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

The article considers the solution to the problem of autonomous navigation of moving objects over long periods of time. The main problem associated with using inertial navigation systems arises from 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 inertial measurement results by strapdown inertial navigation systems with methods for reducing the dimension of the vector of navigation parameters in trajectory segments (intervals) described by analytical models. Orthodromic (shortest) and circular intervals, the most typical trajectories programmed for transportation infrastructure (highways, railroads, airlines, etc.), are considered as such trajectory segments. For circular intervals, analytical dependences between the spatial coordinates of strapdown inertial navigation systems were obtained for the first time. These dependences enable a reduction in the dimension of the vector of navigation parameters and, as a consequence, the use of equations excluded from the general system of these parameters to construct a model of the autonomous observer of navigation parameters. Stochastic nonlinear filtering is shown to solve the problem of autonomous noise-immune navigation on trajectory intervals described by analytical models. The proposed approach to solving the problem of autonomous navigation of moving objects enables a significant reduction in computational costs in implementing algorithms for the nonlinear filtering of actual navigation parameters as compared to the conventional models of strapdown inertial navigation systems. The effectiveness of the proposed approach is illustrated by a numerical example. The obtained results can be useful in the development of navigation support for various means of transportation moving along programmed trajectories, for example, aircraft designed for various purposes, railway transport, road transport, river transport, etc.