А.V. Ivanov – Dr.Sc. (Eng.), Professor,

Tambov State Technical University

E-mail: resbn@jesby.tstu.ru

V.О. Surkov – Post-graduate Student,

Tambov State Technical University

E-mail: surkov-v@mail.ru

N.А. Lezhneva – Investigator,

LLC Airport Management Company Limited (Domodedovo)

E-mail: Volchitsa9389@mail.ru

Abstract

The article discusses the synthesis of identification quasi-optimal algorithms and adaptive estimation of discrete-continuous processes.

When using global satellite navigation system in navigation systems, several problems have to be solved simultaneously: coordinates and motion parameters estimation of mobile objects;

evaluation of radio signals at the input of equipment for receiving signals from global satellite  navigation systems; assessment of transmitted service information; monitoring the integrity of navigation data.

Theoretically, the solution of these problems is reduced to the problem solution of identification and adaptive estimation of discretecontinuous processes. A feature of the problem is that discrete-continuous processes are evaluated in conjunction with the identification problem. Identification is the refinement of slowly changing processes observations that describe meter errors. Due to the fact that these processes at long intervals of time are almost constant, their sharp change is associated with a violation of the navigation data integrity. In this case, the identification problem is considered as a problem of parametric estimation. The novelty is that the discrete process is a two-component composite process, each component of which is a vector process, and the continuous process is a multicomponent diffusion process.

The problem of synthesis of optimal identification algorithms and adaptive estimation of discrete-continuous processes is formulated. To describe the change discrete processes states, a mathematical model is used in the form of discrete Markov processes. The change in the multicomponent diffusion process in time is described by a vector-matrix differential stochastic equation.

To obtain optimal algorithms, a joint vector discrete-continuous process is formed. Using the methods of the Markov theory of random process estimation according to the maximum a posteriori probability density criterion, optimal identification algorithms and adaptive estimation of discrete-continuous processes are obtained. However, the optimal algorithms implementation based on the posterior distributions calculation is associated with significant difficulties. Using a Gaussian approximation method, an a posteriori probability density of a slowly changing process is obtained in the a normal distribution form. Expressions are derived in the recurrence equations form describing the normal distribution parameters, namely: the mathematical expectation vector and the matrix of posterior variances of estimation errors.

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