﻿ 基于CEEMD-MI的目标回波参数估计
 舰船科学技术  2023, Vol. 45 Issue (22): 155-159    DOI: 10.3404/j.issn.1672-7649.2023.22.029 PDF

Target echo parameter estimation based on CEEMD-MI
LIU Qian, LI Mei
Shanghai Marine Electronic Equipment Research Institute, Shanghai 201108, China
Abstract: Aiming at the degradation of estimating the parameters of target echo under low signal to noise ratio, a target echo parameter estimation algorithm based on complementary ensemble empirical mode decomposition-mutual information（CEEMD-MI） is proposed. Complementary ensemble empirical mode decomposition（CEEMD） is used to adaptively decompose the target echo under low signal to noise ratio, select the intrinsic mode function which contains signal component via MI to reconstruct the signal, then estimate the parameters of the reconstructed signal. The processing results of simulation and experiment data show that, using the proposed method, the estimation error of center frequency and initial phase can be less than 0.2% and 2.5%.
Key words: CEEMD     MI     signal reconstruction     parameter estimation
0 引　言

1 基于CEEMD-MI的目标回波参数估计 1.1 算法流程

1.2 基于CEEMD-MI的目标回波去噪 1.2.1 CEEMD算法

 $\left[ \begin{gathered} x_i^ + (t) \\ x_i^ - (t) \\ \end{gathered} \right] = \left[ {\begin{array}{*{20}{c}} 1&{ 1} \\ 1&{ - 1} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {x(t)} \\ {{u_i}(t)} \end{array}} \right] \text{，} i = 1,2,...,N ，$ (1)

 $\left[ \begin{gathered} x_i^ + (t) \\ x_i^ - (t) \\ \end{gathered} \right] = \left[ \begin{gathered} x(t) + {u_i}(t) \\ x(t) - {u_i}(t) \\ \end{gathered} \right] \text{，} i = 1,2,...,N 。$ (2)

 $h_i^ + (t) = x_i^ + (t) - m_i^ + (t)，$ (3)
 $h_i^ - (t) = x_i^ - (t) - m_i^ - (t) 。$ (4)

 $h_{i1}^ + (t) = h_i^ + (t) - m_{i1}^ + (t) ，$ (5)
 $h_{i1}^ - (t) = h_i^ - (t) - m_{i1}^ - (t) 。$ (6)

 $h_{ik}^ + (t) = h_{i（k - 1）}^ + (t) - m_{ik}^ + (t) ，$ (7)
 $h_{ik}^ - (t) = h_{i（k - 1）}^ - (t) - m_{ik}^ - (t)。$ (8)

 $c_{i1}^ + (t) = h_{ik}^ + (t) ，$ (9)
 $c_{i1}^ - (t) = h_{ik}^ - (t) 。$ (10)

$c_{i1}^ + (t)$ $c_{i1}^ - (t)$ 分别是 $x_i^ + (t)$ $x_i^ - (t)$ 筛选出的第一个IMF分量。

 $r_{i1}^ + (t) = x_i^ + (t) - c_{i1}^ + (t)，$ (11)
 $r_{i1}^ - (t) = x_i^ - (t) - c_{i1}^ - (t) 。$ (12)

$r_{i1}^ + (t)$ $r_{i1}^ - (t)$ 分别视为信号 $x_i^ + (t)$ $x_i^ - (t)$ ，重复步骤1~步骤3，可得：

 $\begin{split} & r_{i2}^ + (t) = r_{i1}^ + (t) - c_{i2}^ + (t)，\\ & r_{i2}^ - (t) = r_{i1}^ - (t) - c_{i2}^ - (t) ，\\ &\vdots \\ & r_{im}^ + (t) = r_{i（m - 1）}^ + (t) - c_{im}^ + (t)，\\ & r_{im}^ - (t) = r_{i（m - 1）}^ - (t) - c_{im}^ - (t)。\end{split}$ (13)

 $x_i^ + (t) = \sum\limits_{k = 1}^m {c_{ik}^ + (t) + } r_{im}^ + (t) ，$ (14)
 $x_i^ - (t) = \sum\limits_{k = 1}^m {c_{ik}^ - (t) + } r_{im}^ - (t)，$ (15)

$x_i^ + (t)$ $x_i^ - (t)$ 的第k个IMF分量求平均可得：

 $IM{F_{ik}} = {{[c_{ik}^ + (t) + c_{ik}^ - (t)]} \mathord{\left/ {\vphantom {{[c_{ik}^ + (t) + c_{ik}^ - (t)]} 2}} \right. } 2}，$ (16)

 $IM{F_k} = {{\sum\limits_{i = 1}^N {IM{F_{ik}}} }/ N}。$ (17)

1.2.2 互信息

 $I（X;Y） = \sum\limits_{x \in X} {\sum\limits_{y \in Y} {p(x,y)} } \log \left(\frac{{p(x,y)}}{{p(x)p()y}}\right)。$ (18)

1.3 目标回波信号参数估计

 ${y_R}(t) = {x_R}(t) \cdot \frac{1}{{\text{π} t}}。$ (19)

 ${z_R}(t) = {x_R}(t) + j{y_R}(t) = {a_R}(t){e^{j{\varphi _R}(t)}} 。$ (20)

2 仿真分析 2.1 降噪性能分析

 图 1 去噪前信号 Fig. 1 Signal before denoising

$x(t)$ 进行CEEMD分解，得到的各个固有模态函数的时域波形及频谱如图2所示。

 图 2 固有模态函数 Fig. 2 Intrinsic mode function

 图 3 各个固有模态函数分量与原信号互信息 Fig. 3 Mutual information of IMFs and original signal

 图 4 重构信号（CEEMD-MI去噪处理） Fig. 4 Reconstructed signal（CEEMD denoising）

2.2 不同信噪比下参数估计性能分析

 图 5 估计信号与原信号差值 Fig. 5 Difference between estimated signal and original signal
3 试验数据验证

 图 6 水听器接收信号 Fig. 6 Hydrophone receive signal

 图 7 估计信号与目标回波差值 Fig. 7 Difference between estimated signal and target echo
4 结　语

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