On sequential estimation of a periodic signal on the background of an autoregressive noise

We consider the problem of estimating coefficients of a trigonometric signal in a discrete time from observations with an additive noise described by a stationary autoregressive process with unknown parameters and unknown distribution. A one-step sequential procedure to estimate signal coefficients is proposed, which provides a given root-mean-square accuracy of estimates for any values of the nuisance parameters. An asymptotic formula for the mean duration of the procedure is constructed.