On estimating the orders of an autoregressive moving-average process with uncertain observations

A method is proposed for estimating the orders of an autoregressive moving-average process solely from the observations of the noise-corrupted output. The order of the autoregressive (number of poles) can be determined by testing the singularity of the correlation matrix, while the order of the moving-average (number of zeros) can be determined from observing the repetitive pattern of the correlation equations.