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Effective algorithm for statistical digital filtering

A. N. Detkov


A rigorous mathematical solution of the problem of statistical synthesis of recursive digital filters based on R. L. Stratonovich’s theory of conditional Markov processes was given in [1]. However, the distortions specific for microprocessors due to rounding of numbers and limitation of the word length, which lead to substantial estimation errors, were not taken into account here. These errors are caused by loss of positive definiteness and ill condition of the correlation matrices. To overcome the indicated difficulties, the method of taking the square roots of matrices is used successfully in Kalman filters [2]. Algorithms for digital filtering resistant to computational errors related to limitation of the word length of microprocessors on which the digital filter is realized are obtained in the work by means of the given method…

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