{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:08:29Z","timestamp":1760242109638,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,23]],"date-time":"2018-12-23T00:00:00Z","timestamp":1545523200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61871472"],"award-info":[{"award-number":["61871472"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Complex Electromagnetic Space (CEMS), which consists of physical space and the complex electromagnetic environment, plays an essential role in our daily life for supporting remote communication, wireless network, wide-range broadcast, etc. In CEMS, the electromagnetic activities might work differently from the ideal situation; the typical case is that undesired signal would disturb the echo of objects and overlap into it resulting in the mismatch of matched filter and the reduction of the probability of detection. The lacking mathematical description of CEMS resulting from the complexity of electromagnetic environment leads to the inappropriate design of detection method. Therefore, a mathematical model of CEMS is desired for integrating the electromagnetic signal in CEMS as a whole and considering the issues in CEMS accurately. This paper puts forward a geometric model of CEMS based on vector bundle, which is an abstract concept in differential geometry and proposes a geometric detector for change detection in CEMS under the geometric model. In the simulation, the proposed geometric detector was compared with energy detector and matched filter in two scenes: passive detection case and active detection case. The results show the proposed geometric detector is better than both energy detector and matched filter with 4\u223c5 dB improvements of SNR (signal-to-noise ratio) in two scenes.<\/jats:p>","DOI":"10.3390\/e21010010","type":"journal-article","created":{"date-parts":[[2018,12,24]],"date-time":"2018-12-24T10:37:49Z","timestamp":1545647869000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Vector Bundle Model of Complex Electromagnetic Space and Change Detection"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8679-1274","authenticated-orcid":false,"given":"Hao","family":"Wu","sequence":"first","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0127-384X","authenticated-orcid":false,"given":"Yongqiang","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7687-7720","authenticated-orcid":false,"given":"Xiaoqiang","family":"Hua","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongqiang","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/62.286787","article-title":"An ECCM model and the technical development trends to the demands of the future EW combat","volume":"9","author":"Benren","year":"1994","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13638-015-0498-8","article-title":"Modeling and analyzing interference signal in a complex electromagnetic environment","volume":"2016","author":"Liu","year":"2016","journal-title":"Eurasip J. Wirel. Commun. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, C., Wu, R., He, Z., Zhao, X., Li, H., and Wang, P. (2016). Modeling and Analyzing Electromagnetic Interference Signal in Complex Battlefield Environments. Proceedings of the 2015 International Conference on Communications, Signal Processing, and Systems, Springer.","DOI":"10.1007\/978-3-662-49831-6_35"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cai, X.F., and Song, J.S. (2009, January 25\u201327). Analysis of complexity in battlefield electromagnetic environment. Proceedings of the IEEE Conference on Industrial Electronics and Applications, Xi\u2019an, China.","DOI":"10.1109\/ICIEA.2009.5138640"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1109\/18.930911","article-title":"Information geometry on hierarchy of probability distributions","volume":"47","author":"Amari","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"203","DOI":"10.2307\/1969996","article-title":"Homogeneous Vector Bundles","volume":"66","author":"Bott","year":"1957","journal-title":"Ann. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/JSTARS.2015.2453996","article-title":"Radar High-Speed Target Detection Based on the Frequency-Domain Deramp-Keystone Transform","volume":"9","author":"Zheng","year":"2016","journal-title":"IEEE J. Sel. Topi. Appl. Earth Obs. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2156","DOI":"10.1109\/TSP.2015.2507544","article-title":"Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured Plus Gaussian Interference Via Invariance","volume":"64","author":"Orlando","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1109\/JSTSP.2015.2465304","article-title":"Cognitive Radar Framework for Target Detection and Tracking","volume":"9","author":"Bell","year":"2015","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1109\/TAES.2017.2667223","article-title":"Multistatic Detection for Passive Radar With Direct-Path Interference","volume":"53","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3115","DOI":"10.1109\/TAES.2017.2728978","article-title":"Design and Validation of a Passive Radar Concept for Ship Detection Using Communication Satellite Signals","volume":"53","author":"Daniel","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2596","DOI":"10.1109\/TAES.2016.140207","article-title":"A wireless passive radar system for real-time through-wall movement detection","volume":"52","author":"Tan","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.sigpro.2015.01.006","article-title":"On the performance of the cross-correlation detector for passive radar applications","volume":"113","author":"Liu","year":"2015","journal-title":"Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Rao, C.R. (1992). Information and the Accuracy Attainable in the Estimation of Statistical Parameters. Breakthroughs in Statistics: Foundations and Basic Theory, Springer.","DOI":"10.1007\/978-1-4612-0919-5_16"},{"key":"ref_15","unstructured":"\u010cencov, N.N. (1982). Statistical Decision Rules and Optimal Inference, American Mathematical Society."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1176343282","article-title":"Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency)","volume":"3","author":"Efron","year":"1975","journal-title":"Ann. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1214\/aos\/1176344130","article-title":"The Geometry of Exponential Families","volume":"6","author":"Efron","year":"1978","journal-title":"Ann. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Amari, S.I., and Nagaoka, H. (2007). Methods of Information Geometry, American Mathematical Society.","DOI":"10.1090\/mmono\/191"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1214\/aos\/1176345779","article-title":"Differential Geometry of Curved Exponential Families-Curvatures and Information Loss","volume":"10","author":"Amari","year":"1982","journal-title":"Ann. Stat."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Cheng, Y., Hua, X., Wang, H., Qin, Y., and Li, X. (2016). The Geometry of Signal Detection with Applications to Radar Signal Processing. Entropy, 18.","DOI":"10.3390\/e18110381"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3514","DOI":"10.1109\/TSP.2011.2152399","article-title":"Tracking and Localizing Moving Targets in the Presence of Phase Measurement Ambiguities","volume":"59","author":"Cheng","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5674","DOI":"10.1109\/TSP.2011.2166547","article-title":"Optimal Nonlinear Estimation for Localization of Wireless Sensor Networks","volume":"59","author":"Cheng","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1239\/aap\/1077134463","article-title":"Bayesian and Geometric Subspace Tracking","volume":"36","author":"Srivastava","year":"2004","journal-title":"Adv. Appl. Probab."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3084","DOI":"10.1109\/TAES.2012.6324679","article-title":"On Information Resolution of Radar Systems","volume":"48","author":"Cheng","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Barbaresco, F. (2008, January 26\u201330). Innovative tools for radar signal processing Based on Cartan\u2019s geometry of SPD matrices and Information Geometry. Proceedings of the Radar Conference, Rome, Italy.","DOI":"10.1109\/RADAR.2008.4720937"},{"key":"ref_26","unstructured":"Barbaresco, F. (2011, January 7\u20139). Robust statistical Radar Processing in Fr\u00e9chet metric space: OS-HDR-CFAR and OS-STAP Processing in Siegel homogeneous bounded domains. Proceedings of the International Radar Symposium, Leipzig, Germany."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Hua, X., Cheng, Y., Wang, H., and Qin, Y. (2018). Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold. Entropy, 20.","DOI":"10.3390\/e20040219"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.dsp.2017.06.019","article-title":"Matrix CFAR detectors based on symmetrized Kullback-Leibler and total Kullback-Leibler divergences","volume":"69","author":"Hua","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Hua, X., Cheng, Y., Wang, H., and Qin, Y. (2018). Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence. Entropy, 20.","DOI":"10.3390\/e20040258"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Hua, X., Fan, H., Cheng, Y., Wang, H., and Qin, Y. (2018). Information Geometry for Radar Target Detection with Total Jensen-Bregman Divergence. Entropy, 20.","DOI":"10.3390\/e20040256"},{"key":"ref_31","unstructured":"Chern, S.S., Chen, W.H., and Lam, K.S. (2009). Lectures on Differential Geometry, World Scientific."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Amari, S.I. (2016). Information Geometry and Its Applications, Springer Publishing Company, Incorporated. [1st ed.].","DOI":"10.1007\/978-4-431-55978-8"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0893-9659(94)00112-P","article-title":"Statistical tests based on geodesic distances","volume":"8","author":"Menendez","year":"1995","journal-title":"Appl. Math. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.inffus.2012.02.005","article-title":"Information geometry of target tracking sensor networks","volume":"14","author":"Cheng","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On Information and Sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yosida, K. (1978). Functional Analysis, Springer-Verlag.","DOI":"10.1007\/978-3-642-96439-8"},{"key":"ref_37","first-page":"251","article-title":"Functional analysis","volume":"21","author":"Schmitt","year":"1977","journal-title":"Zahnarzt"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1109\/PROC.1967.5573","article-title":"Energy detection of unknown deterministic signals","volume":"55","author":"Urkowitz","year":"1967","journal-title":"Proc. IEEE"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1080\/00401706.1997.10485133","article-title":"Monte Carlo: Concepts, Algorithms, and Applications","volume":"39","author":"Wasserstein","year":"1996","journal-title":"Technometrics"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1109\/TIT.1960.1057571","article-title":"An introduction to matched filters","volume":"6","author":"Turin","year":"1960","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_41","unstructured":"Miller, I., and Freund, J.E. (1990). Probability and Statistics for Engineers, Prentice Hall."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:35:50Z","timestamp":1760196950000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,23]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["e21010010"],"URL":"https:\/\/doi.org\/10.3390\/e21010010","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,12,23]]}}}