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Method of the neural network assessments reproduction in determining the linear dependency parameters containing normal and non-stationary noise

Keywords:

Е. А. Samoylin – Dr.Sc. (Eng.), Professor, Military educational-scientific center of air forces «Military air academy professor N.E. Zhukovskiy and Yu.A. Gagarin». E-mail: es977@mail.ru
М. А. Pantuyhin – head of Department of the research center, Military educational-scientific center of air forces «Military air academy professor N.E. Zhukovskiy and Yu.A. Gagarin». E-mail: ol-max@mail.ru


The method of the neural network assessments reproduction while determining the linear dependency parameters is offered. The observations include both normal and non-stationary noise. The results of numerical study confirm higher accuracy characteristics as compared to the standard least-squares procedure and well-known neural network methods. Currently there is a wide range of tasks connected with the functional dependencies parameters estimation by the experimental data. Such tasks include the trajectory radar data processing while testing rocketry and aviation equipment, the price range prediction, etc. The errors of measurement in such tasks can be normal (stationary with some dispersion and null mathematical expectation) and abnormal (non-stationary with unkhown or unstochastic structure). The standard procedures such as the least-squares method and the convergence method did real good in normal noise conditions, while neural networks are successfully used in the presence of abnormal noise. Particularly the learning set cortege method, which presupposes determining the degree of each error abnormality and subsequent exchange of the learning set in a way that teaching neural network was in order of noise abnormality reduction, is used. It allows to significantly raise the accuracy of required dependencies parameters estimation. Whereas, the high level parallelism of neurons in such models opens up new possibilities like parallel processing of the same assessments in case of input data pattern variations with the further density generating of these assessments. This fact underlay the suggested method of the neural network assessments reproduction. It involves multiple random selection of learning pairs from the initial set and the subsequent creation of neural network assessments. With regards to accumulated multitude assessment densities are built, which allows to make a decision about reliable values based on their maximum. The results of numerical study produce higher accuracy characteristics as compared to the standart least-squares procedure in normal-abnormal conditions. Moreover it can be modified by adding the training set cortege procedure to raise the accuracy of the estimation even more.
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