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Aerospace Instrument-Making

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Analytical solution of linear differential error equations of strapdown inertial navigation system, functioning in the normal geographic reference frame, for the object, following the earth parallel with constant speed and on the constant height
Chelnokov Y.N. Loginov M.Y.

Analytical solution of linear differential error equations of strapdown inertial navigation system, functioning in the normal geographic reference frame, for the object, following the Earth parallel with constant speed and on the constant height, is derived. The solution describes the influence of the inaccurate initial conditions of integration (initial alignment of the strapdown INS) on the precision of determination of altitude, longitude and latitude of the object, and also the projections of ground velocity of an object on the axes of the normal geographical frame. The roots of the auxiliary equation, which are used for deriving the solution, are expressed in terms of unperturbed motion parameters. The solution is represented in the form, which is convenient for the analysis.The solution is valid for the case when there are no instrumental errors of gyroscopes and accelerometers. Obtained results can be used, for example, for analysis of the accuracy of strapdown inertial navigation system. The example of using a solution is shown, in which for some specific case of object motion the analysis of INS errors and also the analysis of harmonic components of the solution is performed.
Key words: inertial navigation, strapdown inertial navigation systems, strapdown INS errors, analytical solution of error equations, parallel.


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