{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:32:15Z","timestamp":1760236335480,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T00:00:00Z","timestamp":1636675200000},"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":["61701139"],"award-info":[{"award-number":["61701139"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Photon counting lidar for long-range detection faces the problem of declining ranging performance caused by background noise. Current anti-noise methods are not robust enough in the case of weak signal and strong background noise, resulting in poor ranging error. In this work, based on the characteristics of the uncertainty of echo signal and noise in photon counting lidar, an entropy-based anti-noise method is proposed to reduce the ranging error under high background noise. Firstly, the photon counting entropy, which is considered as the feature to distinguish signal from noise, is defined to quantify the uncertainty of fluctuation among photon events responding to the Geiger mode avalanche photodiode. Then, the photon counting entropy is combined with a windowing operation to enhance the difference between signal and noise, so as to mitigate the effect of background noise and estimate the time of flight of the laser pulses. Simulation and experimental analysis show that the proposed method improves the anti-noise performance well, and experimental results demonstrate that the proposed method effectively mitigates the effect of background noise to reduce ranging error despite high background noise.<\/jats:p>","DOI":"10.3390\/e23111499","type":"journal-article","created":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T08:10:22Z","timestamp":1636704622000},"page":"1499","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Entropy-Based Anti-Noise Method for Reducing Ranging Error in Photon Counting Lidar"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5549-6494","authenticated-orcid":false,"given":"Mingwei","family":"Huang","sequence":"first","affiliation":[{"name":"School of Physics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zijing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Physics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaheng","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Physics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahuan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Physics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6241","DOI":"10.1364\/AO.48.006241","article-title":"Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting","volume":"48","author":"McCarthy","year":"2009","journal-title":"Appl. Opt."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8904","DOI":"10.1364\/OE.21.008904","article-title":"Kilometer-range, high resolution depth imaging via 1560 nm wavelength single-photon detection","volume":"21","author":"McCarthy","year":"2013","journal-title":"Opt. Express"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11919","DOI":"10.1364\/OE.25.011919","article-title":"Single-photon three-dimensional imaging at up to 10 km range","volume":"25","author":"Pawlikowska","year":"2017","journal-title":"Opt. Express"},{"key":"ref_4","first-page":"1","article-title":"High-speed photon-counting laser ranging for broad range of distances","volume":"8","author":"Du","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1364\/PRJ.390091","article-title":"Single-photon computational 3D imaging at 45km","volume":"8","author":"Li","year":"2020","journal-title":"Photonics Res."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Yu, Y., Liu, B., Chen, Z., and Hua, K. (2020). Photon Counting LIDAR Based on True Random Coding. Sensors, 20.","DOI":"10.3390\/s20113331"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ma, Y., Zhang, W., Sun, J., Li, G., Wang, X.H., Li, S., and Xu, N. (2019). Photon-counting lidar: An adaptive signal detection method for different land cover types in coastal areas. Remote Sens., 11.","DOI":"10.3390\/rs11040471"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5561","DOI":"10.1364\/AO.49.005561","article-title":"Range accuracy limitation of pulse ranging systems based on Geiger mode single-photon detectors","volume":"49","author":"Wang","year":"2010","journal-title":"Appl. Opt."},{"key":"ref_9","unstructured":"Clarke, C.B., Degnan, J.J., McGarry, J.F., and Pavlis, E.C. (2013, January 11\u201315). Processing single photon data for maximum range accuracy. Proceedings of the 18th International Workshop on Laser Ranging, Fujiyoshida, Japan."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40623-015-0204-4","article-title":"A method to calculate zero-signature satellite laser ranging normal points for millimeter geodesy-a case study with Ajisai","volume":"67","author":"Kucharski","year":"2015","journal-title":"Earth Planets Space"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5388","DOI":"10.1364\/AO.42.005388","article-title":"Detection and false-alarm probabilities for laser radars that use Geiger-mode detectors","volume":"42","author":"Fouche","year":"2003","journal-title":"Appl. Opt."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"9247","DOI":"10.1364\/OE.21.009247","article-title":"A real-time noise filtering strategy for photon counting 3D imaging lidar","volume":"21","author":"Zhang","year":"2013","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/TCI.2017.2706028","article-title":"A few photons among many: Unmixing signal and noise for photon-efficient active imaging","volume":"3","author":"Rapp","year":"2017","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"229","DOI":"10.3390\/photonics8060229","article-title":"Efficient and Noise Robust Photon-Counting Imaging with First Signal Photon Unit Method","volume":"Volume 8","author":"Hua","year":"2021","journal-title":"Photonics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"33911","DOI":"10.1364\/OE.23.033911","article-title":"Underwater depth imaging using time-correlated single-photon counting","volume":"23","author":"Maccarone","year":"2015","journal-title":"Opt. Express"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"031204","DOI":"10.1117\/1.OE.56.3.031204","article-title":"Continuously scanning time-correlated single-photon-counting single-pixel 3-D lidar","volume":"56","author":"Henriksson","year":"2016","journal-title":"Opt. Eng."},{"key":"ref_17","first-page":"1","article-title":"Full waveform analysis for long-range 3D imaging laser radar","volume":"2010","author":"Wallace","year":"2010","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Xie, D., Wang, F., and Chen, J. (2019). Extended Target Echo Detection Based on KLD and Wigner Matrices. Sensors, 19.","DOI":"10.3390\/s19245385"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"11701","DOI":"10.3390\/s150511701","article-title":"Entropy-Based TOA Estimation and SVM-Based Ranging Error Mitigation in UWB Ranging Systems","volume":"15","author":"Yin","year":"2015","journal-title":"Sensors"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Pan, X., Zhang, X., Jiang, Z., and Wang, S. (2017, January 24\u201326). Anti-noise possibilistic clustering based on maximum entropy. Proceedings of the 2017 12th International Conference on Intelligent Systems and Knowledge Engineering (ISKE), Nanjing, China.","DOI":"10.1109\/ISKE.2017.8258729"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JPHOT.2020.3038350","article-title":"Security Analysis of QAM Quantum-Noise Randomized Cipher System","volume":"12","author":"Chen","year":"2020","journal-title":"IEEE Photonics J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/S0264-3707(02)00045-5","article-title":"Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements","volume":"34","author":"Degnan","year":"2002","journal-title":"J. Geodyn."},{"key":"ref_23","unstructured":"Kamerman, G.W. (2003). Laser Radar Technology and Applications VIII, SPIE."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"15924","DOI":"10.1364\/OE.26.015924","article-title":"Theoretical ranging performance model and range walk error correction for photon-counting lidars with multiple detectors","volume":"26","author":"Ma","year":"2018","journal-title":"Opt. Express"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, X., Yang, B., Xie, X., Li, D., and Xu, L. (2018). Influence of Waveform Characteristics on LiDAR Ranging Accuracy and Precision. Sensors, 18.","DOI":"10.3390\/s18041156"},{"key":"ref_26","first-page":"1","article-title":"A Method for Maintaining the Stability of Range Walk Error in Photon Counting Lidar With Probability Distribution Regulator","volume":"11","author":"Xie","year":"2019","journal-title":"IEEE Photonics J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/11\/1499\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:29:22Z","timestamp":1760167762000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/11\/1499"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,12]]},"references-count":26,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["e23111499"],"URL":"https:\/\/doi.org\/10.3390\/e23111499","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,11,12]]}}}