Guaranteed Estimation of a Periodic Signal Distorted by an Autoregressive Noise with Unknown Parameters

The problem of estimating coefficients of a trigonometric signal from observations with an additive noise is considered, where the noise is a stationary autoregressive process with unknown parameters and unknown distribution. Based on the least-squares method, a sequential procedure for estimation of signal coefficients is constructed, which guarantees a specified mean-square estimation accuracy for any values of the nuisance parameters. Asymptotic formulas for the duration of the procedure are obtained. The asymptotical normality of the estimators proposed and the duration of estimation is established.