Application of interval methods to the analysis of multisensory systems

When solving the calibration problem within the statistical approach, ignoring the fact that interference models in experimental and in real conditions have different sources and are generated by different factors can lead to a significant distortion of error estimates of the measuring system and the formation of an inadequate transformation characteristic. Moreover, there are known theoretical difficulties in constructing a model inverse to the regression model and in determining the error corridor of the model, e.g., there is a problem of determining the distribution of a random variable inverse to a normally distributed. Here we use an interval approach as an alternative to the statistical approach, under the assumption that all variables are measured inaccurately during the experiment and the results of the calibration experiment are presented in the interval form. It is also assumed that the interval certainly contains an unknown true value. The developed approach is used in analysis of single-factor multisensory systems under the assumption that the errors of the calibration experiment are limited in magnitude. The problem of constructing a calibration characteristic of a separate sensor which can be solved using methods of constructing direct and inverse static characteristics is also briefly considered. Thus, we have developed: a new approach to the analysis of interval data at the output of single-factor multi-sensor systems, which, on a set of specified sensors, allows solving the problems of rejecting obviously unsuitable sensors and choosing the best sensor; the procedure for constructing a calibration characteristic in the form of a spline function integrating the readings of several selected sensors in the absence of the best sensor. Various estimates are proposed to integrate the information obtained from different sensors, including the arithmetic mean of intervals, which provides determination both of the point value of the average and the error of determination (which is applicable for any intervals, including non-intersecting ones); the weighted mean of intervals, which allows the use of a priori information about the reliability of sensor readings (accuracy, reliability, character of the dependence, etc.); the intersection of intervals, tending to the true value of the measured variable as the number of experiments increases; the intersection of the intervals with a given level, which is applicable in case of a very narrow area of the intersection of measurement error intervals and can also be useful at the stage of preliminary analysis of the reliability of predicted values.

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