The paper considers methods for calculating the mode of a stationary random process when solving the problem of processing measurement results under conditions of a priori uncertainty. The results of the conducted studies allowed us to conclude that the most effective method for calculating the mode for a given sample is the proposed method, which allows to increase the accuracy of its calculation by at least 8 times, compared to methods based on the construction of histograms. It should be noted that the proposed method allows to provide an estimate with an error of at least 5% for samples with a number of measurements of about 5 value.
The paper discusses the issues of minimizing the error in selecting a useful signal in the presence of the “flip” effect of the approximating function, which are solved by compensating for the approximation error by eliminating the “flip” effect by mirroring it relative to a certain line, which is determined by the methods proposed in this work. The proposed method for choosing a line for mirroring the estimate of the useful signal function has
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8 times smaller, with a spread of values that is characterized by
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which is more than 70 times less.
The paper is devoted to the analytical substantiation of a new approach to the processing of signals representing a collection of some piecewise linear signals under conditions of a priori uncertainty about its parameters. The results of computer simulation fully confirm the main theoretical results and allow us to conclude that the new method is highly efficient in processing piecewise linear signals under conditions of a priori uncertainty about the useful signal function and the statistical characteristics of the additive noise component. The developed method makes it possible to reduce the dispersion of the additive noise component up to 10 times, however, as the dispersion of the noise increases, the efficiency decreases.
The paper discusses the issues of practical implementation of increasing the accuracy of signal extraction, which is achieved by eliminating the «flip» of the approximating function when dividing the measured process into intervals under conditions of a priori uncertainty about the signal function, which significantly increases the error of allocating a useful signal. The probability of a «flip» of the approximating function depends significantly on the variance of the additive noise and the sample length. The use of the proposed methods and their software implementation makes it possible to increase the accuracy of the useful signal extraction up to 30 percent in the absence of a priori information about the function of the measured process for complex signals and at least 20% for simpler ones. The use of the proposed methods will significantly increase the processing efficiency in the conditions of a priori uncertainty about the function of the measured process (useful signal) and the statistical characteristics of the additive noise components.
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