On Sequential Classification of Autoregressive Processes with Unknown Variance of Noise

The problem of guaranteed discrimination of a finite number of hypotheses for an autoregressive process from direct and indirect observations (with an additive noise) is considered. Under each hypothesis, the autoregressive parameters are assumed to be known, whereas the variances of the process noise and interference in the observation channel may take arbitrary values. Sequential procedures of classification with a guaranteed probability of the correct decision are proposed. Asymptotic formulas for duration of the procedures are obtained.