Parameter Estimation for a Sinusoidal Signal with a Time-Varying Amplitude

This paper addresses the parameter estimation problem of a non-stationary sinusoidal signal with a time-varying amplitude, which is given by a known function of time multiplied by an unknown constant coefficient. A robust estimation algorithm is proposed for identifying the unknown frequency and the amplitude coefficient in real-time. The estimation algorithm is constructed based on the Volterra integral operator with suitably designed kernels and sliding mode adaptation laws. It is shown that the parameter estimation error converges to zero within an arbitrarily small finite time, and the robustness against bounded additive disturbances is certified by bounded-input-bounded-output arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools through numerical simulations.