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Doppler-warping变换及其应用在声学目标运动速度估计

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## Doppler-warping transform and its application to estimating acoustic target velocity

Gao De-Yang, Gao Da-Zhi, Chi Jing, Wang Liang, Song Wen-Hua
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• #### 摘要

当声源和接收器之间存在相对运动时, 接收到的信号会发生多普勒频移, 多普勒频移和目标运动参数有关. 针对声学多普勒频移问题提出Doppler-warping变换, 运用该变换可以实现多普勒信号相位的线性化, 推导出warping算子, 提出一种利用该变换估计目标运动参数的算法. 首先构造不同运动参数下的Doppler-warping算子, 再利用算子对接收的时域信号进行时间重采样, 然后求出变换之后信号的频谱函数, 最后利用频谱函数熵最小来实现目标参数估计. 仿真结果证明了该方法的有效性, 对于低信噪比的海试数据, 渔船真实速度为4.5 m/s, 采用传统的最小均方误差(MMSE)速度估计方法得到的结果为5.2 m/s, 误差达到15.56%, 本文提出的Doppler-warping变换方法较为准确地估计了目标运动速度, 估计结果为4.7 m/s, 误差为4.44%.

#### Abstract

When there appears the relative motion between the sound source and the receiver, the received tonal signal will produce Doppler shift, and the Doppler information is relevant to the motion parameters of the target. According to the acoustic Doppler shift frequency, we propose the Doppler-warping transformation. The phase linearization of the Doppler signal can be realized by using the transformation. Then, we deduce the warping operator and propose an algorithm for estimating the target motion parameters by using the proposed transformation. Firstly, the Doppler-warping operator under different motion parameters is constructed. Secondly, the time resampling of the received time-domain signal is performed by using the operator. Then, the spectral function of the transformed signal is calculated. Finally, the spectral function entropy is minimized to estimate the objective parameter. The simulation results show the effectiveness of the proposed method. For a low signal-to-noise ratio of sea trial data, where the real speed of a fishing boat is 4.5 m/s, the result from the traditional minimum mean square error (MMSE) velocity estimation method is 5.2 m/s, and the estimation error is 15.56%. The proposed Doppler-warping transform method can estimate the target velocity more accurately, specifically, it is 4.7 m/s and its corresponding estimation error is 4.44%.

#### 作者及机构信息

###### 通信作者: 高大治, dzgao@ouc.edu.cn
• 基金项目: 国家自然科学基金(批准号: 11874331)和青岛海洋科学与技术国家实验室开放基金(批准号: QNLM2016ORP0106)资助的课题

#### Authors and contacts

###### Corresponding author: Gao Da-Zhi, dzgao@ouc.edu.cn
• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874331) and the Open Foundation of Qingdao National Laboratory for Marine Science and Technology, China (Grant No. QNLM2016ORP0106)

#### 施引文献

• 图 1  声源运动接收器静止示意图

Fig. 1.  Moving sound source and stationary receiver.

图 2  (a)多普勒信号时频图; (b)瞬时频率真实值和估计值; (c)最小均方误差估计的速度值和真实值对比

Fig. 2.  (a) Time-frequency distribution of Doppler signal; (b) real and estimated instantaneous frequency; (c) comparison of real velocity and estimation velocity obtained by MMSE.

图 3  (a)不同速度值下Doppler-warping变换后的信号频谱; (b) Doppler-warping变换估计速度的结果

Fig. 3.  (a) Signal spectra after the Doppler-warping transform under different velocity values; (b) result of velocity estimation by the Doppler-warping transform.

图 4  不同信噪比下估计的速度结果

Fig. 4.  Estimated velocity results under different SNRs.

图 5  SNR = –10 dB时的(a)时频分布图, (b)瞬时频率真实值和估计值, 以及(c) v = 5 m/s 条件下Doppler-warping变换后的频谱和原始信号频谱的对比

Fig. 5.  (a) Time-frequency distribution; (b) real and estimated instantaneous frequency; (c) comparison of signal spectrum after the Doppler-warping transform with v = 5 m/s and the spectrum of the original signal. SNR = –10 dB.

图 6  (a)目标船运动轨迹; (b)水体声速剖面

Fig. 6.  (a) Track of the target ship; (b) sound speed profile.

图 7  海试数据分析　(a)时频图; (b)瞬时频率理论值和估计值; (c) MMSE计速度的结果; (d) Doppler-warping变换估计速度的结果

Fig. 7.  Analysis of the sea trial data: (a) Time-frequency distribution; (b) theoretical and estimated instantaneous frequency; (c) result of velocity estimation by MMSE; (d) result of velocity estimation by the Doppler-warping transform.