Guaranteed estimation of signals with bounded variances of derivatives

Consideration is given to the problem of signal estimation against the background of the white noise when the information about the signal is represented in the form of numerical characteristics such as constraints on the variance of the signal itself and variances of some its derivatives. We proposed a method to solve this problem using the technique of filtering in the time domain by minimizing the functional that is a combination of the $H_2$-norm of the transfer function from the measurement noise to the error of estimation and the $H_\infty$-norm of the transfer function from the generating noise to the error of estimation.