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Optimal Dynamic Measurement Method Using the Savitsky - Golay Digital Filter


Alevtina Viktorovna Keller

Voronezh State Technical University, Russia
Doctor of Physical and Mathematical Sciences


We consider one of the mathematical models of the theory of optimal dynamic measurements to solve the problem of recovering a dynamically distorted signal in the presence of noise. The measuring device is simulated by a Leontief-type system which is a finite-dimensional analogue of a Sobolev-type equation, and its initial state is given by the Showalter -- Sidorov condition. In order to find the input signal from the known observed signal, an optimal control problem, namely the minimization of the penalty functional in which the simulated and observed output signals are compared should be solved. The solution of this problem is called the optimal dynamic measurement. The theorem on the existence of a unique exact solution of the problem posed and the algorithm of the spline method for finding an approximate solution are given. At the same time, the presence of noise at the output of the measuring device does not give a possibility to solve the problem of recovering a dynamically distorted signal satisfactorily. In the article we propose to use in the numerical algorithm the Savitsky-Golay digital filter for the observed signal. As a result, we obtain an observation smoothed by the filter, which is then used in the penalty functional. The choice of parameters for the Savitsky-Golay digital filter is discussed, and the results of computational experiments on the data of bench tests are presented.

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