The paper presents a mathematical model for assessing the situational awareness of the space system. The model includes a set of algorithms, the main ones being the algorithm for simulating the motion of a spacecraft in a highly elliptical orbit, the algorithm for determining the observability of a given controlled area by a given spacecraft in a highly elliptical orbit at a given time, and the algorithm for determining the observability of a given controlled area by a spacecraft in a geostationary orbit. The model allows the assessment of the information capabilities of a space system of various ballistic structures and compositions. A model numerical example is considered, which makes it possible to compare observability indices of a given control region with two possible variants of a ballistic construction of a spacecraft constellation. The results of the numerical experiment showed the correctness of the proposed mathematical model.
Interval systems of linear algebraic equations (ISLAE) are considered in the context of constructing of linear models according to data with interval uncertainty. Sufficient conditions for boundedness and convexity of an admissible domain (AD) of ISLAE and its belonging to only one orthant of an n-dimensional space are proposed, which can be verified in polynomial time by the methods of computational linear algebra. In this case, AD ISLAE turns out to be a convex bounded polyhedron, entirely lying in the corresponding ortant. These properties of AD ISLAE allow, firstly, to find solutions to the corresponding ISLAE in polynomial time by linear programming methods (while finding a solution to ISLAE of a general form is an NP-hard problem). Secondly, the coefficients of the linear model obtained by solving the corresponding ISLAE have an analogue of the significance property of the coefficient of the linear model, since the coefficients of the linear model do not change their sign within the limits of the AD. The formulation and proof of the corresponding theorem are presented. The error estimation and convergence of an arbitrary solution of ISLAE to the normal solution of a hypothetical exact system of linear algebraic equations are also investigated. An illustrative numerical example is given.
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