归一化频率自适应梳状滤波器的稳定性分析

采用多个归一化频率估计器并联形成梳状滤波器, 以跟踪和检测平稳概周期信号各正弦成分的未知频率和未知幅值. 滤波器包括相互耦合的状态估计和频率估计两个非线性微分方程. 运用慢积分流形实现两个微分方程之间的解耦, 获得关于多个频率估计值的概周期非线性动力系统, 再应用平均方法导出估计频率的非线性自治方程. 分析了自治系统的三种局部稳定性: 孤立平衡点的指数稳定性, 中心流形存在性与半稳定性以及结构扰动下的有界性. 说明幅值估计与信号跟随的收敛性和有界性. 给出滤波器参数对频率跟踪和幅值估计的暂态和稳态性能的影响. 算法实现了在给定频率区间而不是给定数值条件下的正弦分量及其幅值的准确跟随, 并且响应速度不受正弦分量幅值大小的影响. 通过仿真验证了算法的有效性.     

基于自适应滤波器的时频分析

采用最小方差原则和梯度下降方法, 经过旋转变换, 获得频率参数和带宽参数可调的自适应二维线性正弦跟踪滤波器, 实现信号跟随与幅值估计. 把多个跟踪器并联, 形成带宽可调的多频点梳状滤波器, 得到多维线性常系数微分动力系统. 用不变原理证明梳状滤波器是一致渐近稳定的. 用拉普拉斯变换导出频率特性, 单正弦输入时为向量形式, 针对多正弦分量时为频率特性矩阵. 当输入信号所有正弦分量的频率都等于梳状滤波器频率参数时, 本算法能够同时准确跟随所有分量及其幅值. 分析了算法的频域格栅效应以及带宽参数对稳态精度的影响, 通过仿真说明了算法的有效性.     

基于基波频率估计的多谐波分析

采用自适应陷波滤波器实现基波频率可变的多谐波(包含整数次谐波和非整数次间谐波)分析. 算法包括基波频率估计器和多个二维正弦跟踪器, 形成缓慢自适应积分流形, 用李雅普诺夫定理和平均方法证明积分流形的存在性和稳定性. 若滤波器频率系数和信号的谐波结构相同, 该自适应陷波滤波器是一致渐近稳定的, 可按指数收敛准确跟随基波频率、每个谐波(间谐波)及其幅值. 导出了频率特性表达式和频率特性矩阵, 分析了滤波器参数对稳态频率特性的影响. 通过仿真证实算法的有效性, 并说明减小滤波器带宽参数和自适应增益能够获得更好的噪声特性.     

基于MDL准则的MUSIC信号频率估计算法

在正弦信号频率估计方法中,高分辨率谱估计的MUSIC算法利用信号子空间和噪声子空间的正交性进行信号频率的估计,可以得到很高的测频精度.但是信号源数的选择将会影响此方法的有效性.本文研究了基于最小描述长度(MDL)准则的MUSIC算法,信号子空间和噪声子空间的估计以及信号源数的确定同时进行,解决了MUSIC算法中信号源数对估计结果的影响.仿真结果表明利用该方法可准确地估计多个正弦信号的频率值.     

滑动频率估计算法在微波测量液位中的应用

在微波测量液位的系统中,正弦信号的频率估计是实现液位测量的关键.比较并分析了离散FFT变换的两种正弦信号频率估计方法:Rife比值法和三角形法,提出了一种滑动频率估计方法,通过实时确定比例因子,得到了滑动频谱校正算法.实验结果表明,该方法频率估计精度较高,估计性能优于单一的Rife法、三角形法,适合于低信噪比条件下的实...     

基于快速傅里叶变换的正弦信号频率高精度估计算法

为了进一步提高加性高斯白噪声背景中正弦信号的频率估计精度,提出了一种新的基于插值快速傅里叶变换(FFT)的正弦信号频率估计算法.首先,对N点正弦采样序列进行等长度时域补零延长,再进行 2N 点FFT; 然后, 搜索幅度最大离散谱线位置得到频率粗估计值; 最后, 采用幅度最大谱线以及原信号的离散时间傅里叶变换(DTFT)在幅度最大谱线左右两侧的两点抽样值进行精估计.仿真结果表明,当信号实际频率位于FFT两条离散谱线之间任意位置时,所提算法的频率估计均方根误差均接近克拉美罗下限,具有较好的一致性,估计精度高于Candan算法、Fang算法、三谱线合理结合(RCTSL)算法和Aboutanios算法, 且信噪比阈值较低,估计性能优于现有频率估计算法.     

电磁定位耦合信号提取方法研究

电磁定位系统中,正弦耦合信号提取是关键,其结果将直接影响定位精度.在多频正弦信号耦合系统中,由于电子元器件和系统误差等原因,会导致信号频率有偏差,而且可能存在饱和畸变,对参数提取造成了困难.基于最小二乘法原理和频率逼近思想,提出一种用于有频偏的多频率有饱和正弦信号幅值和相位的提取方法.该方法在有饱和畸变的正弦信号中提取未饱和的样本,通过最小二乘法拟合计算,估计信号参数,然后改变信号频率逐渐逼近最佳频率,使得误差平方和最小,从而提取准确参数.仿真分析了噪声、信号饱和程度和采样点数对参数提取的影响.最后通过实验验证了该方法的有效性和实用性.     

FMCW微波液位测量的快速频率估计算法

在FMCW(调频连续波)微波液位测量系统中,回波差拍正弦信号的频率检测是实现距离测量的关键.本文比较了基于离散傅里叶变换的正弦信号频率估计方法:矩形窗比值公式法和能量重心校正法,并分析了这两种算法在频率估计中各自存在的问题,通过分析噪声对频率测量的影响并结合两者的优势,提出一种基于FFT的快速频率估计算法,实验结果表明该方法的测量精度高,计算量小,具有实现简单、快速实时等特点.     

一种新的复正弦信号二维频率估计算法

如何从遥感图像中实时而有效的估计出二维频率一直是一个难题,提出了一种二维复正弦信号的相似最大似然频率估计迭代算法.通过建立最大似然二维频率估计信号模型,并且结合最大似然估计价值函数,给出了两种新的频率估计价值函数;针对所提及的算法进行了均值和方差分析,分析结果显示该算法是近似无偏估计的,并且满足Cramer-Rao边界条件;最后对所提出的算法进行了仿真,并给出了其在干涉合成孔径雷达(INSAR)去平地相位中的应用.结果表明:算法具有较高的频率估计精度和较小的计算量.     

基于频率自适应滤波算法的脉冲电能计量方法

准确估计电力电子设备工作时所产生谐波的功率对脉冲电能计量具有十分重要的意义.提出归一化频率自适应的谐波功率计量算法.首先通过该方法分解出电机模型电路中被污染信号的各次谐波成分,进而实现对电机中谐波有功功率的实时跟踪.接着,以一组富含时变谐波的实测电火花信号为待处理信号,验证该算法在典型电火花脉冲电源信号谐波功率计量方面的应用.仿真结果表明,该算法在频率时变脉冲信号的电能计量方面具有快速性和准确性.     

Accuracy analysis of complex sinusoid amplitude and phase estimation by means of the interpolated discrete-time Fourier transform algorithm

In this paper the accuracy of the complex sinusoid amplitude and phase estimators provided by the Interpolated Weighted Discrete-Time Fourier Transform (IpWDTFT) algorithm is analyzed. It is shown that the use of the WDTFT spectral sample corresponding to the estimated sinusoid frequency allows to minimize the estimator asymptotic Mean Square Error (MSE) due to additive wideband noise. Also, the expression of the asymptotic expected sum-squared fitting error in the reconstruction of the complex sinusoid by means of the IpWDTFT algorithm is derived. All the derived expressions are verified through computer simulations.     

Comparison of two novel MRAS based strategies for identifying parameters in permanent magnet synchronous motors

Two model reference adaptive system (MRAS) estimators are developed for identifying the parameters of permanent magnet synchronous motors (PMSM) based on the Lyapunov stability theorem and the Popov stability criterion, respectively. The proposed estimators only need online measurement of currents, voltages, and rotor speed to effectively estimate stator resistance, inductance, and rotor flux-linkage simultaneously. The performance of the estimators is compared and verified through simulations and experiments, which show that the two estimators are simple, have good robustness against parameter variation, and are accurate in parameter tracking. However, the estimator based on the Popov stability criterion, which can overcome parameter variation in a practical system, is superior in terms of response speed and convergence speed since there are both proportional and integral units in the estimator, in contrast to only one integral unit in the estimator based on the Lyapunov stability theorem. In addition, the estimator based on the Popov stability criterion does not need the expertise that is required in designing a Lyapunov function.     

离散实正弦信号参数估计的Cramer Rao方差下限

研究了高斯白噪声背景下根据离散现测值估计实正弦信号的参数问题。分析了实正弦信号幅度、频率和相位估计的方差下限．并讨论了实正弦信号参数的最大似然(ML)估计。给出了观测数据长度N较大时实正弦信号参数估计的Cramer Rao方差下限的计算公式。指出了实正弦信号参数估计方差下限与观测数据长度N、信号频率及初相有关，当N较大时实信号参数估计的方差下限约为对应的复信号的参数估计的方差下限的2倍。在不同的信噪比下进行了计算机模拟．模拟结果与本文分析结果吻合。     

Normalized estimation of fundamental frequency and measurement of harmonics/interharmonics

An adaptive notch filter is presented to estimate the fundamental frequency and measure both harmonics and interharmonics of an almost periodic signal with unknown time-variant fundamental frequency, which has the robustness that the convergence speed is determined by neither amplitude nor frequency of fundamental component. The algorithm forms a one-dimensional slow adaptive integral manifold whose existence and stability are proved by averaging method and Lyapunov stability theorem. The local exponential stability and the ultimate boundedness of fundamental frequency estimation are proved. The local exponential stability makes sure that the fundamental frequency, the harmonic and interharmonic components can be all fast tracked. The principle for adjusting the parameters with their influences on transient and steady-state performance is investigated and decreasing parameters can improve noise characteristic. The validity is verified by simulation results.     

低信噪比条件下正弦信号幅度盲估计

研究了电子侦察信号处理中正弦信号幅度盲估计问题。提出了一种基于相关累加及线性回归的正弦信号幅度盲估计算法。先对接收到的信号进行频率估计,建立参考信号,将接收信号与参考信号相关后变换到基带并作累加,后将相关累加曲线进行最小二乘线性回归,以回归得到的直线斜率值作为信号幅度的估计值。仿真结果表明,当信噪比大于[-3 dB]时,方法的估计均方根误差小于1.1倍克拉美罗限,可在低信噪比条件下,实现正弦信号幅度的盲估计。     

Design of Asymptotically Convergent Frequency Estimator Using Contraction Theory

The problem of estimating unknown frequencies of a sinusoidal signal simultaneously is a classical problem in signal and system theory. Many approaches and algorithms are proposed in literature to develop estimators for a measurable sinusoidal signal having multiple sinusoids with unknown amplitudes, frequencies and phases. In this work, an asymptotically convergent frequency estimator is given for estimation of n-unknown frequencies of a measurable sinusoidal signal. The contraction theory approach is adopted to show the asymptotic convergence of the proposed estimator in quite a simplified manner. Approach given here exploits the results of contraction theory related to semi-contracting systems. The nonlinear estimator based on dynamic system approach, guarantees global boundedness and convergence of the state and frequency estimation for all initial conditions and frequency values. It further ensures simultaneous globally convergent estimation of states and frequencies of a sinusoid involving multiple frequencies. Numerical simulations are presented for different combinations of frequencies to justify the claim.