A smoothing filter based on an analogue of a Kalman filter for a guaranteed estimation of the state of dynamical systems

The equations of a smoothing filter are obtained based on a filter for the guaranteed estimation of the state of dynamical systems, similar to the classical Kalman filter. Particular attention is paid to the link between the probabilistic approach to the processing of inexact measurements of the phase vector of dynamical systems with uncertainties and the method of ellipsoids. The procedure for applying the relations obtained is demonstrated using a simple mechanical system as an example.