基于局部相位多项式逼近的脉内无意调频估计

Instantaneous Frequency Estimation Based on Local Polynomial Approximation of Phase

针对电子侦察中所遇到的脉内无意调频(Unintentional Frequency Modulation on Pulse,UFMOP)估计问题,提出了一种基于相位局部多项式逼近(Local Polynomial Approximation of Phase,LPAP)的瞬时频率估计方法。该方法利用时间窗,通过对窗内信号的相位进行局部多项式逼近来估计该窗中心时刻的瞬时频率。为确保LPAP法的有效性,所确定的时间窗长度须尽可能实现估计偏差和方差的折中。本文在比较分析置信区间交集(Intersectionof Confidence Intervals,ICI)与范-吉布斯带宽选择(Fan and Gijbels’s Bandwidth Selection,FGBS)两种经典窗长选择算法的基础上,选择更适于无意调频估计的FGBS算法用于LPAP法进行自适应窗长选择。仿真与实测数据分析实验表明本文方法对脉内无意调频的估计性能优于其他算法,同时也验证了有关窗长选择算法的分析结论。

The problem of estimating unintentional frequency modulation on pulse （UFMOP） which is frequently con- fronted in electronic ce is considered. A new instantaneous frequency method based on local polynomial approx- imation of phase （LPAP） is proposed. This method utilizes a sliding time window and estimates the instantaneous frequency of the central time of the analysis window, through approximating the phases of signal samples within the window locally. The approximation process is realized by using polynomial function. To ensure the efficiency of the proposed method, the se- lected window length should enable a bias-variance tradeoff as good as possible. In this paper, we compare the classical in- tersection of confidence intervals （ICI） and the Fan and Gijbels＇ s bandwidth selection （FGBS） window length selection al- gorithms. Based on the comparison, we recommend adopting the FGBS, which is found to be more suitable for UFMOP esti- mation, to select the window length adaptively for the LPAP. Simulations and real data analysis show that our method out- performs other commonly used instantaneous frequency estimation methods, and verify the conclusion derived from the com- parison of window-length-selection algorithms.