基于分形盒维数的线性调频信号参数估计

针对当前线性调频（linear frequency modulation, LFM）信号参数估计算法中对调频斜率的估计复杂度高、实时性差且信噪比适应范围较小等缺点，提出了基于分形盒维数的LFM信号调频斜率估计方法。该方法通过计算信号调频斜率与盒维数的关系曲线，利用盒维数对LFM信号的调频斜率进行估计，探讨了信号的幅度和相位对信号盒维数的影响，计算了不同信噪比下的估计误差，并与传统的基于匹配傅里叶变换（matching Fourier transform， MFT）的LFM信号参数估计算法进行了对比仿真，绘制了脉冲宽度、调频带宽与盒维数三者的关系曲线图。仿真结果表明，该算法在建立了对应关系数据库后，在信噪比变化范围比较大的情况下的估计误差仍然比较小，且算法简单，对于实时性估计具有很好的应用价值。

Parameter estimation of LFM signals based on fractal box dimension

Many parameter estimation algorithms have been proposed for frequency modulation(FM) slope of linear frequency modulation(LFM) signals,in which,however,there are some issues such as high complexity,bad real-time and a small adaptive range of the signal to noise ratio(SNR).An improved algorithm based on fractal box dimension is proposed,which uses box-counting dimension to estimate the FM slope of LFM signals through calculating the relationship curves of FM slope and box-counting dimension.The influence of the amplitude and phase of the signal to the box-counting dimension is discussed and the estimation errors under different SNRs is calculated,and the curves relationship of the pulse width,FM bandwidth and box-counting dimension is drawn to compare with the traditional parameter estimation algorithm based on matching Fourier transform.Simulation results show that,after establishing the corresponding relation database,the estimation errors are comparatively small under the larger variation scope of SNR,and the algorithm is simple.It owns good application value for real-time estimation.