改进复调制的频率校正算法研究
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摘要
为实现雷达信号处理中频率的精确估计,减少快速傅里叶变换分析频谱时由于栅栏效应和频谱泄漏产生的测量误差,满足高精度频率测量要求,提出了一种利用复调制算法和牛顿插值的频率校正方法。待测频谱经复调制算法细化后,通过牛顿插值函数将离散频谱变为连续谱,利用最大峰值对应的采样点及其相邻采样点的插值函数关系对频率进行校正,减少了细化倍数对复调制算法的影响,提高了频率测量精度。通过列举三点校正和四点校正两种情形,说明不同采样点在不同条件下对频率校正精度的影响及各自的均方根误差。仿真结果表明,所提方法在频率估计方面具有很好的效果,与复调制算法相比,频率的测量误差减少了30%。
In order to achieve accurate frequency estimation in radar signal processing and reduce the measurement error caused by fence effect and spectrum leakage in fast Fourier transform(FFT) spectrum analysis,a frequency correction method based on multiple modulation algorithm and Newton interpolation is proposed. After the spectrum being measuring is refined by multiple modulation algorithm,the discrete spectrum is transformed into continuous spectrum by Newton interpolation function,and the frequency is corrected by the interpolation function relationship between the sampling points corresponding to the maximum peak value and the adjacent sampling points,which reduces the influence of the refinement factor on the multiple modulation algorithm and improves the accuracy of frequency measurement. By enumerating three-point correction and four-point correction,the influence of different sampling points on frequency correction accuracy under different conditions and the magnitude of root mean square error are described. The simulation results show that the proposed method has good effect in frequency estimation. Comparing with the multiple modulation algorithm,the frequency measurement error is reduced by 30%.
In order to achieve accurate frequency estimation in radar signal processing and reduce the measurement error caused by fence effect and spectrum leakage in fast Fourier transform(FFT) spectrum analysis,a frequency correction method based on multiple modulation algorithm and Newton interpolation is proposed. After the spectrum being measuring is refined by multiple modulation algorithm,the discrete spectrum is transformed into continuous spectrum by Newton interpolation function,and the frequency is corrected by the interpolation function relationship between the sampling points corresponding to the maximum peak value and the adjacent sampling points,which reduces the influence of the refinement factor on the multiple modulation algorithm and improves the accuracy of frequency measurement. By enumerating three-point correction and four-point correction,the influence of different sampling points on frequency correction accuracy under different conditions and the magnitude of root mean square error are described. The simulation results show that the proposed method has good effect in frequency estimation. Comparing with the multiple modulation algorithm,the frequency measurement error is reduced by 30%.
引文
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[3]侯盼卫,杨录,岳文豹.应用FFT的高精度FMCW雷达频率测量算法[J].自动化仪表,2014,35(3):17-19.
[4]ANDERSSON F,CARLSSON M.Fixed-point algorithms for frequency estimation and structured low rank approximation[J]Applied&Computational Harmonic Analysis,2017(1):1-22.
[5]MAMANDIPOOR B,RAMASAMY D,MADHOW U.Frequency estimation for a mixture of sinusoids:A near-optimalsequential approach[C]//IEEE Global Conference on Signal and Information Processing.IEEE,2016:205-209.
[6]DIAO R,MENG Q.An interpolation algorithm for discrete Fourier transforms of weighted damped sinusoidal signals[J].IEEETransaction Instrument Measurement,2014,63(6):1503-1515.
[7]顿丛丛,李跃华,王剑桥.基于频谱细化的窗谱拟合算法[J].探测与控制学报,2011,33(6):6-11.
[8]AIQUDSI B,JORAM N,STROBEL A,et al.Zoom FFT for precise spectrum calculation in FMCW radar using FPGA[J].Information Technology,2013:337-340.
[9]WANG X,QIN Y,QIAN W,et al.Afamily of Newton type iterative methods for solving nonlinear equations[J].Algorithm,2015,8(3):786-798.
[10]RIFE D,BOORSTY N.Single tone parameter estimation from discrete-time observations[J].IEEE Transaction on Information Theory,1974,20(3):591-598.