This paper presents an adaptive method for tracking the amplitude, phase, and frequency of a time-varying sinusoid in white noise. Although the conventional techniques like adaptive linear elements and discrete or fast Fourier transforms are still widely used in many applications, their accuracy and convergence speed pose serious limitations under sudden supply frequency drift, fundamental amplitude, or phase variations. This paper, therefore, proposes a fast and low-complexity multiobjective Gauss-Newton algorithm for estimating the fundamental phasor and frequency of the power signal instantly and accurately. Further, the learning parameters in the proposed algorithm are tuned iteratively to provide faster convergence and better accuracy. The proposed method can also be extended to include time-varying harmonics and interharmonics mixed with noise of low signal-to-noise ratio with a great degree of accuracy. Numerical and experimental results are presented in support of the effectiveness of the new approach.