{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T15:48:47Z","timestamp":1786722527307,"version":"3.56.0"},"reference-count":36,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T00:00:00Z","timestamp":1663977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Naval University of Engineering, PLA Scientific Research Development Fund Self-establishment Program","award":["425317S091"],"award-info":[{"award-number":["425317S091"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The accuracy of time delay estimation seriously affects the accuracy of sound source localization. In order to improve the accuracy of time delay estimation under the condition of low SNR, a delay estimation optimization algorithm based on singular value decomposition and improved GCC-PHAT weighting (GCC-PHAT-\u03c1\u03b3 weighting) is proposed. Firstly, the acoustic signal collected by the acoustic sensor array is subjected to singular value decomposition and noise reduction processing to improve the signal-to-noise ratio of the signal; then, the cross-correlation operation is performed, and the cross-correlation function is processed by the GCC-PHAT-\u03c1\u03b3 weighting method to obtain the cross-power spectrum; finally, the inverse transformation is performed to obtain the generalized correlation time domain function, and the peak detection is performed to obtain the delay difference. The experiment was carried out in a large outdoor pool, and the experimental data were processed to compare the time delay estimation performance of three methods: GCC-PHAT weighting, SVD-GCC-PHAT weighting (meaning: GCC-PHAT weighting based on singular value decomposition) and SVD-GCC-PHAT-\u03c1\u03b3 weighting (meaning: GCC-PHAT-\u03c1\u03b3 weighting based on singular value decomposition). The results show that the delay estimation optimization algorithm based on SVD-GCC-PHAT-\u03c1\u03b3 improves the delay estimation accuracy by at least 37.95% compared with the other two methods. The new optimization algorithm has good delay estimation performance.<\/jats:p>","DOI":"10.3390\/s22197254","type":"journal-article","created":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T03:34:17Z","timestamp":1664163257000},"page":"7254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Optimization Algorithm for Delay Estimation Based on Singular Value Decomposition and Improved GCC-PHAT Weighting"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3588-0736","authenticated-orcid":false,"given":"Shizhe","family":"Wang","sequence":"first","affiliation":[{"name":"Academy of Weapony Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zongji","family":"Li","sequence":"additional","affiliation":[{"name":"Academy of Weapony Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pingbo","family":"Wang","sequence":"additional","affiliation":[{"name":"Academy of Electronic Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huadong","family":"Chen","sequence":"additional","affiliation":[{"name":"Academy of Weapony Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2449","DOI":"10.1007\/s11071-020-05615-5","article-title":"Adaptive robust decoupling control of multi-arm space robots using time-delay estimation technique","volume":"100","author":"Zhang","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kali, Y., Ayala, M., Rodas, J., Saad, M., Doval-Gandoy, J., Gregor, R., and Benjelloun, K. (2019). Current control of a six-phase induction machine drive based on discrete-time sliding mode with time delay estimation. Energies, 12.","DOI":"10.3390\/en12010170"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.advengsoft.2018.04.009","article-title":"Vibration control of an active vehicle suspension systems using optimized model-free fuzzy logic controller based on time delay estimation","volume":"127","author":"Mustafa","year":"2019","journal-title":"Adv. Eng. Softw."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.advengsoft.2018.01.004","article-title":"Model-free based adaptive nonsingular fast terminal sliding mode control with time-delay estimation for a 12 DOF multi-functional lower limb exoskeleton","volume":"119","author":"Han","year":"2018","journal-title":"Adv. Eng. Softw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.neucom.2017.06.055","article-title":"Model-free based neural network control with time-delay estimation for lower extremity exoskeleton","volume":"272","author":"Zhang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1128","DOI":"10.1109\/TSMC.2019.2895588","article-title":"Adaptive high-order terminal sliding mode control based on time delay estimation for the robotic manipulators with backlash hysteresis","volume":"51","author":"Ahmed","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.isatra.2019.07.030","article-title":"Time-delay estimation based computed torque control with robust adaptive RBF neural network compensator for a rehabilitation exoskeleton","volume":"97","author":"Han","year":"2020","journal-title":"ISA Trans."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1109\/TASLP.2020.2983589","article-title":"Frequency-sliding generalized cross-correlation: A sub-band time delay estimation approach","volume":"28","author":"Cobos","year":"2020","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.measurement.2019.04.092","article-title":"Distributed optical fiber vibration sensor using generalized cross-correlation algorithm","volume":"144","author":"Wang","year":"2019","journal-title":"Measurement"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Catur, H.A.H.B.B., and Saputra, H.M. (2019, January 23\u201324). Azimuth estimation based on generalized cross correlation phase transform (GCC-PHAT) using Equilateral triangle microphone array. Proceedings of the 2019 International Conference on Radar, Antenna, Microwave, Electronics, and Telecommunications (ICRAMET), Tangerang, Indonesia.","DOI":"10.1109\/ICRAMET47453.2019.8980432"},{"key":"ref_11","first-page":"271","article-title":"Improved generalized cross correlation-phase transform based time delay estimation by frequency domain autocorrelation","volume":"37","author":"Lim","year":"2018","journal-title":"J. Acoust. Soc. Korea"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1121\/1.5094419","article-title":"On the use of modified phase transform weighting functions for acoustic imaging with the generalized cross correlation","volume":"145","author":"Padois","year":"2019","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Glentis, G.O., and Angelopoulos, K. (2022, January 16\u201319). Using Generalized Cross-Correlation estimators for leak signal velocity estimation and spectral region of operation selection. Proceedings of the 2022 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Ottawa, ON, Canada.","DOI":"10.1109\/I2MTC48687.2022.9806476"},{"key":"ref_14","first-page":"207","article-title":"Study on the pre-processors to improve the generalized-cross-correlation based time delay estimation under the narrow band single tone signal environments","volume":"39","author":"Lim","year":"2020","journal-title":"J. Acoust. Soc. Korea"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ye, D., Lu, J.Y., Zhu, X.J., and Lin, H. (2016, January 21\u201323). Generalized cross corre-lation time delay estimation based on improved waveletthreshold function. Proceedings of the 2016 Sixth International Confer-ence on Instrumentation & Measurement, Computer, Communication and Control, Harbin, China.","DOI":"10.1109\/IMCCC.2016.72"},{"key":"ref_16","first-page":"104","article-title":"Wheel\/Rail Force Signal Denoising Based on Wavelet Packet and Improved EMD","volume":"36","author":"Zhang","year":"2016","journal-title":"Noise Vib. Control"},{"key":"ref_17","first-page":"562","article-title":"Second correlation time delay estimation based on empirical mode de-composition reconstruction","volume":"56","author":"Zhou","year":"2016","journal-title":"Telecommun. Eng."},{"key":"ref_18","first-page":"52","article-title":"Cross-correlation delay estimation optimization algorithm based on singular value decomposition","volume":"43","author":"Wei","year":"2020","journal-title":"Electron. Meas. Technol."},{"key":"ref_19","first-page":"47","article-title":"Generalized Cross Correlation Time Delay Estimation Based on Singular Value Decomposition","volume":"36","author":"Zhang","year":"2017","journal-title":"J. Lanzhou Jiaotong Univ."},{"key":"ref_20","first-page":"6354","article-title":"Time delay estimation simulation of robot fish obstacle avoidance based on PHAT-\u03b2 generalized cross-correlation in the transformer","volume":"21","author":"Zhang","year":"2021","journal-title":"Sci. Technol. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fokin, G., Kireev, A., and Al-odhari, A.H.A. (2018, January 14\u201315). TDOA positioning accuracy performance evaluation for arc sensor configuration. Proceedings of the 2018 Systems of Signals Generating and Processing in the Field of on Board Communications, Moscow, Russia.","DOI":"10.1109\/SOSG.2018.8350644"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"107774","DOI":"10.1016\/j.sigpro.2020.107774","article-title":"TDOA-based localization with NLOS mitigation via robust model transformation and neurodynamic optimization","volume":"178","author":"Xiong","year":"2021","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1002\/2017RS006389","article-title":"A novel long-time accumulation method for double-satellite TDOA\/FDOA interference localization","volume":"53","author":"Wu","year":"2018","journal-title":"Radio Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.ifacol.2018.03.062","article-title":"Compression and noise reduction of biomedical signals by singular value decomposition","volume":"51","author":"Schanze","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4093","DOI":"10.1109\/TIM.2019.2945826","article-title":"Partial discharge random noise removal using Hankel matrix-based fast singular value decomposition","volume":"69","author":"Govindarajan","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3220","DOI":"10.1109\/TII.2020.3001376","article-title":"A bearing fault diagnosis method based on enhanced singular value decomposition","volume":"17","author":"Li","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1111\/1365-2478.12576","article-title":"Noise suppression for microseismic data by non-subsampled shearlet transform based on singular value decomposition","volume":"66","author":"Liang","year":"2018","journal-title":"Geophys. Prospect."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"035116","DOI":"10.1063\/1.5089582","article-title":"A fusion of principal component analysis and singular value decomposition based multivariate denoising algorithm for free induction decay transversal data","volume":"90","author":"Liu","year":"2019","journal-title":"Rev. Sci. Instrum."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.ymssp.2018.08.056","article-title":"Research on bearing fault feature extraction based on singular value decomposition and optimized frequency band entropy","volume":"118","author":"Li","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.infrared.2018.06.028","article-title":"Echo signal extraction method of laser radar based on improved singular value decomposition and wavelet threshold denoising","volume":"92","author":"Xu","year":"2018","journal-title":"Infrared Phys. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"8866","DOI":"10.1109\/TIM.2020.2996717","article-title":"Partial discharge signal denoising based on singular value decomposition and empirical wavelet transform","volume":"69","author":"Zhong","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_32","first-page":"102424","article-title":"Red-cyan anaglyph image watermarking using DWT, Hadamard transform and singular value decomposition for copyright protection","volume":"50","author":"Devi","year":"2020","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Villadangos, J.M., Ure\u00f1a, J., Garc\u00eda-Dom\u00ednguez, J.J., Jim\u00e9nez-Mart\u00edn, A., Hern\u00e1ndez, \u00c1., and P\u00e9rez-Rubio, M.C. (2021). Dynamic adjustment of weighted gcc-phat for position estimation in an ultrasonic local positioning system. Sensors, 21.","DOI":"10.3390\/s21217051"},{"key":"ref_34","unstructured":"Padois, T., Doutres, O., Nelisse, H., and Sgard, F. (2019, January 7\u201311). Acoustic imaging using different weighting functions with the generalized cross correlation based on the generalized mean. Proceedings of the 26th International Congress on Sound and Vibration, Montreal, QC, Canada."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Yang, X., Bao, C., and Cui, Z. (2022). Weighting function modification used for phase transform-based time delay estimation. China Commun.","DOI":"10.23919\/JCC.2022.00.012"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Tan, C.S., Mohd-Mokhtar, R., and Arshad, M.R. (2019). Improved Generalized Cross Correlation Phase Transform Algorithm for Time Difference of Arrival Estimation. Proceedings of the 10th National Technical Seminar on Underwater System Technology 2018, Springer.","DOI":"10.1007\/978-981-13-3708-6_26"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7254\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:56Z","timestamp":1760143136000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/19\/7254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,24]]},"references-count":36,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["s22197254"],"URL":"https:\/\/doi.org\/10.3390\/s22197254","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,24]]}}}