微多普勒瞬时频率估计算法对噪声的适应性能研究

微多普勒特征提取的关键在于瞬时频率的计算,峰值检测法和一阶时间条件矩法是基于高分辨时频分布的两种瞬时频率估计算法.本文对两种瞬时频率估计算法对噪声的适应性能进行了理论分析和仿真计算,结果表明,当信号受噪声污染后,在一定的信噪比条件下,峰值检测法瞬时频率估计算法对能量分布的变化不敏感,但一阶时间条件矩法瞬时频率估计算法对时频域能量分布十分敏感,因此,峰值检测法较一阶时间条件矩法对噪声具有鲁棒性.实际中雷达接收到的信号都是受噪声污染的,分析两种算法对噪声的适应性能对工程实际应用具有重要参考价值.     

一种基于互局部化Wigner-Ville分布的瞬时频率估计

本文提出一种基于互局部化Wigner-Ville分布(Cross Localized Wigner-Ville Distribution,X-LWVD)的迭代瞬时频率估计方法,以解析方法分析了无噪声情况下该方法的收敛性,用计算机仿真方法比较了在噪声背景中其与谱图(Spectrogram)峰值检测、Wigner-Ville分布(Wigner-Ville Distribution,WVD)峰值检测的性能,证明了该方法是一种统计有效的瞬时频率估计方法。     

基于自项窗的WVD交叉项抑制技术

为了解决维格纳-维利分布(WVD)的交叉项干扰问题,提出一种覆盖自项支撑区的时频窗——自项窗,通过对信号的WVD进行加窗处理,得到改进的时频分布。首先分析了多分量信号WVD中自项和交叉项的不同特点,接着论述了自项窗法的原理及自项窗的构造方法,分析了改进的时频分布的性质,最后进行了仿真验证。结果表明,自项窗法能够有效消除WVD中的交叉项,并保留WVD良好的时频分辨率和能量聚集性,适合于非平稳信号的时频分析。     

基于频率模型和时频分析的正弦信号频率高精度估计算法

利用时频分析方法估计信号瞬时频率,在低信噪比条件下估计性能较差,但在时频图中,信号频率的变化趋势具有一定的规律,基本上都是围绕着信号的真实频率。基于此,给出了一种结合时频分析和信号频率模型相结合的方法,以实现信号瞬时频率的高精度估计。利用时频分析具有的良好时频分布的特点,采用最大能量方法（ME）预先估计得到信号的预估计瞬时频率（EIF）;再利用瞬时频率连续性、平滑性的先验信息,建立了信号瞬时频率估计模型,并采用概率最大原理(MP)估计瞬时频率概率最大的统计变化,估计得到预估计瞬时频率的滤波起始点;最后利用卡尔曼滤波和平滑算法对预估计瞬时频率进行滤波和平滑,从而得到信号频率的精确估计。      

瞬时频率和时频分布

本文首先介绍了瞬时频率(IF)的概念和IF的传统计算方法解析信号法,然后从联合时频分析的角度讨论了IF的物理含义及其与时频分布之间的联系,指出二维时频分布的任务之一是对IF进行估计,并且通过对几种时频分布估计性能的比较说明分布形式的选择对估计效果有较大影响。最后,本文提出并初步论证了自适应旋转投影分解法(AOP)计算IF的有效性。     

一种基于时频分布的跳频信号检测方法的研究

对于混杂着噪声的跳频信号,将其进行频率调制(FM)得到其解析信号,再对解析信号应用基于WVD的峰值检测算法,可以有效地恢复原始信号。对于包含高斯白噪声的信号,在信噪比较低的情况下,提出了迭代进行峰值检测的估计方法,仿真结果表明该迭代算法在较低的信噪比情况下也可以得到理想的结果。     

一种多分量跳频信号参数盲估计方法

首先提出了将谱图与平滑伪Wigner-Ville分布(SPWVD)组合,利用谱图的无交叉项和SPWVD的时频聚焦性能,得到了一种清晰稳健的时频分布;然后基于此分布运用二维二次差分峰值检测方法检测出该时频图的峰值,并利用求平面重心的方法修正峰值,得到正确的峰值位置;将峰值分别在频率轴上和时间轴投影,即可得到信号载频的估计值和每跳的中心时刻(CT,central time);最后采用逐次CT差值直方图法得到跳周期(HD,hop duration)的估计,并根据估计出的跳周期值和每跳的CT值得到跳时(hop timing)估计.     

应用WVD估计AM-FM信号的瞬时频率

该文研究了应用WVD谱峰检测估计AM-FM信号的瞬时频率的方法及其性能。理论分析表明;对线性调频的AM-FM信号,只要其幅度的WVD在频率为零处取得最大值在任意时刻都成立,则基于WVD谱峰检测得到的瞬时频率估计是无偏的,并给出了估计的方差。仿真实验使用高斯包络的线性调频信号表明,利用WVD可以有效地估计AM-FM信号的瞬时频率。     

基于条件对抗生成时频分布的多分量信号瞬时频率估计

瞬时频率（Instantaneous Frequency,IF）估计在多分量信号处理中具有重要意义,而现有方法在信号分量的IF曲线相近或相交时估计准确度不佳。针对这一问题,本文提出一种基于条件对抗生成时频分布的多分量信号IF估计方法。该方法首先采用时频分析产生信号的时频图像（例如掩膜维格纳分布）作为条件生成对抗网络（Conditional Generative Adversarial Networks, CGAN）的原始数据集,通过训练CGAN进行学习之后生成接近理想时频分布的时频图像。根据这些图像,本文利用一种改进的维特比算法提取出不同分量的IF曲线。其改进点在于增加了一个线段梯度的惩罚项,使维特比算法在分量相交的时频区域仍有准确的IF估计。实验结果表明,该方法能够有效且准确地估计分量相近或相交情况下信号的IF信息。      

STTFD的特性分析及其在线性调频信号 参数估计中的应用

 精确地估计线性调频(LFM)信号的中心频率和调频率值,在雷达信号处理中有着十分重要的作用.WVD变换具有估计线性调频信号的中心频率和调频率特性,但当存在多个线性调频分量时,交叉项会严重影响线性调频信号中心频率和调频率的估计.针对这一问题,本文提出了基于STTFD(时频分布尺度变换)的线性调频信号参数估计的方法,即在时频平面内对信号进行尺度变换,去除信号瞬时时间和相关函数延迟量的耦合,使线性调频信号的频率随时间变化呈线性分布变为不随时间变化的常数分布,再通过在时频平面内沿时间轴做FFT积累所得到的信号峰值位置来估计信号的中心频率和调频率参数值,并且对STFD的特性以及相关函数延迟量和尺度变换常数对STTFD的影响进行了详细的分析.在本文最后,通过仿真数据验证了STTFD的特性及其精确估计线性调频信号参数的有效性.     

Signal enhancement by time-frequency peak filtering

Time-frequency peak filtering (TFPF) allows the reconstruction of signals from observations corrupted by additive noise by encoding the noisy signal as the instantaneous frequency (IF) of a frequency modulated (FM) analytic signal. IF estimation is then performed on the analytic signal using the peak of a time-frequency distribution (TFD) to recover the filtered signal. This method is biased when the peak of the Wigner-Ville distribution (WVD) is used to estimate the encoded signal's instantaneous frequency. We characterize a class of signals for which the method implemented using the pseudo WVD is approximately unbiased. This class contains deterministic bandlimited nonstationary multicomponent signals in additive white Gaussian noise (WGN). We then derive the pseudo WVD window length that gives a reduced bias when TFPF is used for signals from this class. Testing of the method on both synthetic and real life newborn electroencephalogram (EEG) signals shows clean recovery of the signals in noise level down to a signal-to-noise ratio (SNR) of -9 dB.     

Adaptive instantaneous frequency estimation of multicomponent FMsignals using quadratic time-frequency distributions

An adaptive approach to the estimation of the instantaneous frequency (IF) of nonstationary mono- and multicomponent FM signals with additive Gaussian noise is presented. The IF estimation is based on the fact that quadratic time-frequency distributions (TFDs) have maxima around the IF law of the signal. It is shown that the bias and variance of the IF estimate are functions of the lag window length. If there is a bias-variance tradeoff, then the optimal window length for this tradeoff depends on the unknown IF law. Hence, an adaptive algorithm with a time-varying and data-driven window length is needed. The adaptive algorithm can utilize any quadratic TFD that satisfies the following three conditions: First, the IF estimation variance given by the chosen distribution should be a continuously decreasing function of the window length, whereas the bias should be continuously increasing so that the algorithm will converge at the optimal window length for the bias-variance tradeoff, second, the time-lag kernel filter of the chosen distribution should not perform narrowband filtering in the lag direction in order to not interfere with the adaptive window in that direction; third, the distribution should perform effective cross-terms reduction while keeping high resolution in order to be efficient for multicomponent signals. A quadratic distribution with high resolution, effective cross-terms reduction and no lag filtering is proposed. The algorithm estimates multiple IF laws by using a tracking algorithm for the signal components and utilizing the property that the proposed distribution enables nonparametric component amplitude estimation. An extension of the proposed TFD consisting of the use of time-only kernels for adaptive IF estimation is also proposed     

基于Radon-Ambiguity变换的LFM信号时/频差快速联合估计

提出了一种基于Radon-Ambiguity变换(Radon-Ambiguity Transform, RAT)的线性调频(Linear Frequency Modulated, LFM)信号时/频差快速联合估计的算法.根据LFM信号在多个不同角度上的RAT峰值位置建立一组以信号间时差和频差为未知量的方程组,求解方程组即可得到时/频差的估计值.对于存在噪声的信号,RAT误差会导致方程组不能直接求解,为了抑制噪声干扰,采用最小二乘法估计时/频差.本文算法无需计算二维平面上各点的模糊函数值,并且由于离散RAT可以通过快速傅里叶变换快速实现,具有所需运算量低的优点.仿真实验表明,相比于常见的基于模糊函数峰值搜索的时/频差估计算法,本文算法在保证时/频差估计精度的同时能够显著提高运算效率.     

Alpha稳定分布噪声下时频重叠信号的载波频率估计方法

针对Alpha稳定噪声下时频重叠信号载波频率估计困难的问题,该文提出一种Alpha稳定噪声下时频重叠信号的载波频率估计方法。该方法首先提出时频重叠信号的广义四阶循环累积量的定义,然后检测离散谱线所对应的广义四阶循环累积量幅度谱的循环频率,进而估计出各个信号分量的载波频率,最后进行渐近性的理论分析,证明了该估计方法是渐近无偏和一致的。仿真结果表明,在Alpha稳定分布噪声下,该方法具有良好的估计性能和稳健性。     

采用Radon-Wigner变换的二维波达方向估计

针对宽带多线性调频信号2维波达方向(2-D DOA)估计精度低的问题,该文提出了一种基于Radon-Wigner变换(RWT)的2-D DOA估计方法。该方法利用RWT在多目标环境下能够有效抑制交叉项干扰和噪声,具有很好的时频汇聚性特点,通过峰值搜索确定目标个数并重构信号阵列,最后利用MUSIC空间谱分析方法实现了对多个LFM信号的2-D DOA估计。仿真实验表明,基于RWT的DOA估计方法能对非平稳信号进行有效的2-D DOA估计。     

Carrier frequency estimation method of time-frequency overlapped signals based on cyclic correntropy spectrum

According to the performance degradation problem of the carrier frequency estimation method of time-frequency overlapped BPSK signals in Alpha-stable distribution noise,a novel carrier frequency estimation algorithm of the time-frequency overlapped BPSK signals based on the cyclic correntropy spectrum was proposed.The relationship between cyclic frequency and carrier frequency on the zero frequency section of the cyclic correntropy spectrum was deduced,which could be utilized for carrier frequency estimation.The proposed method can suppress the impulse noise and has better estimation performance than that of the contrastive methods.Simulation results are presented to demonstrate the effectiveness and robustness of the proposed method.     

Robust Wigner distribution with application to the instantaneousfrequency estimation

The Wigner distribution (WD) produces highly concentrated time-frequency (TF) representation of nonstationary signals. It may be used as an efficient signal analysis tool, including the cases of frequency modulated signals corrupted with the Gaussian noise. In some applications, a significant amount of impulse noise is present. Then, the WD fails to produce satisfactory results. The robust periodogram has been introduced for spectral estimation of this kind of noisy signals. It can produce good concentration for pure harmonic signals. However, it is not so efficient in the cases of signals with rapidly varying frequency. This is the motivation for introducing the robust WD. It is a reliable TF representation tool for wide class of nonstationary signals corrupted with impulse noise. This distribution produces good accuracy of the instantaneous frequency (IF) estimation. Using the Huber (1981) loss function, a generalization of the WD is presented. It includes both the standard and the robust WD as special cases. This distribution can be used for TF analysis of signals corrupted with a mixture of impulse and Gaussian noise. The presented theory is illustrated on examples, including applications on the IF estimation and time-varying filtering of signals corrupted with a mixture of the Gaussian and impulse noise. The case study analysis of the IF estimators' accuracy, based on the standard and the robust WD forms, is performed. In order to improve the IF estimation, a median filter is applied on the obtained IF estimate     

Instantaneous frequency estimation of nonlinear frequency-modulatedsignals in the presence of multiplicative and additive noise

This paper addresses the problem of estimating the instantaneous frequency (IF) of monocomponent nonlinear, not necessarily polynomial, frequency modulated (FM) signals affected by stationary multiplicative and additive noise. Both noise processes are assumed to be complex circular Gaussian and independent. The peak of the polynomial Wigner-Ville distribution (PWVD) is proposed here as an IF estimator. We derive analytical expressions for the bias and asymptotic variance of the estimator and propose an algorithm to select the optimal window length to resolve the bias-variance tradeoff in the IF estimation. Simulation results are presented to confirm the theoretical results