An iterative algorithm for finding stable solutions to the covariance or modified covariance autoregressive modeling methods

While the covariance and modified covariance methods of linear prediction have many desirable properties for spectral estimation, they are not guaranteed to yield stable model estimates. In this paper we present a simple iterative method for finding the best stable solution to the covariance or modified covariance problems. The technique alternates between a data extrapolation step and calculating an "infinite interval" covariance method estimate. Each iteration reduces the prediction error and thus improves the parameter estimates. Furthermore, convergence can be guaranteed to either the solution to the original covariance problem (if it is stable), or else to a set of polynomials with one or more zeroes on the unit circle and the rest inside. Several examples are shown comparing the iterative methods with the unconstrained covariance and modified covariance methods, and with Burg\´s algorithm.