二阶自适应陷波器频率估计方法统计性能分析

为对如何提高自适应陷波器频率估计精度提供参考，通过评估自适应陷波器频率估计方法性能，对基于均方误差函数的自适应陷波器频率估计方法进行了统计性能分析。首先，根据误差函数的不同，将自适应陷波器划分为自适应FIR陷波器和自适应IIR陷波器。然后，将自适应FIR陷波器看作自适应IIR陷波器的特例，重点分析了自适应陷波器的误差函数及稳态下的频率估计统计性能，讨论了自适应陷波器参数对正弦信号频率估计精度和收敛速度的影响。最后，给出正弦信号的频率估计计算结果。结果表明，实际计算结果同理论计算结果一致，证明了统计性能分析的正确性。 

Statistical performance analysis of frequency estimation method with second order adaptive notch filter

To provide a reference for how to improve the adaptive notch filter frequency estimation accuracy, the statistical performance analysis for mean square error function based ANF method is derived according to evaluate frequency estimation method of adaptive notch filter (ANF) for time invariant signal and time varying signal. Firstly, according to different error function of ANF, the ANF is classified into two kinds, one is FIR-ANF, and the other is IIR-ANF. Meanwhile, FIR-ANF can be taken as a special case of the IIR-ANF, the error function of IIR-ANF is much sharper than the error function of FIR-ANF, but its convergence speed is slower than FIR-ANF due to the flattened characteristic of the error function when the initial frequency is far away from the optimum solution. The statistical performance analyses of frequency estimation for FIR-ANF and IIR-ANF at steady state are given, the bias and MSE generated by IIR-ANF is much closer to zero than FIR-ANF, and the influences of the parameter of FIR-ANF and IIR-ANF to sinusoidal frequency estimation accuracy and convergence speed are discussed. Finally, the simulation results for frequency estimation of sinusoid signal are provided to confirm the statistical performance analysis, and verify that the IIR-ANF is much more suitable for estimate time varying signal frequency than FIR-ANF.