Model Engineering of the Task of the Platform-Less Navigation System's Orientation
- Paper number
IAC-06-E2.3.05
- Author
Mrs. Tatjana Mokschankina, Dniepropetrovsk National University, Ukraine
- Coauthor
Mr. Dmitriy Fedorenko, Ukraine
- Year
2006
- Abstract
The task of model engineering of the object’s orientation parameters in platform-less inertial navigation system (PINS) is being considered. There are three methods of determination of the object’s orientation parameters for the mathematical modeling of the inertial coordinate system in PINS (the determination of the transition matrix from coordinate system with fixed axis to inertial coordinate system). They are: • Using Euler’s kinematic equations; • Integration of the elements of the direction cosine matrix; • Using quaternion’s instrument. The application of quaternions allows expressing orthogonal converting in the form of quaternion’s multiplication. The operations on quaternions assume the matrix formulation. Quaternions are used for determination of the orientation parameters of the solid in any attitude, in contrast to Euler’s kinematic equations, which degenerate for some value of Euler - Krilov’s angles. The method of determination of the solid’s attitude using Euler’s kinematic equations is more bulky in comparison with determination of the solid’s attitude using quaternion’s instrument. While integrating of the elements of the direction cosine matrix the order of the differential equations can be reduced from the ninth to the sixth. The elements of the third row of the matrix are determined by vector product: In this method the object’ orientation angles are not determined. In all three methods of determination of the direction cosine matrix in right parts of the differential equations the information of the rotational sensors is used. The algorithm and the software of the task solution of navigation are developed for two methods of determination of the orientation parameters and different models of theEarth’s gravitation field. The development of the quaternion’s algebra software is done. The comparative description of the object’s navigation and orientation parameters is realized. The expediency of using different methods of determination of the object’s orientation parameters is illustrated. In the software preference is given to the method of using quaternion’s instrument.
- Abstract document