A New Adaptive Filter for Estimating and Tracking the Delay and the Amplitude of a Sinusoid

In this paper, we propose a new adaptive filter for estimating and tracking the delay and the relative amplitude of a sinusoid vis-a-vis a reference sinusoid of the same frequency. By careful choice of the sampling period, a two-tap finite-impulse response (FIR) filter model is constructed for the delayed signal. The delay and the amplitude are estimated by identifying the FIR filter for which a delay variable and an amplitude variable are updated in an LMS-like manner, deploying, however, separate step sizes. Convergence analysis proving convergence (in mean) of the delay and the amplitude updates to their respective true values is provided, and necessary convergence conditions are established. Stability regions in the step-size plane are also identified that guarantee bounded steady-state error variance for the delay and the amplitude estimates. The proposed method is computationally simple as the primary computation is a rotation of a vector that can efficiently be implemented using CORDIC processors. MATLAB-based simulation studies confirm satisfactory estimation performance of the proposed algorithm.