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A mathematical model for studying the structure of errors the parameters of motion the aircraft at smoothed processing of trajectory measuring information with use of methods the dynamic filtration


V.G. Naidenov, V.I. Polyakov, A.N. Sсhukin

Since received as a result of statistical processing of the primary trajectory measurements evaluation of the parameters of motion of aircraft are random processes, and analysis of errors of such assessments should be carried out with the use of probabilistic characteristics inherent in the random processes. With this purpose in the article for the first time solved the problem of constructing practically implemented the algorithm of formation the correlation function of error the estimate of the vector the parameters of motion the aircraft for the case of smooth processing of trajectory measurements using dynamic filtering, which allows you to define the structure of the errors the estimates the vector of this parameters and evaluate a number of their other probabilistic characteristics. In addition, the developed mathematical apparatus enables to construct the correlation functions of discrete stochastic processes errors estimation of the vector of parameters of movement of aircraft during the smooth processing of trajectory measurements for the cases when the values of the coefficients of stochastic equations that describe the real dynamic model of the motion of aircraft in the space of states and a real model errors primary trajectory measurements that match or do not match with the corresponding values of coefficients, given in the estimated the models that have been selected to build a particular algorithm of processing of trajectory measurement information. The results of the study developed a mathematical model for estimation of the structure of the errors the parameters of the motion the aircraft in the smooth processing of trajectory measurements with the use dynamic filtration have shown its performance. The application of such a model makes it possible to determine the structure of the errors of the parameters of motion the aircrafts during a smooth processing of trajectory measuring information, evaluate the variance and correlation times of these errors. In addition, the developed model allows to estimate the influence on the values of the unknown the parameters of motion the aircrafts residuals between the values of the coefficients in the estimated models partially observed processes inherent in the filter parameters and values, which correspond to the real picture of the natural measuring experiment.
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