The paper presents a new approach for the identification of minimum-phase autoregressive (AR) systems in the presence of heavy noise. A damped cosine model for the ramp cepstrum of the one-sided autocorrelation function of a noise-free AR signal is proposed to estimate the AR parameters. The AR parameters are obtained directly from the estimated damped cosine model parameters. The proposed method overcomes the failure of conventional cepstrum and correlation based techniques in noisy AR system identification at a very low signal-to-noise ratio (SNR). Computer simulations are carried out based on. both synthetic AR systems and natural speech signals, showing superior identification results even at an SNR of -5 dB for which most of the existing methods would fail.