Dynamical-model approach to observer and smooth filter design

A smoothing procedure, used as a filter and an observer is proposed. Given a linear dynamical process modeled by its input-output equation, where the output is supposed to be corrupted by a zeromean noise, we develop the numerical algorithm to smooth the real measured output and compute the reliable estimates of its derivatives by solving a constrained optimization problem. First we form an equivalent discrete norm to the L₂-norm of the input-output equation and consider that the solution of the smoothing problem is a spline function which minimizes the formed criterion subject to a linear inequality. Using the definition of the algebraic observability, the system states are then estimated. Satisfactory results of such a procedure is proved by numerical simulations