In this paper, we report an experimental investigation on the influence of colored noise (generated by the Ornstein–Uhlenbeck (OU) process) on thermoacoustic coupling in an electro-acoustic Rijke tube simulator. In the absence of noise, the simulator exhibits subcritical Hopf bifurcation. Although noise in a practical system has a finite correlation time, yet the system identification methods are based on the assumption of white noise. In this study, we investigate the effects of correlation time, and intensity of colored noise on the estimation of the growth rates of acoustic oscillations determined using Fokker–Planck equation in stable, bistable, and linearly unstable regions. Subsequently, we compare the findings against results obtained considering white noise approximations. We report the observed deviation of the estimated growth rates from the actual values as a function of noise intensity and correlation time. We find that with the colored noise model, the deviation in the estimated growth rates lies within the range of 0–10% compared to the deviation of 5–25% observed considering the white noise approximation. We also report that increasing noise amplitudes leads up to a deviation of approximately 30% in the estimated growth rates from the actual values.