Estimation of the accuracy of determining the coordinates of the observed object by the space triangulation system

Аuthors

Belikhin E. N.^*, Shchelkov D. A.

Mlitary spaсe Aсademy named after A.F. Mozhaisky, Saint Petersburg, Russia

*e-mail: Saint Petersburg, Russia 1vka@mil.ru

Abstract

The authors of the article note topicality of the space objects’ position determining task. This statement is being set forth forcefully by the growing number of space objects of various origins threatening domestic spacecraft. The authors choose the space triangulation method as a position determining method. Further, the authors point at the necessity for studying the system accuracy characteristics impact on the object under observation position determining error.
The article indicates the initial data, as well as accepted limitations and assumptions. Besides, it introduces the concepts of the error longitudinal and transverse components in the distance determining between the spacecraft of an orbital segment.
Subsequently, the authors present one of the basic equations of the space triangulation, intended for computing the distance to the object being observed. With trigonometric transformations based on the said equation, the authors obtained analytical expressions, which reflected the measurement error dependence on the distance determining error between the spacecraft in the orbital segment. These expressions are employed to the graphs plotting. Analyzing the graphs, the authors of the article draw several conclusions. Firstly, as the transverse component of the error increases, the measurement error increases nonlinearly. Secondly, the appearance of the graphs depends on the combination of viewing angles of the space object. For example, with the sum of the angles of ninety degrees, the measurement error is minimal. Thirdly, the transverse component of the error contributes significantly to the overall error in determining the position of the space object being observed.
The authors of the article note that the materials presented in the article may be used in the future when conducting studies on the orbital constellation functioning for triangulation observation of the outer space, as well as formulating requirements to the characteristics of measurement equipment located onboard the spacecraft as a part of this constellation.

Keywords:

space triangulation, measurement error, observation of space objects

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