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Solving problem of movement distribution based on Riccatti equation proportions


V. I. Kuzmin, A. F. Gadzaov

For effective analysis of empirical data it is often required to divide the original series on the trend and oscillating components. In the case when the trend equations are unknown, identification of species depending on the trend causes great difficulties, that leads, in some cases, to the uncertainties of results obtained for the vibrations of the results. Standard methods of data processing does not guarantee the exclusion of the trend without losing essential information about the process or the occurrence of oscillations was not originally present in the research study of empirical data. To eliminate the trend without losing essential information about the process a method based on the properties of the Riccati equation has been developed This equation allows us to describe a wide class of trends and general properties can become a basis for developing models and algorithms of eliminating of trend. After exclusion of the trend there is a need to identify the periods corresponding to the analyzed data without using of functions with a fixed structure. Such request satisfies the shear class of functions that determine the distance in the functional space The system almost periods defined by the minima of the function of the shear. Effectiveness of the method is illustrated by the analysis of the data flow of solar radio emission at a wavelength of 10.7 cm In carrying out this work is designed layout opto-electronic channel for the optical star sensor with a frequency of 30 frames/sec, 10-3 sec exposure and gain 103 on the basis of the gated image intensifier, a fiber-optic articulated focones with CCD, and conducted laboratory tests. The analysis of the results of ground tests confirm the efficiency of the layout method of increasing the accuracy of the orientation of the spacecraft using optical star sensors with an electron-optical converters. Proposed method for increasing the accuracy of determining the maximum energy center of the star with subpixel accuracy by a single photon and photon group. The method consists in post-processing of the image using the bilateral filter. This filter eliminates noise and sudden changes in the intensities of neighboring pixels. The use of such filters in image processing, image intensifier Small signal, is very promising because it allows essentially smooth the image and remove the effects of background photons, without affecting the larger objects such as «star».

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