In this paper, a recursive Gauss-Newton (RGN) algorithm is first developed for adaptive tracking of the amplitude, frequency and phase of a real sinusoid signal in additive white noise. The derived algorithm is then simplified for computational complexity reduction as well as improved with the use of multiple forgetting factor (MFF) technique to provide a flexible way of keeping track of the parameters with different rates. The effectiveness of the simplified MFF-RGN scheme in sinusoidal parameter tracking is demonstrated via computer simulations.