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.

Stability Analysis of Normalized Frequency Adaptive Comb Filter

A normalized frequency adaptive comb filter composed of a number of normalized frequency estimators in parallel is proposed to track unknown frequency and unknown amplitude of each component of an almost periodic signal. The filter consists of two coupled nonlinear differential equations respectively for updating frequencies and estimating state variables. A nonlinear autonomous equation for frequency estimation is deduced after average method is applied to the almost periodic dynamic system resulting from system decoupling by slow integral manifold. Three kinds of local stability of the autonomous system: the exponential stability of isolated equilibrium point, the semistability on center manifold, and the robustness under unknown periodic disturbance are proved. The convergence and the boundedness of amplitude estimation and signal tracking as well as the effect of parameters on the transient and steady-state performance of frequency and amplitude are investigated. Each sinusoidal component and its amplitude are accurately tracked on the condition of given intervals instead of the values of frequencies. The response speed is independent of the component amplitude. Simulation results reveal the validity of the proposed algorithm.