The center frequency of a narrowband, discrete-time random process, such as a reflected ultrasound signal, is estimated from the parameter values of a reduced, second-order autoregressive (AR) model. This approach is proposed as a fast estimator that performs better than the zero-crossing count estimate for determining the center-frequency location. The parameter values are obtained through a linear prediction analysis on the correlated random process, which in this case is identical to the maximum entropy method for spectral estimation. The frequency of the maximum of the second-order model spectrum is determined from these parameters and is used as the center-frequency estimate. This estimate can be computed very efficiently, requiring only the estimates of the first three terms of the process autocorrelation function. The bias and variance properties of this estimator are determined for a random process having a Gaussian-shaped spectrum and compared to those of the ideal FM frequency discriminator, zero-crossing count estimator and a correlation estimator. It is found that the variance values for the reduced-order AR model center-frequency estimator lie between those for the ideal FM frequency discriminator and the zero-crossing count estimator.