Time Delay Estimation of Target Echo Signal Based on Multi-bright Spot Echoes

Abstract

Accurate time delay estimation of target echo signals is a critical component of underwater target localization. In active sonar systems, echo signal processing is vulnerable to the effects of reverberation and noise in the maritime environment. This paper proposes a novel method for estimating target time delay using multi-bright spot echoes, assuming the target’s size and depth are known. Aiming to effectively enhance the extraction of geometric features from the target echoes and mitigate the impact of reverberation and noise, the proposed approach employs the fractional order Fourier transform-frequency sliced wavelet transform to extract multi-bright spot echoes. Using the highlighting model theory and the target size information, an observation matrix is constructed to represent multi-angle incident signals and obtain the theoretical scattered echo signals from different angles. Aiming to accurately estimate the target’s time delay, waveform similarity coefficients and mean square error values between the theoretical return signals and received signals are computed across various incident angles and time delays. Simulation results show that, compared to the conventional matched filter, the proposed algorithm reduces the relative error by 65.9%–91.5% at a signal-tonoise ratio of -25 dB, and by 66.7%–88.9% at a signal-to-reverberation ratio of -10 dB. This algorithm provides a new approach for the precise localization of submerged targets in shallow water environments.

Keywords

Multi-bright spot echoes / Time-delay estimation; Target echo signal / Frequency sliced wavelet transform / Fractional order fourier transform

References

[1] Challinor C, Cegla F. Pulse compression with and without matched filtering: Why codes beat chirps. NDT & E International, 2024, 147: 103180

[2] Ding FL, Chi C, Li Y, Huang HN. Variational Bayesian inference time delay estimation for passive sonars. Journal of Marine Science and Engineering, 2023, 11(1): 3-15

[3] Drake SP, Mckerral JC, Anderson BDO. Single channel multiple signal classification using Pseudo-Doppler. IEEE Signal Processing Letters, 2023, 30: 1587-1591

[4] Guo Y, Yang LD. LFM signal optimization time-fractional-frequency analysis: Principles, method and application. Digital Signal Processing, 2022, 126: 103505

[5] Hama Y, Ochiai H. Performance analysis of matched-filter detector for MIMO spatial multiplexing over Rayleigh fading channels with imperfect channel estimation. IEEE Transactions on Communications, 2019, 67(53220-3233

[6] Hu MT, Wang GF, Ma ML, Cao ZH, Yang S. Bearing performance degradation assessment based on optimized EWT and CNN. Measurement, 2021, 172: 108868

[7] Jiang J, Yang TC, Pan X. Beam-time delay domain deconvolved scheme for high-resolution active localization of underwater targets. The Journal of the Acoustical Society America, 2020, 148: 3762-3771

[8] Li GD, Wu JS, Tang TL, Chen ZX, Chen J, Huang L. Underwater acoustic time delay estimation based on envelope differences of correlation functions. Sensors, 2019, 19(51259

[9] Nicos E, Sheraz A, Tzioyntmprian TR, Michalis PM, Herodotos H. Enhancing prediction accuracy of vessel arrival times using machine learning. Journal of Marine Science and Engineering, 2024, 12(81362

[10] Omair A, Ahmet S. LFM signal parameter estimation in the fractional Fourier domains: Analytical models and a high-performance algorithm. Signal Processing, 2024, 214: 109224

[11] Qasaymeh MM, Gami H, Tayem N, Sawan ME, Pendse R. Joint time delay and frequency estimation without Eigendecomposition. IEEE Signal Processing Letters, 2009, 16(5422-425

[12] Shen SY, Zhang XY, Liu YF, Xu SL, Fang JJ, Hu YH. Degree of polarization calculation for laser backscattering from typical geometric rough surfaces at long distance. Remote Sensing, 2022, 14(236001

[13] Sheng ZP, Xu YG, Zhang K. Applications in bearing fault diagnosis of an improved Kurtogram algorithm based on flexible frequency slice wavelet transform filter bank. Measurement, 2021, 174: 108975

[14] Shi C, Wang YJ, Wang F, Salous S, Zhou JJ. Low probability of intercept-based OFDM radar waveform design for target time delay estimation in a cooperative radar-communications system. IET Radar, Sonar and Navigation, 2019, 13(101697-1704

[15] Sun SJ, Li XK, Meng XX. Time-frequency domain blind source separation of geometrical structure of underwater target echo. Journal of Harbin Engineering University, 2015, 36(81030-1035

[16] Tang G, Qi C, Liu G. Time delay estimation of Gaussian signal in non-Gaussian spatially correlated noise. Neural Networks & Signal Processing, Nanjing, China, 2004639642

[17] Wang J, Wang H, Bourennane YW. Low complexity joint angle and delay estimation for underwater multipath acoustic channel based on sparse Bayesian learning. Applied Acoustics, 2023, 214: 109-123

[18] Wang YY, Chen JT, Fang WH. TST-MUSIC for joint DOAdelay estimation. IEEE Transactions on Signal Processing, 2001, 49(4): 721-729

[19] Wu TY. New methods for time delay estimation of non- Gaussian signal in unknown Gaussian noises using third-order cumulants. Electronics Letter, 2000, 38: 930-931

[20] Xia Z, Li X, Meng X. High resolution time-delay estimation of underwater target geometric scattering. Applied Acoustics, 2016, 114: 111-117

[21] Yan FG, Jin M, Zhou HJ, Wang J, Shuai L. Low-degree root- MUSIC algorithm for fast DOA estimation based on variable substitution technique. Science China-Information Sciences, 2020, 63(5): 159206

[22] Yan Z, Miyamoto A, Jiang Z. Frequency slice algorithm for modal signal separation and damping identification. Computers and Structures, 2011, 89(114-26

[23] Yan Z, Sun R, Jiang S, Song TT, Gao TZ. Improved variable step adaptive filtering algorithm and its application in time delay estimation for continuous wave dual-sensor pulse signals. Geoenergy Science and Engineering, 2023, 230: 221-238

[24] Zhang ZH, Zhong YT, Xiang JW, Jiang YY. Phase correction improved multiple signal classification for impact source localization under varying temperature conditions. Measurement, 2020, 152: 107374

[25] Zhao G, Zheng W, Sun NW, Shen S, Wu XY. Acoustic shooting and bounce ray method for calculating echoes of complex underwater targets. Applied Sciences, 2022, 12(2211707

[26] Zhao Z, Liu C, Li YW, Li YX, Wang LY, Lin BS, Li JQ. Noise rejection for wearable ECGs using modified frequency slice wavelet transform and convolutional neural networks. IEEE Access, 2019, 7: 34060-34067

[27] Zhou F, Fan J, Wang B, Zhou YL, Huang JF. Acoustic barcode based on the acoustic scattering characteristics of underwater targets. Applied Acoustics, 2022, 18: 1-12

[28] Zhou H, Bao XP, Zhang HG. Scale property prediction of typical multi-highlight target echoes and its experimental validation. IEEE Access, 2024, 12: 164672-164681

RIGHTS & PERMISSIONS

Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature