A new cosine cepstrum model-based scheme is presented for the parameter estimation of a minimum-phase autoregressive (AR) system under low levels of signal-to-noise ratio (SNR). A ramp cosine cepstrum (RCC) model for the one-sided autocorrelation function (OSACF) of an AR signal is first proposed by considering both white noise and periodic impulse-train excitations. Using the RCC model, a residue-based least-squares optimization technique that guarantees the stability of the system is then presented in order to estimate the AR parameters from noisy output observations. For the purpose of implementation, the discrete cosine transform, which can efficiently handle the phase unwrapping problem and offer computational advantages as compared to the discrete Fourier transform, is employed. From extensive experimentations on AR systems of different orders, it is shown that the proposed method is capable of estimating parameters accurately and consistently in comparison to some of the existing methods for the SNR levels as low as −5 dB. As a practical application of the proposed technique, simulation results are also provided for the identification of a human vocal tract system using noise-corrupted natural speech signals demonstrating a superior estimation performance in terms of the power spectral density of the synthesized speech signals.