Estimation of Underwater Acoustic Doppler Factor and time Delay based on time-frequency Analysis of multi-component LFM Signals
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摘要: 在水声多普勒因子和时延估计研究实用化的进程中，利用多分量线性调频(LFM)信号实现估计的算法研究越来越普遍。针对多分量LFM信号时频域存有交叉项时各分量参数估计不准确的问题，提出基于非完全残差与脊线段匹配的自适应模态分解方法。该方法采用非完全残差函数保留了交叉点处的部分时频信息，利用脊线段匹配方法提供更精确的预设时频脊线，改进了各分量LFM信号调频斜率和起始频率的估计精度。联合两个估计量进一步给出了多普勒因子和时延估计的算法。仿真结果表示，较现有模态分解算法，所提改进方法有效解决了估计分量过程中交叉区间断裂带来的估计误差；水声多径的条件下，该方法的多普勒因子和时延估计精度优于对比的现有方法。Abstract: The use of the multicomponent Linear Frequency Modulated (LFM) signals for estimating the underwater acoustic Doppler factor and time delay estimation is increasingly common in the practical process. An adaptive chirp-mode-decomposition algorithm based on incomplete residual and ridge segment matching is proposed to solve the problem of inaccurate parameter estimation for multicomponent LFM with cross-terms in the time–frequency domain. The incomplete residual function is used to retain part of the time-frequency information at the intersection point, and the ridge segment matching method is used to provide a more accurate time-frequency ridge, improving the estimation accuracy of the frequency modulation slope and starting frequency of each component of LFM signal. A combination of these two estimators provides the algorithm for estimating the Doppler factor and time delay. The results showed the proposed method effectively solves the estimation error induced by the break of cross-interval, compared with the existing mode-decomposition algorithms. The accuracy of the proposed method for estimating the Doppler factor and time delay is better than that of the existing methods in underwater acoustic multipath propagation.
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表 1 IRSM-ACMD时频方法步骤
步骤1：获取一个预分量。提取第1个分量时将X(t)赋值给非完全残差IR(t)，提取第m个分量时依式(5)获取非完全残差IR(t)，对IR(t)进行
STFT得到时频分布TF(t,f)，基于最大能量片段的寻找，利用式(12)—式(14)进行片段匹配后从TF(t,f)中获得其中1个分量的初始瞬时频率
即预分量。步骤2：模态分解。根据预分量及非完全残差IR(t)，利用式(3)—式(4)估计出一个分量$\tilde{x}_{{w} }(t)$和它的瞬时频率$ {\tilde{F}}_{m}\left(t\right) $、瞬时幅度$ {\tilde{A}}_{m}\left(t\right) $。
并用最小二乘法拟合瞬时频率值，按式(8)更新IR(t)。步骤3：判断与循环。由式(6)判断所估计时频脊线是否重复，不重复的估计按式(7)更新到IRth(t)中，否则返回步骤1。由式(9)计算已提取
分量信号的总能量，随后由式(10)判断估计是否结束，未结束返回步骤1继续估计，若结束则由式(11)获得分量估计的自适应时频谱。
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表 2 发送信号为单分量LFM信号时多径信道对应的时延和多普勒因子仿真参数
路径 时延(s) 多普勒因子 路径1(L1) 0.4562 –0.0898 路径2(L2) 0.123 0.028 路径3(L3) 3.6656 0.0898
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表 3 发送信号为时频域有交叉多分量LFM信号时的仿真参数
仿真参数 分量1 分量2 分量3 调频斜率(kHz/s) 1.17 3.7 1.7 起始频率(kHz) 40 35 45 截止频率(kHz) 47 57 55 多普勒因子 0.025 0.035 0.045 时延(s) 1.216 2 0.902 6 1.465 6
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表 4 低频段时频域有交叉多分量LFM信号的仿真参数
仿真参数 分量1 分量2 分量3 调频斜率(Hz/s) 800 –700 1200 起始频率(Hz) 1700 1400 800 截止频率(Hz) 2500 700 2000 多普勒因子 0.0025 0.0035 0.0045 时延(s) 0.514 3 0.543 2 0.516 6
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