UDC 519.68:15:681.5

V.M. Grinyak, T.M. Grinyak, Y.S. Ivanenko

Current paper is about problem observation system based on range or range difference measurer. The paper discusses the formulation and approaches to the solution of the two-coordinate task of the exhibition (local coordinate binding) of a multi-position system intended for monitoring mobile objects for various special purposes (underwater, surface, surface, air, etc.). Such systems continue to be relevant both for traditional navigation tasks and for new types of surveillance tasks, for example, navigation of mobile devices based on GSM or WiFi data. The mathematical model of the exhibition problem based on equations of the “state-measurement” type of continuous type and finite-dimensional representations of the method of least squares is formulated. Because of the initial nonlinearity of the problem, it is proposed to linearize it about some support solution that characterizes the a priori notions of the state of the observation system. Attention is paid to the problem of resolvability of the problem from the point of view fundamental resolvability (observability) and resolvability in conditions of instrumental measurement errors. The first aspect of solvability is interpreted by the completeness of the rank of the corresponding system of linear algebraic equations, the second by the conditionality of the problem and the convergence of the iterative estimation procedure. The results of numerical simulation of the problem for typical situations are presented. It is shown that achievable accuracy of the exhibition is sufficient for a qualitative solution of navigational problems.

Keywords: beacon system, observation, navigation, positioning, observability, conditionality, range, distance difference.

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