Article 9313

Title of the article

RECURSIVE ESTIMATION OF THE PARAMETERS
OF A MATRIX OUTPUT IN MULTIVARIATE LINEAR AUTOREGRESSIVE INTERFERENCE IN OUTPUT 

Authors

Ivliev Aleksandr Sergeevich, Postgraduate student, Samara State University of Railway Transport (18 1st Bezymyannyy lane, Samara, Russia), Sanja_ivliev@mail.ru 

Index UDK

519.254 

Abstract

Background. There is quite a number of recursive methods of simulation of dynamic systems with noise in the input and output signals, which differ in required a priori information about the signals and noise, volume calculations, the accuracy of the estimates. With a variety of dynamic system parameters, input signals and interference different methods show the best results in individual cases. In this respect, the most urgent task is to develop simulation methods that would combine high estimation accuracy, low a priori information about the object with moderate computational complexity for different system parameters, the input signal and noise.
Materials and methods. This article deals with the problem of identification using the recursive parameter estimation matrix linear autoregression. The described recurrent algorithm is applied in finding estimates of parameters of the model by stationary hindrances in the form of white noise supervision in output signals in case
there is no information on their laws of distribution.
Results. The proposed stochastic gradient algorithm of minimization proves strong consistency of estimation of
the parameters of the matrix and shows the convergence of the matrix parameters and their true values. One of the main factors of safe railway transportation is to ensure the safety of the trains, which, in turn, depends on the values of the geometric parameters of the rail track. According to this, the most urgent task is to construct a mathematical model of such a dynamical system and prognosticate geometrical parameters on the base of this analytical model.
Conclusions. The implementation of the proposed algorithm allows to create software that can form the basis of new highly automated process control systems and mathematical models in various fields of science. This article represents a model of predicting geometric parameters of a dynamic system, which is a tool for solving the problem of simulation. 

Key words

identification, strongly consistent estimates, linear autoregression, positive definiteness, random Markov process. 

Download PDF
References

1. Katsyuba O. A., Ivanov D. V. Novye informatsionnye tekhnologii v issledovanii slozhnykh struktur: tezisy dokladov Sed'-moy Rossiyskoy konferentsii s mezhdunarodnym uchastiem [New information technologies in research of complex structures: abstracts of VII Russian conference with international participants]. Tomsk: Izd-vo NTL, 2008, p. 97.
2. Derevitskiy D. P., Fradkov A. L. Prikladnaya teoriya diskretnykh adaptivnykh sistem upravleniya [Applied theory of discrete adaptive control systems]. Moscow: Nauka, 1991, 215 p.
3. L'yung L. Identifikatsiya sistem. Teoriya dlya pol'zovatelya [System identification. Theory for a user]. Moscow: Nauka, 1991, 432 p.
4. Tsypkin Ya. Z. Informatsionnaya teoriya identifikatsii [Information theory of identification]. Moscow: Nauka, 1995, 336 p.
5. Gantmakher F. R. Teoriya matrits [Matrix theory]. Moscow: Nauka, 2010, 560 p.

 

Дата создания: 28.08.2014 14:01
Дата обновления: 28.08.2014 15:56