Spectral Estimation of All-Pole Processes Using Bayesian Techniques.

摘要

The problem considered in the spectral estimation of Mth order stationary Gaussian processes which possess an all-pole spectral representation. This spectral estimate is determined through the application of Bayes Rule, to find the post probability density functions. The problem is cast as a Bayesian parameter estimation problem. The use of a finite dimensional set of sufficient statistics facilitates the problem solution. The solutions presented are limited to the M=1, and M=2 case, but these results can be extended to higher order finite dimensional processes. Because the M=2 problem exhibits the characteristics of higher dimensional processes, the emphasis of the simulation study is placed here. The main concern in the simulation study is the use of the simple measurements described by the sufficient statistics, to develop the final estimate, and the circumstances under which this approach can be used.