Navigation"},{"issue":"22","key":"1232_CR25","doi-asserted-by":"publisher","first-page":"5746","DOI":"10.1109\/TSP.2019.2945991","volume":"67","author":"W Zhao","year":"2019","unstructured":"W. Zhao, W. Liu, M. Jin, Spectral norm based mean matrix estimation and its application to radar target CFAR detection. IEEE Trans. Signal Process. 67(22), 5746\u20135760 (2019)","journal-title":"IEEE Trans. Signal Process."},{"key":"1232_CR26","doi-asserted-by":"publisher","first-page":"2502","DOI":"10.1109\/TSP.2023.3291448","volume":"71","author":"W Zhao","year":"2023","unstructured":"W. Zhao, G. Cui, M. Jin, Y. Wang, Radar target detection via global optimality conditions for binary quadratic programming. IEEE Trans. Signal Process. 71, 2502\u20132517 (2023)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"1232_CR27","doi-asserted-by":"publisher","first-page":"123","DOI":"10.2307\/3318584","volume":"3","author":"P B\u00fchlmann","year":"1997","unstructured":"P. B\u00fchlmann, Sieve bootstrap for time series. Bernoulli 3(2), 123\u2013148 (1997)","journal-title":"Bernoulli"},{"key":"1232_CR28","doi-asserted-by":"publisher","DOI":"10.1201\/9780429246593","volume-title":"An Introduction to the Bootstrap","author":"B Efron","year":"1994","unstructured":"B. Efron, R.J. Tibshirani, An Introduction to the Bootstrap (CRC Press, Boca Raton, Florida, 1994)"},{"key":"1232_CR29","doi-asserted-by":"publisher","first-page":"104298","DOI":"10.1016\/j.dsp.2023.104298","volume":"145","author":"C Qu","year":"2024","unstructured":"C. Qu, X. Wang, J. Yin, Sea clutter radar target detector based on autoregressive sieve bootstrap. Digital Signal Process. 145, 104298 (2024)","journal-title":"Digital Signal Process."},{"issue":"40","key":"1232_CR30","doi-asserted-by":"publisher","first-page":"14150","DOI":"10.1073\/pnas.0506715102","volume":"102","author":"WB Wu","year":"2005","unstructured":"W.B. Wu, Nonlinear system theory: another look at dependence. Proc. Natl. Acad. Sci. 102(40), 14150\u201314154 (2005)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"6","key":"1232_CR31","doi-asserted-by":"publisher","first-page":"2294","DOI":"10.1214\/009117907000000060","volume":"35","author":"WB Wu","year":"2007","unstructured":"W.B. Wu, Strong invariance principles for dependent random variables. Ann. Probab. 35(6), 2294\u20132320 (2007)","journal-title":"Ann. Probab."},{"key":"1232_CR32","volume-title":"Martingale Limit Theory and Its Application","author":"P Hall","year":"2014","unstructured":"P. Hall, C.C. Heyde, Martingale Limit Theory and Its Application (Academic press, San Diego, California, 2014)"},{"key":"1232_CR33","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"G.H. Golub, C.F. Van Loan, Matrix Computations (JHU press, Baltimore, Maryland, 2013)"},{"key":"1232_CR34","doi-asserted-by":"crossref","unstructured":"X. Cao, Y. Cheng, H. Wu, Z Yang, H. Jing, H. Wang, Kernel function based mean matrix estimation and its application to radar target detection. In: Journal of Physics: Conference Series, IOP Publishing (2021)","DOI":"10.1088\/1742-6596\/2031\/1\/012028"},{"key":"1232_CR35","doi-asserted-by":"crossref","unstructured":"T.J. Nohara, S. Haykin, Canadian east coast radar trials and the k-distribution. In: IEE Proceedings F (Radar and Signal Processing), pp. 80\u201388. IET (1991)","DOI":"10.1049\/ip-f-2.1991.0013"},{"issue":"2","key":"1232_CR36","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1137\/1109053","volume":"9","author":"A Vershik","year":"1964","unstructured":"A. Vershik, Some characteristic properties of gaussian stochastic processes. Theory Probability Appl. 9(2), 353\u2013356 (1964)","journal-title":"Theory Probability Appl."},{"key":"1232_CR37","doi-asserted-by":"crossref","unstructured":"E. Conte, M. Longo, Characterisation of radar clutter as a spherically invariant random process. In: Proceedings F Communications, Radar and Signal Processing, 191\u2013197 (1987). IET","DOI":"10.1049\/ip-f-1.1987.0035"},{"issue":"5","key":"1232_CR38","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIT.1973.1055076","volume":"19","author":"K Yao","year":"1973","unstructured":"K. Yao, A representation theorem and its applications to spherically-invariant random processes. IEEE Trans. Inf. Theory 19(5), 600\u2013608 (1973)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"06","key":"1232_CR39","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1049\/iet-spr.2016.0547","volume":"11","author":"X Hua","year":"2017","unstructured":"X. Hua, Y. Cheng, H. Wang, Y. Qin, Y. Li, Geometric means and medians with applications to target detection. IET Signal Proc. 11(06), 711\u2013720 (2017)","journal-title":"IET Signal Proc."},{"key":"1232_CR40","unstructured":"IPIX Radar File: IPIX Radar Dataset Files in Grimsby on the Shores of Lake Ontari. http:\/\/soma.mcmaster.ca\/ipix.php (2003)"},{"issue":"2","key":"1232_CR41","first-page":"456","volume":"12","author":"J Guan","year":"2023","unstructured":"J. Guan, N. Liu, G. Wang, H. Ding, Y. Dong, Y. Huang, K. Tian, M. Zhang, Sea-detecting radar experiment and target feature data acquisition for dual polarization multistate scattering dataset of marine targets. J. Radars 12(2), 456\u2013469 (2023)","journal-title":"J. Radars"},{"key":"1232_CR42","unstructured":"N. Liu, H. Ding, Y. Huang, Y. Dong, G. Wang, K. Dong, Annual progress of sea-detecting x-band radar and data acquisition program. J. Radars (2021)"},{"issue":"5","key":"1232_CR43","first-page":"656","volume":"8","author":"N Liu","year":"2019","unstructured":"N. Liu, Y. Dong, G. Wang, H. Ding, Y. Huang, J. Guan, X. Chen, Y. He, Sea-detecting x-band radar and data acquisition program. J. Radars 8(5), 656\u2013667 (2019)","journal-title":"J. Radars"},{"key":"1232_CR44","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1109\/LSP.2025.3537329","volume":"32","author":"C Qu","year":"2025","unstructured":"C. Qu, J. Chen, X. Wang, J. Hu, J. Yin, An adaptive cfar target detector based on the quadratic sum of sample autocovariances. IEEE Signal Process. Lett. 32, 786\u2013790 (2025)","journal-title":"IEEE Signal Process. Lett."},{"issue":"1","key":"1232_CR45","first-page":"9","volume":"23","author":"Y He","year":"2001","unstructured":"Y. He, J. Guan, X. Meng, D. Lu, Y. Peng, Survey of automatic radar detection and CFAR processing. Syst. Eng. Electronics 23(1), 9\u201314 (2001)","journal-title":"Syst. Eng. Electronics"},{"key":"1232_CR46","doi-asserted-by":"crossref","unstructured":"S.D. Himonas, Adaptive censored greatest-of CFAR detection, 247\u2013255. IET (1992)","DOI":"10.1049\/ip-f-2.1992.0032"},{"issue":"3","key":"1232_CR47","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1049\/ip-rsn:20010301","volume":"148","author":"R Srinivasan","year":"2001","unstructured":"R. Srinivasan, Fast simulation of smallest-of and geometric-mean CFAR detectors. IEE Proceed. Radar Sonar Navigation 148(3), 186\u2013191 (2001)","journal-title":"IEE Proceed. Radar Sonar Navigation"},{"key":"1232_CR48","doi-asserted-by":"crossref","unstructured":"H. Rohling, Radar CFAR thresholding in clutter and multiple target situations. IEEE Transactions on Aerospace and Electronic Systems AES-19, 608\u2013621 (1983)","DOI":"10.1109\/TAES.1983.309350"},{"issue":"3","key":"1232_CR49","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.1109\/TAES.2010.5545205","volume":"46","author":"M Greco","year":"2010","unstructured":"M. Greco, P. Stinco, F. Gini, M. Rangaswamy, Impact of sea clutter nonstationarity on disturbance covariance matrix estimation and CFAR detector performance. IEEE Trans. Aerosp. Electron. Syst. 46(3), 1502\u20131513 (2010)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-025-01232-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13634-025-01232-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13634-025-01232-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T19:03:19Z","timestamp":1750446199000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/s13634-025-01232-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,20]]},"references-count":49,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["1232"],"URL":"https:\/\/doi.org\/10.1186\/s13634-025-01232-9","relation":{},"ISSN":["1687-6180"],"issn-type":[{"value":"1687-6180","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,20]]},"assertion":[{"value":"14 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"21"}}