Reaserch On The Extraction Of The Variation Characteristics Of Satellite Based On Fractal Dimension

As an important part of morden nonlinear science,Fractal is widely used in many fields.This paper uses its self-similarity to realize the abnormal state detection. Self-similarity means the measurement of fractal dimension is very close for the same condition,so as to realize the detection of abnormal state.In this paper,based on the basic theory of fractal,combining with the fractal dimension characteristic by using three methods to measure the signal.For single fractal method,fractal dimension is used as the main characteristics under the specific measure, according to different state to take multiple signal classification dimension range, by determining the unknown stated numerical belong interval so as to realize the state of the judgement,simple and intuitive,convenient and practical.But the signal measurement is not comprehensive under different measurement,which makes it has many restrictions.Multi-fractal method can avoid the limitatior of signle-fractal by measuring of signal characteristic under multiple measure,which makes characteristic features from a single dimension into dimension sequence.For multifractal method,the key point is how to select the appropriate template signal under various measure to complete objective statement of the signal.In this paper,by calculating the correlation coefficient of the mean from collecting more groups of the template signal,we can reduce the negative impact caused by a single template too volatile.Matrix-Fractal method,on the basis of signal decomposition based on multifractal component signals respectively.Characteristic from the dimensions of the two-dimensional sequence to the dimensions of the three-dimensional matrix,due to the volatility better suppress the dimension,so as to make the distinction better.By the way, improving the method of correlation coefficient of determination in order to get matrix forms points correlation coefficient calculation method. For Matrix-Fractal method,the key is to select the appropriate template signal and using scientific signal decomposition method,the former is similar to multifractal by collecting more groups of signal as a template with template to calculate the sum of the correlation coefficient as a judge.The latter should be combined with the characteristics signal decomposition method, in view of the matrix is built and the selection of component signals make some adjustments. Such as the commonly used method of empirical mode decomposition method to get a lot of residual, resulting from the decomposition of residual items should be ignored is not used to build fractal matrices, can effectively detect abnormal. At the same time, in order to obtain the ability to distinguish between optimal weight signal, the signal filtering method based on correlation coefficient,combined with the template signal, select the ability to distinguish between optimal weight signal is used to construct the optimal matrix, the fractal can be greatly enhanced ability to distinguish between, better realize the judgement of state.