Reduction of all-pole parameter estimator bias by successive autocorrelation

Conventional all-pole parameter estimators applied to noise corrupted all-pole sequences result in biased estimates. This paper describes a procedure by which reduction of this bias is accomplished by applying pole-preserving, signal to noise ratio improving functions to the sequence. Correlation like pole-preserving functions are investigated and pole dependent signal to noise ratio improvement is described. An all-pole parameter estimator using successive application of a pole-preserving function (successive autocorrelation) is given. Comparison is made with the least squares combination of the higher order Yule-Walker equations, an approach to bias reduction reported by Cadzow. Successive autocorrelation is found to result in improved performance, with estimates of higher Q poles being most effectively enhanced.