﻿ 基于经验小波变换的目标加速度估计算法
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Estimation of target's acceleration based on empirical wavelet transform
CHEN Hao, GUO Junhai ,Qi Wei
Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China
Abstract:Target's accelerations lead to spectrum shift and broadening of target's echo signal, resulting in the inaccuracy estimation of target's Doppler frequency with traditional pulse radar velocity measurement method. To overcome the effect of acceleration on pulse radar velocity measurement, an empirical wavelet transform (EWT) based radial acceleration estimation method was proposed. The instantaneous frequency of the echo signal can be extracted through EWT and energy-oriented principal frequency components extraction method. The high order coefficients of the phase were obtained through robust least square fitting on the instantaneous frequency, which correspond to the radial velocity and radial acceleration respectively. After compensating the echo signal with estimated accelerations, the Doppler frequency of echo signal can be accurately estimated. Simulations show that the EWT method is a fast algorithm with high estimation accuracy, and the estimation error is close to Cramer-Rao lower bound. Applying EWT method on measured pulse radar data of high speed vehicle, the estimated acceleration error is smaller than 0.4 m/s2. EWT method is applicable in real time pulse radar acceleration estimation.
Key words: radial acceleration     non-stationary signal     empirical wavelet transform     instantaneous frequency     frequency extraction

1 经验小波变换

 图 1 Foureier坐标系的分割 Fig. 1 Partitioning of the Fourier axis

2 基于EWT速度与加速度估计方法 2.1 问题分析

2.2 频率主成分提取

X(t)作EWT变换得到不同的经验模式Xk(t),即X(t)=∑kXk(t).对Xk(t)作Hilbert变换,可得

2.3 基于EWT的参数估计性能分析

EWT方法是一种小波分析算法,利用Mallat算法[17]可实现快速计算.而传统的FRFT方法是二维搜索算法,其计算量远大于EWT算法,导致数据处理速度较慢.因此,EWT算法比FRFT算法更适用于实时数据处理.

3 仿真与分析 3.1 理论数据仿真

 图 2 利用经验小波变换(EWT)算法得到的 经验模式和瞬时频率 Fig. 2 Estimated intrinsic mode functions (IMF) and instantaneous frequency (IF) using empirical wavelet transform (EWT) method

 图 3 一次相位系数f0估计误差 Fig. 3 Estimating error of coefficient f0

 图 4 二次相位系数k估计误差 Fig. 4 Estimating error of coefficient k

 图 5 具有三阶相位系数信号的瞬时频率 Fig. 5 Estimated instantaneous frequency (IF) of signal with the third order phase coefficients

 图 6 三阶相位系数估计误差 Fig. 6 Estimating error of the third order phase coefficient
3.2 实测数据仿真

 图 7 加速度补偿后的速度误差 Fig. 7 Velocity error after acceleration compensation

 图 8 实测数据加速度误差 Fig. 8 Estimated acceleration error of measured data
4 结 论

1) 仿真表明该算法在不同的信噪比条件下均能以较高的精度估计信号的参数,估计精度高于传统FRFT算法和EEMD算法,且估计误差逼近于C-R下界;

2) 计算速度要远远快于传统算法;

3) 脉冲雷达实测I/Q数据表明,该算法估计的加速度误差小于0.4m/s2,加速度的补偿后估计的速度误差小于0.05m/s.

 [1] 袁斌,陈曾平,徐世友,等.基于距离单元筛选快速最小熵的含旋转部件目标相位补偿方法[J].电子与信息学报,2013,35(5):1128-1134.Yuan B,Chen Z P,Xu S Y,et al.Phase compensation for targets with rotating parts based on range bins selection in fast minimum entropy[J].Journal of Electronics & Information Technology,2013,35(5):1128-1134(in Chinese). Cited By in Cnki [2] 夏猛,杨小牛.基于三次相位补偿的运动目标参数估计[J].电子科技大学学报,2013,42(4):559-564.Xia M,Yang X N.Parameter estimation for moving target based on three-phase compensation[J].Journal of University of Electronic Science and Technology of China,2013,42(4):559-564(in Chinese). Cited By in Cnki [3] Cao S,Bing P,Lu J,et al.Seismic data time-frequency analysis by the improved Hilbert-Huang transform[J].Oil Geophysical Prospecting,2013,48(2):246-254. [4] Wang Z Z,Liu F,Huang Y,et al.Digitized periodic wigner-hough transform and its performance analysis[J].Telecommunications Engineering,2012,52(9):1452-1458. [5] 欧国建,陈玲珑,何俞璟.一种多分量LFM信号参数估计的快速仿真算法[J].重庆邮电大学学报:自然科学版,2013,25(4):459-463.Ou G J,Chen L L,He Y J.A simulation fast algorithm for parameters estimationof the multicomponent LFM signals[J].Journal of Chongqing University of Posts and Telecommunications,2013,25(4):459-463(in Chinese). Cited By in Cnki [6] Yu Y.Detection and parameter estimation of linear frequency modulated signals based on radon transform[J].Journal of Modern Defence Technology,2013,41(1):136-141. [7] Zhu Y W,Zhao Y J,Jia W G.Fast parameter estimation method for LFM signal based on ambiguity function slice and FrFT[J].Journal of Information Engineering University,2012,13(2):218-223. [8] Mohindru P,Khanna R K R,Bhatia S S.Analysis of chirp signal with fractional Fourier transform[J].Majlesi Journal of Multimedia Processing,2013,2(1):314-322. [9] Dinç E,Duarte F B,Machado J A T,et al.Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture[J].Signal,Image and Video Processing,2013,21(10):1-7. Click to display the text [10] Huang N E.The empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysis[J].Proceedings of Royal Society of London,1998,A4(54):903-995. Click to display the text [11] Flandrin P,Rilling G,Goncalves P.Empirical mode decomposition as a filter bank[J].Signal Processing Letters,IEEE,2004,11(2):112-114. Click to display the text [12] 崔华.一种新的线性调频信号的瞬时频率估计方法[J].计算机应用研究,2008,25(8):2532-2533.Cui H.New method for instantaneous frequency estimations of LFM signals[J].Application Research of Computers,2008,25(8):2532-2533(in Chinese). Cited By in Cnki (8) [13] 王燕,邹男,付进,等.基于局部瞬时能量密度级的瞬态信号检测方法[J].电子与信息学报,2013,35(7):1720-1724.Wang Y,Zou N,Fu J,et al.Transient signal detection method based on partial instantaneous energy density level[J].Journal of Electronics & Information Technology,2013,35(7):1720-1724(in Chinese). Cited By in Cnki (4) [14] Wu Z H,Huang N E.Ensemble empirical mode decomposition:a noise assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41. Click to display the text [15] Gilles J.Empirical wavelet transform[J].IEEE Transactions in Signal Processing,2013,61(16):3999-4010. Click to display the text [16] Steven M K.Fundamentals of statistical signal processing, Volume I:estimation theory[M].Beijing:Publishing House of Electronics Industry,2006:25-39. [17] 成礼智.小波的理论与应用[M].北京:科学出版社,2009:75-88.Cheng L Z.Theories and applications of wavelet[M].Beijing:Science Press,2009:75-88(in Chinese)

#### 文章信息

CHEN Hao, GUO Junhai

Estimation of target's acceleration based on empirical wavelet transform

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 154-159.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0036