{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:37:41Z","timestamp":1760060261117,"version":"build-2065373602"},"reference-count":74,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T00:00:00Z","timestamp":1755043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFC2206100","2022YFC2204602","12175076","2023010201010048"],"award-info":[{"award-number":["2023YFC2206100","2022YFC2204602","12175076","2023010201010048"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2023YFC2206100","2022YFC2204602","12175076","2023010201010048"],"award-info":[{"award-number":["2023YFC2206100","2022YFC2204602","12175076","2023010201010048"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Knowledge Innovation Program of Wuhan-Basi Research","award":["2023YFC2206100","2022YFC2204602","12175076","2023010201010048"],"award-info":[{"award-number":["2023YFC2206100","2022YFC2204602","12175076","2023010201010048"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Space-borne gravitational wave (GW) detection is poised to significantly advance the frontiers of astrophysics, gravitation, and cosmology, which might make it possible to measure the fundamental symmetries of space-time. A critical component in GW detection is the employment of ultra-stable oscillators (USOs) on each satellite, serving as precision timing references to drive analog-to-digital converters (ADCs) for digital sampling of GW signals. Achieving the required sensitivity in GW detection hinges on highly accurate clock timing. However, the challenges posed by ADC aperture jitter and sampling clock jitter cannot be overlooked. They disrupt sampling timing, introduce clock noise, and distort the digitized signal, thus limiting the effectiveness of GW detection in space. To overcome this problem, researchers have developed pilot tone correction techniques and proposed innovative clock noise calibrated time-delay interferometry (TDI), optical comb TDI techniques, and sideband arm locking techniques that effectively suppress the effects of clock noise. This study provides an in-depth and comprehensive summary of the current status of clock noise and its suppression techniques in the space-borne GW detection. Through a systematic review and analysis, the aim is to provide theoretical and experimental technical support and optimization suggestions for the implementation of China\u2019s space-borne GW detection mission.<\/jats:p>","DOI":"10.3390\/sym17081314","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T13:30:38Z","timestamp":1755091838000},"page":"1314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Clock Noise Suppression Techniques in Space-Borne Gravitational Wave Detection: A Review"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-0036-580X","authenticated-orcid":false,"given":"Yijun","family":"Xia","sequence":"first","affiliation":[{"name":"National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Aoting","family":"Fang","sequence":"additional","affiliation":[{"name":"National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Mingyang","family":"Xu","sequence":"additional","affiliation":[{"name":"National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3124-2777","authenticated-orcid":false,"given":"Yujie","family":"Tan","sequence":"additional","affiliation":[{"name":"National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Chenggang","family":"Shao","sequence":"additional","affiliation":[{"name":"National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1002\/andp.19163540702","article-title":"Die grundlage der allgemeinen relativit\u00e4tstheorie","volume":"354","author":"Einstein","year":"1916","journal-title":"Annalen der Physik"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"061102","DOI":"10.1103\/PhysRevLett.116.061102","article-title":"Observation of gravitational waves from a binary black hole merger","volume":"116","author":"Abbott","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"241103","DOI":"10.1103\/PhysRevLett.116.241103","article-title":"GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence","volume":"116","author":"Abbott","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"260461","DOI":"10.1007\/s11433-023-2099-5","article-title":"Revealing the amplitude of primordial curvature perturbations on small scales from Primordial black hole binaries for gravitational wave detection","volume":"66","author":"Cai","year":"2023","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"240411","DOI":"10.1007\/s11433-023-2293-2","article-title":"Gravitational waves and primordial black hole productions from gluodynamics by holography","volume":"67","author":"He","year":"2024","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, C.W.Z., Zhu, J.B., Huang, G.Q., and Shu, F.W. (2024). Testing the first law of black hole mechanics with gravitational waves. arXiv.","DOI":"10.1007\/s11433-024-2442-3"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cervantes-Cota, J.L., Galindo-Uribarri, S., and Smoot, G.F. (2016). A brief history of gravitational waves. Universe, 2.","DOI":"10.3390\/universe2030022"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.cjph.2016.10.014","article-title":"A brief history of gravitational wave research","volume":"55","author":"Chen","year":"2017","journal-title":"Chin. J. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109513","DOI":"10.1007\/s11433-023-2179-9","article-title":"Detecting gravitational wave with an interferometric seismometer array on lunar nearside","volume":"66","author":"Li","year":"2023","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"119531","DOI":"10.1007\/s11433-023-2215-4","article-title":"Perceiving deci-Hertz gravitational waves over the Moon","volume":"66","author":"Shao","year":"2023","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"259511","DOI":"10.1007\/s11433-023-2308-x","article-title":"Detection of astrophysical gravitational wave sources by TianQin and LISA","volume":"67","author":"Huang","year":"2024","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"269532","DOI":"10.1007\/s11433-024-2390-9","article-title":"FAST unveils a new era in the discovery of long-period pulsars in globular clusters","volume":"67","author":"Han","year":"2024","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_13","unstructured":"Amaro-Seoane, P., Audley, H., Babak, S., Baker, J., Barausse, E., Bender, P., Berti, E., Binetruy, P., Born, M., and Bortoluzzi, D. (2017). Laser Interferometer Space Antenna. arXiv."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"035010","DOI":"10.1088\/0264-9381\/33\/3\/035010","article-title":"TianQin: A space-borne gravitational wave detector","volume":"33","author":"Luo","year":"2016","journal-title":"Class. Quantum Gravity"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1093\/nsr\/nwx116","article-title":"The Taiji program in space for gravitational wave physics and the nature of gravity","volume":"4","author":"Hu","year":"2017","journal-title":"Natl. Sci. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"044002","DOI":"10.1088\/2058-9565\/ac7df9","article-title":"Fundamental physics with a state-of-the-art optical clock in space","volume":"7","author":"Derevianko","year":"2022","journal-title":"Quantum Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"124043","DOI":"10.1103\/PhysRevD.94.124043","article-title":"Gravitational wave detection with optical lattice atomic clocks","volume":"94","author":"Kolkowitz","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"249512","DOI":"10.1007\/s11433-024-2573-3","article-title":"Space-based optical lattice clocks as gravitational wave detectors in search for new physics","volume":"68","author":"Wang","year":"2025","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_19","unstructured":"Weaver, G., Garstecki, J., and Reynolds, S. (2010, January 15\u201318). The performance of ultra-stable oscillators for the Gravity Recovery and Interior Laboratory (GRAIL). Proceedings of the Annual Precise Time & Time Interval Systems & Applications Meeting, Reston, VA, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"022002","DOI":"10.1103\/PhysRevD.64.022002","article-title":"Elimination of clock jitter noise in spaceborne laser interferometers","volume":"64","author":"Hellings","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"015008","DOI":"10.1088\/0264-9381\/25\/1\/015008","article-title":"Modulator noise suppression in the LISA time-delay interferometric combinations","volume":"25","author":"Tinto","year":"2007","journal-title":"Class. Quantum Gravity"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"205003","DOI":"10.1088\/0264-9381\/29\/20\/205003","article-title":"TDI and clock noise removal for the split interferometry configuration of LISA","volume":"29","author":"Otto","year":"2012","journal-title":"Class. Quantum Gravity"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"042003","DOI":"10.1103\/PhysRevD.98.042003","article-title":"Time-delay interferometry and clock-noise calibration","volume":"98","author":"Tinto","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"123027","DOI":"10.1103\/PhysRevD.103.123027","article-title":"Clock-jitter reduction in LISA time-delay interferometry combinations","volume":"103","author":"Hartwig","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"106900","DOI":"10.1016\/j.rinp.2023.106900","article-title":"Clock noise reduction in geometric time delay interferometry combinations","volume":"53","author":"Yang","year":"2023","journal-title":"Results Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"042002","DOI":"10.1103\/PhysRevD.92.042002","article-title":"Time-delay interferometry with optical frequency comb","volume":"92","author":"Tinto","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"044010","DOI":"10.1103\/PhysRevD.106.044010","article-title":"Modified time-delay interferometry with an optical frequency comb","volume":"106","author":"Tan","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"102003","DOI":"10.1103\/PhysRevD.110.102003","article-title":"Clock-jitter noise reduction by sideband arm locking for space-borne gravitational wave detectors","volume":"110","author":"Xu","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"211103","DOI":"10.1103\/PhysRevLett.104.211103","article-title":"Experimental demonstration of time-delay interferometry for the Laser Interferometer Space Antenna","volume":"104","author":"Ware","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"122006","DOI":"10.1103\/PhysRevD.86.122006","article-title":"Hardware-based demonstration of time-delay interferometry and TDI-ranging with spacecraft motion effects","volume":"86","author":"Mitryk","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/s12217-022-09982-z","article-title":"Proof-of-principle experimental demonstration of Time-delay-interferometry for Chinese space-borne gravitational wave detection missions","volume":"34","author":"Li","year":"2022","journal-title":"Microgravity Sci. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"042009","DOI":"10.1103\/PhysRevD.105.042009","article-title":"Experimental verification of intersatellite clock synchronization at LISA performance levels","volume":"105","author":"Yamamoto","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"062002","DOI":"10.1103\/PhysRevD.102.062002","article-title":"Experimental demonstration of time-delay interferometry with optical frequency comb","volume":"102","author":"Vinckier","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1364\/OL.473812","article-title":"Time delay interferometry with a transfer oscillator","volume":"48","author":"Wu","year":"2023","journal-title":"Opt. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1063\/1.2405061","article-title":"Clock noise removal in LISA","volume":"873","author":"Klipstein","year":"2006","journal-title":"AIP Conf. Proc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s00340-009-3682-x","article-title":"EOM sideband phase characteristics for the spaceborne gravitational wave detector LISA","volume":"98","author":"Barke","year":"2010","journal-title":"Appl. Phys. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"34648","DOI":"10.1364\/OE.503164","article-title":"Experimental demonstration of weak-light inter-spacecraft clock jitter readout for TianQin","volume":"31","author":"Zeng","year":"2023","journal-title":"Opt. Express"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"25603","DOI":"10.1364\/OE.20.025603","article-title":"Experimental verification of clock noise transfer and components for space based gravitational wave detectors","volume":"20","author":"Sweeney","year":"2012","journal-title":"Opt. Express"},{"key":"ref_39","unstructured":"Barke, S. (2015). Inter-Spacecraft Frequency Distribution for Future Gravitational Wave Observatories. [Ph.D. Thesis, Leibniz University]."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"122008","DOI":"10.1103\/PhysRevD.105.122008","article-title":"Time-delay interferometry without clock synchronization","volume":"105","author":"Hartwig","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"022004","DOI":"10.1103\/PhysRevD.109.022004","article-title":"Ranging sensor fusion in LISA data processing: Treatment of ambiguities, noise, and onboard delays in LISA ranging observables","volume":"109","author":"Reinhardt","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"122001","DOI":"10.1103\/6n7z-gswn","article-title":"Observable-based reformulation of time-delay interferometry","volume":"111","author":"Yamamoto","year":"2025","journal-title":"Phys. Rev. D"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"113855","DOI":"10.1016\/j.measurement.2023.113855","article-title":"Time synchronization between satellites via inter-satellite link observations of BDS-3 Constellation: Method, experiment and analysis","volume":"224","author":"Guo","year":"2024","journal-title":"Measurement"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s10291-024-01684-w","article-title":"LSTM-based clock synchronization for satellite systems using inter-satellite ranging measurements","volume":"28","author":"Gu","year":"2024","journal-title":"GPS Solut."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s00190-023-01765-7","article-title":"Centimeter-level clock synchronization and space-borne timescale generation for BDS-3 using inter-satellite link measurements","volume":"97","author":"Yang","year":"2023","journal-title":"J. Geod."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"230409","DOI":"10.1360\/SSPMA-2024-0365","article-title":"Research progress on clock noise suppression technique for space-borne gravitational wave detection","volume":"55","author":"Xu","year":"2025","journal-title":"Sci. Sin. Phys. Mech. Astron."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"061303","DOI":"10.1103\/PhysRevD.68.061303","article-title":"Data combinations accounting for LISA spacecraft motion","volume":"68","author":"Shaddock","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"082003","DOI":"10.1103\/PhysRevD.65.082003","article-title":"Time-delay interferometry for LISA","volume":"65","author":"Tinto","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"081101","DOI":"10.1103\/PhysRevD.70.081101","article-title":"Postprocessed time-delay interferometry for LISA","volume":"70","author":"Shaddock","year":"2004","journal-title":"Phys. Rev. D"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41114-020-00029-6","article-title":"Time-delay interferometry","volume":"24","author":"Tinto","year":"2021","journal-title":"Living Rev. Relativ."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"082001","DOI":"10.1103\/PhysRevD.103.082001","article-title":"Time-delay interferometry without delays","volume":"103","author":"Vallisneri","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"044065","DOI":"10.1103\/PhysRevD.108.044065","article-title":"Bayesian time delay interferometry for orbiting LISA: Accounting for the time dependence of spacecraft separations","volume":"108","author":"Page","year":"2023","journal-title":"Phys. Rev. D"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"082001","DOI":"10.1103\/PhysRevD.107.082001","article-title":"Second-generation time-delay interferometry","volume":"107","author":"Tinto","year":"2023","journal-title":"Phys. Rev. D"},{"key":"ref_54","unstructured":"Colpi, M., Danzmann, K., Hewitson, M., Holley-Bockelmann, K., Jetzer, P., Nelemans, G., Petiteau, A., Shoemaker, D., Sopuerta, C., and Stebbins, R. (2024). LISA Definition Study Report. arXiv."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"074501","DOI":"10.1063\/1.4927071","article-title":"Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision","volume":"86","author":"Gerberding","year":"2015","journal-title":"Rev. Sci. Instrum."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"036106","DOI":"10.1063\/1.5011654","article-title":"Note: A new method for directly reducing the sampling jitter noise of the digital phasemeter","volume":"89","author":"Liang","year":"2018","journal-title":"Rev. Sci. Instrum."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"109185","DOI":"10.1016\/j.optlastec.2023.109185","article-title":"Study on picometer-level laser interferometer readout system in TianQin project","volume":"161","author":"Huang","year":"2023","journal-title":"Opt. Laser Technol."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"054501","DOI":"10.1063\/5.0198104","article-title":"Multi-frequency signal acquisition and phase measurement in space gravitational wave detection","volume":"95","author":"Zhang","year":"2024","journal-title":"Rev. Sci. Instrum."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"082001","DOI":"10.1103\/PhysRevD.69.082001","article-title":"Time delay interferometry with moving spacecraft arrays","volume":"69","author":"Tinto","year":"2004","journal-title":"Phys. Rev. D"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Wang, P.P., and Shao, C.G. (2024). Time-Delay Interferometry: The Key Technique in Data Pre-Processing Analysis of Space-Based Gravitational Waves. Universe, 10.","DOI":"10.3390\/universe10100398"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1038\/nphoton.2016.215","article-title":"Photonic microwave signals with zeptosecond-level absolute timing noise","volume":"11","author":"Xie","year":"2017","journal-title":"Nat. Photonics"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1126\/science.abb2473","article-title":"Coherent optical clock down-conversion for microwave frequencies with 10-18 instability","volume":"368","author":"Nakamura","year":"2020","journal-title":"Science"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"4651","DOI":"10.1364\/OL.43.004651","article-title":"Ultra-low noise microwave generation with a free-running optical frequency comb transfer oscillator","volume":"43","author":"Brochard","year":"2018","journal-title":"Opt. Lett."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"026105","DOI":"10.1063\/5.0073843","article-title":"10 GHz generation with ultra-low phase noise via the transfer oscillator technique","volume":"7","author":"Nardelli","year":"2022","journal-title":"APL Photonics"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1126\/science.1095092","article-title":"Optical frequency synthesis and comparison with uncertainty at the 10-19 level","volume":"303","author":"Ma","year":"2004","journal-title":"Science"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.physleta.2003.10.076","article-title":"Laser frequency stabilization by locking to a LISA arm","volume":"320","author":"Sheard","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"102003","DOI":"10.1103\/PhysRevD.80.102003","article-title":"Performance of arm locking in LISA","volume":"80","author":"McKenzie","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"115009","DOI":"10.1088\/1361-6382\/ac69a4","article-title":"Arm locking performance with the new LISA design","volume":"39","author":"Ghosh","year":"2022","journal-title":"Class. Quantum Gravity"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"042006","DOI":"10.1103\/PhysRevD.109.042006","article-title":"Transient analysis of the arm locking controller","volume":"109","author":"Zhang","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"062005","DOI":"10.1103\/PhysRevD.90.062005","article-title":"Arm locking for space-based laser interferometry gravitational wave observatories","volume":"90","author":"Yu","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"062004","DOI":"10.1103\/PhysRevD.110.062004","article-title":"Experimental demonstration of the combined arm- and cavity-locking system for LISA","volume":"110","author":"Valliyakalayil","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"094008","DOI":"10.1088\/0264-9381\/28\/9\/094008","article-title":"Auxiliary functions of the LISA laser link: Ranging, clock noise transfer and data communication","volume":"28","author":"Heinzel","year":"2011","journal-title":"Class. Quantum Gravity"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"107221","DOI":"10.1016\/j.rinp.2023.107221","article-title":"Experimental demonstration of sub-100 picometer level signal extraction with time-delay interferometry technique","volume":"56","author":"Xu","year":"2024","journal-title":"Results Phys."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.37188\/CO.2023-0012","article-title":"Ground-based principle verification of clock noise transfer for the Taiji program","volume":"16","author":"Jiang","year":"2023","journal-title":"Chin. Opt."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1314\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:26:19Z","timestamp":1760034379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1314"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,13]]},"references-count":74,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081314"],"URL":"https:\/\/doi.org\/10.3390\/sym17081314","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,8,13]]}}}