On the statistics of the estimated reflection coefficients of an autoregressive process

The exact statistics of the estimated reflection coefficients for an autoregressive process are difficult to determine. However, since almost all the common methods for estimating the reflection coefficients are maximum likelihood estimates for large data records, the asymptotic distribution of the estimates is multivariate Gaussian with a covariance matrix given by the Cramer-Rao bound. A recursive means of computing the covariance matrix bound is described. Simulation results show that the asymptotic expressions are accurate for large data records. However, for relatively short data records, the asymptotic expressions are accurate only for spectra with a small dynamic range.