A robust variable step-size LMS-like algorithm for a second-order adaptive IIR notch filter for frequency detection

The best adaptive algorithm requires fast convergence speed, low variance, unbias and low steady-state mean square error (MSE) in both low and high signal-to-noise ratio (SNR) situations. We have proposed a robust variable step-size LMS-like algorithm (VS-LMS-L) for a second-order adaptive IIR notch filter for frequency detection in radar, sonar and communication systems. This algorithm is compared with the conventional LMS-like algorithm called the plain gradient algorithm (PG). The time-varying step-size μ(n) is adjusted by using the square of the time-averaged estimate of autocorrelation of the present output signal y(n) and the past one y(n-1). This technique can reject the effect of the uncorrelated noise sequence on the step-size update, resulting in a small MSE due to the small final μ(n). Moreover, this algorithm can also improve the convergence speed by comparison with the PG at the same MSE value.