频点自跟踪自适应频率估计器性能研究

Research on Properties of Frequency Auto-Tracking Adaptive Frequency Estimator

基于二阶自适应陷波滤波器的频率估计器是工程上常用的单频信号频率估计器,其前提是参考信号相对输入信号频偏较小.随着频偏的增大,自适应频率估计的偏差和方差也随之增大.本文分析了自适应频率估计器的性能及频偏的影响,得出了自适应频率估计方差下限的公式及达到此下限的条件.提出了频点自跟踪自适应频率估计器.仿真与理论结果均表明相同条件下该估计器较自适应频率估计器明显减小了估计偏差和方差,在中等信噪比下估计方差可减小到自适应频率估计方差的百分之一.只要信噪比不甚低,频点自跟踪频率估计是无偏的且估计方差接近理论下限.

Frequency estimator which based on two- order adaptive notch filter is the one frequently used for sinnsoid on engineering, with a precondition that there is a small frequency bias of reference signal to input signal. With frequency bias increasing, estimated bias and variance of adaptive frequency estimator （AFE） enlarge. In this paper properties of AFE and influences of frequency bias are analyzed, and formula on estimated variance lower bound is derived, and condition which is required by the bound is got. Frequency auto-tracking adaptive frequency estimator （FATAFE） is brought forward. Simulation and theoretical results show that under the same conditions FATAFE decreases obviously estimated bias and variance relative to AFE, and under medium signal-to-noise ratio condition estimated variance of FATAFE can be declined to one percent of that of AFE. FATAFE realizes unbiased estimation and its estimated variance approaches to theoretical lower bound if only signal-to-noise ratio is not very low.