  The article is devoted to the problem of synthesis of observers of state
variables for linear stationary objects operating under conditions of noise or
disturbances in the measurement channel. The paper considers a fully observable
linear stationary system with known parameters. It is assumed that the state
variables are not measured, and the measured output variable contains a small
amplitude (in general, modulo less than one) additive noise or disturbance. It
is also assumed that there is no a priori information about the disturbance or
noise in the measurement channel (for example, frequency spectrum, covariance,
etc.). It is well known that a large number of methods of observer synthesis
have been obtained for this type of objects, including the Kalman filter, which
has proven itself in practice. Under the condition of complete observability
and the presence of some a priori information about the process (which is
typical for the case when a disturbance in the measurement channel can be
represented as white noise), approaches based on Kalman filtering demonstrate
the highest quality of convergence of estimates of state variables to true
values. Without taking into account the numerous results obtained using the
application of the Kalman filter, an alternative idea of constructing an
observer of state variables is considered in this paper. The alternative of the
new approach is primarily due to the fact that there is no need to use the
usual approaches based on the Luenberger observer. The paper proposes an
approach based on the evaluation of unknown parameters (in this case, an
unknown vector of initial conditions of the variables of the object state) of a
linear regression model.
