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  5. Model of navigation errors in anomal gravitational earth field

Model of navigation errors in anomal gravitational earth field

S. Herasimov, D. Makarchuk, A. Kostenko
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Description: When solving the navigation problem with the help of inertial navigation systems that are under the influence of the Earth's gravitational field, the unknown "anomalous" part of the gravitational field is a source of navigation errors. When analyzing the accuracy of inertial navigation, there is a need for simultaneous consideration of perturbations generated both by an anomalous gravitational field and instrumental errors of sensory elements-gyroscopes, accelerometers, described, as a rule, by methods of the theory of random processes. The aim of the article is to develop a model of errors in the anomalous gravitational field of the Earth. It is established that when analyzing the accuracy of inertial navigation, there is a need for simultaneous consideration of perturbations that are generated both by an anomalous gravitational field and instrumental errors of sensing elements by methods of the theory of random processes. It is shown that significant advantages are obtained when using the model of the anomalous gravitational field of the Earth of a random field given on an infinite plane. This is due, first, to the simplification of the relationships between the characteristics of the field, and secondly, to the possibility of using compact field transformations for random fields on an infinite plane. The model of the description of the anomalous gravitational field of the Earth is improved. Such a model, in contrast to the existing ones, simultaneously takes into account the perturbations that are generated both by the anomalous gravitational field and the instrumental errors of the sensing elements of gyroscopes through the introduction of a random isotropic field given on an infinite plane. Relationships between the errors of the inertial system in the development of coordinates and course of the object, on the one hand, and errors in the construction of the vertical and the inertial three polyhedron from the other are obtained. The resulted equations of errors of construction of a vertical taking into account errors of platform horizon with an accelerometer.


Keywords: gravity field of Earth, model, errors of navigation, gyroscopes, accelerometers

Reference:
 Herasymov, S.V., Makarchuk, D.V. and Kostenko, O.I. (2018), “Model pokhybok navihatsii v anomalnomu hravitatsiinomu poli Zemli” [Model of navigation errors in anomal gravitational earth field], Scientific Works of Kharkiv National Air Force University, Vol. 3(57), pp. 109-114. https://doi.org/10.30748/zhups.2018.57.16.