This paper presents the design and analysis of an adaptive algorithm for tracking the amplitude, phase and frequency of the fundamental, harmonics and interharmonics present in time-varying power sinusoid in white noise. If frequency, amplitude and phase of the multiple sinusoids become nonstationary, they are estimated as an unconstrained optimization problem using robust and low complexity multi-objective Gauss–Newton algorithm. The presented algorithm deals with frequency drift and can accurately estimate frequency variation, amplitude and phase variation, as well as harmonic amplitude and phase variations. Further, the learning parameters in the proposed algorithm are tuned iteratively to provide faster convergence and better accuracy. The excellent tracking capability of proposed multi-objective Gauss–Newton algorithm is shown through simulation and experimental results in a nonstationary environment. Copyright © 2012 John Wiley & Sons, Ltd.