An adaptive nonlinear filter for online parameter estimation of undamped and damped sinusoids

An adaptive non-linear filter (ANF) is presented that estimates and tracks the frequency, phase, and magnitude of an undamped as well as damped sinusoid signal. The structure of this ANF that is similar to that of a phase-locked loop (PLL), however, differs in the method of phase detection by incorporating an adaptive law to provide the phase and frequency discrimination. The stability and convergence property of this ANF is studied using Lyapunov method and is also analysed graphically using the phase plane technique to understand its behaviour and convergence properties under different conditions. It is observed that the proposed ANF, unlike PLL, provides smooth estimate of the magnitude, phase, and frequency of the input sinusoid signal and has a better noise performance. Further, the influence of the design parameters on the tracking and noise performance of the proposed ANF is also investigated. Extensive computer simulations were performed to demonstrate its effectiveness and usefulness.