Minimization of Satellite Measurements in Positioning Objects Moving Along Analytical Model Trajectories

The paper considers the solution to the problem of increasing the accuracy of positioning objects moving along program trajectories by combining nonlinear filtering methods when processing primary satellite measurements with an analytical dependence of the navigation vector components that occurs on individual types of program trajectories and significantly reduces its dimensionality. Equations based only on satellite measurements that describe the dynamics of the spatial coordinates of an object and are invariant to its physical and technical characteristics are obtained, and an equation for an observer of spatial coordinates based on primary pseudorange measurements is derived. A distinctive feature of the approach is the use of the idea of approximating the program trajectory of a moving object with a set of trajectory segments that allow an analytical description in the space of object coordinates. Orthodromic (shortest) and ring intervals that are most typical for program trajectories of ground transport and civil aviation are considered as such segments. For ring trajectories, functional dependencies of spatial coordinates have been obtained for the first time, providing a sharp reduction in the volume of calculations in stochastic estimation algorithms with a simultaneous significant increase in positioning accuracy compared to traditional methods of processing satellite messages. A numerical experiment has been conducted, confirming the possibility of effective practical application of the developed approach.