Adjustment of multiposition observing system with respect to trajectory measurements

• Grinyak V.M.

  Vladivostok State University of Economics and Service
  Vladivostok. Russia

• Lavrushina E.G.

  Vladivostok State University of Economics and Service
  Vladivostok. Russia

• Bogdanova O.B.

  Vladivostok State University of Economics and Service
  Vladivostok. Russia

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 solvability of the problem from the point of view of three interrelated concepts: fundamental solvability (observability), solvability in conditions of instrumental measurement errors and solvability under conditions of finite accuracy of computer calculations. 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; For the latter, a condition of sufficient type that takes into account the relative accuracy of the representation of real numbers in a computer is formulated. The results of numerical simulation of the problem for typical situations are presented, the solvability of the problem is demonstrated for both the two-coordinate case. 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.