Estimation of the Variance of a Random Signal with an Unknown Frequency Bandwidth

We consider the problem of estimating the variance of a Gaussian stationary stochastic signal with a regular spectral density and a priori unknown frequency bandwidth. Two methods for overcoming an a priori uncertainty are proposed, namely, the quasi-likelihood algorithm and the joint maximum-likelihood estimation of all unknown parameters. The structural schemes are developed and the estimation characteristics are found for the synthesized algorithms. The estimation-accuracy loss because of the a priori ignorance of the spectral-density width of a useful signal are determined.