Stable solution to the problem of autonomous navigation of moving objects on analytical trajectory intervals based on the results of inertial measurements

Abstract

Provision of solution of the problem of autonomous navigation on a long time interval is considered. The main problem when using inertial navigation systems is caused by the accumulation of positioning and angular orientation errors. It is shown that this problem can be solved by combining methods of nonlinear filtering in processing the results of inertial measurements of platform-free inertial navigation systems and methods of reducing the dimensionality of the vector of navigation parameters on trajectory sections described by analytical models. Orthodromic (shortest) and circular intervals, most typical for program trajectories of transport objects – highways, railroads, airlines, etc., are considered as such trajectory sections. For circular intervals, analytical dependencies of the spatial coordinates of strapdown inertial navigation systems were obtained for the first time. These dependencies make it possible to reduce the dimension of the vector of navigation parameters and, as a consequence, to build a model of an autonomous observer of navigation parameters to use equations excluded from the general system of these parameters. It is shown that using stochastic nonlinear filtering methods it is possible to solve the problem of noise-resistant autonomous navigation on trajectory intervals described by analytical models. The proposed approach to solving the problem of autonomous navigation of moving objects makes it possible to significantly reduce computational costs in the practical implementation of algorithms for nonlinear filtering of current navigation parameters in comparison with traditional models of strapdown inertial navigation systems. The effectiveness of the proposed approach is illustrated with a numerical example. The results obtained are useful in developing navigation support for various transport objects moving along program trajectories, for example, aircraft for various purposes, railway, road, river transport, etc.