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.