Yu.G. Bulychev – Honored Scientist of RF, Dr.Sc.(Eng.), Professor, 

JSC «VNII «Gradient» (Rostov-on-Don)

E-mail: ProfBulychev@yandex.ru

A.V. Melnikov – Ph.D.(Econ.), General Director Assistent, 

JSC «Rossiskaya Elektronika» (Moscow)

E-mail: alex1338@yandex.ru

A.G. Kondrashov – General Director

JSC «Scientific Production Association «Kvant» (V.Novgorod) E-mail: ao@kvant-vn.ru.

P.Yu. Radu – Engineer,

JSC «Kaluga Scientific Research Radio Engineering Institute» E-mail: radupavel@ya.ru

Among well-known works based on the methods of supporting integral curves and the generalized optimal invariant-unbiased estimation, a uniform method is developed for approximate analytical solution of an equation describing a dynamic object and calculating the values of various continuous linear functionals (hereinafter also referred to as the numerical characteristics) of the dynamic object integral curves based on the incorrect data. It was about the data that may contain singular disturbance. In addition to the above, the set of supporting integral curves was used to build the solution, and the idea of autocompensation optimal estimation which is invariant to singular disturbance and does not require the traditional state space extension, was used to find values of the continuous linear functionals.

The disadvantages of this method include the fact that only a scalar dynamic object is considered, and the integral curve of the dynamic object directly serves as the measured parameter, and this, as a rule, does not exactly complies with the needs of the practice. In addition, this means only estimation of the continuous linear functionals of this curve although the estimation of numerical characteristics (for example, derivatives of various orders) of the measured output of the dynamic object is more relevant for most applied problems. Thus, the task of finding the derivatives of bearings (azimuth and elevation) of the moving emission sources, measured by each receiving station of the system, is very important for triangulation measurement systems. The use of the above numerical characteristics allows to solve critical tasks of predicting angular trajectories (in the case of breakdown and omission of observations) and identification of bearings.

The present article is concerned with removing the shortcomings of the well-known method and focused on real data measuring systems, the construction of which «accuracy-efficiency» criterion is basic taking into account the severe restrictions to the computing resources, which requires ensuring the greatest possible decomposition and parallelization of the applied algorithms. Two-stage numerical analytic method should be developed for solution of the multi-dimensional dynamic object equation, depending on all its parameters, as well as autocompensation-decomposition estimation of the continuous linear functionals from the measured parameters of the multi-dimensional dynamic object output, which does not require state space extension, calculating spectral coefficients, as well as introducing linearization procedures (even with nonlinear vector equations of the dynamic object state and measurements).

1. Bulychev Yu.G., Melnikov A.V. Chislenno-analiticheskii metod issledovaniya povedeniya dinamicheskoi sistemy po rezultatam nekorrektnykh nablyudenii bez rasshireniya prostranstva sostoyanii. Zhurnal vychisl. matem. i matem. fiz. 2019. T. 59. № 6. S. 937−950. (in Russian)
2. Bulychev Yu.G. Metod opornykh integralnykh krivykh resheniya zadachi Koshi dlya obyknovennykh differentsialnykh uravnenii. Zhurnal vychisl. matem. i matem. fiz. 1988. T. 28. № 10. S. 1482−1490. (in Russian)
3. Bulychev Yu.G., Eliseev A.V. Vychislitelnaya skhema invariantno-nesmeshchennogo otsenivaniya znachenii lineinykh operatorov zadannogo klassa. Zhurnal vychisl. matem. i mat. fiz. 2008. T. 48. № 4. S. 580−592. (in Russian)
4. Vorobev L.M. K teorii poleta raket. M.: Mashinostroenie. 1970. (in Russian)