Closed-form analytical representations of the rigid body orientation quaternion, angular velocity vector and the external moment vector satisfying kinematic equations and equations of motion are derived. In order to analyze errors of orientation algorithms for strapdown inertial navigation systems, reference models for specific rigid body rotation cases are formulated. Based on solutions, analytical expressions for ideal signals of angular velocity sensors in the form of quasi-coordinates are derived. For several sets of parameters, numerical implementations of the reference models are performed and trajectories in the configuration space of orientation parameters are presented. Numerical analysis of the drift error for the third-order orientation algorithm is performed. The results show that the value of the accumulated drift error using the derived two-frequency models exceeds the value of the accumulated drift error in the conventional case of a regular precession.
On the basis of a programmed-numerical approach, new values of the coefficients in the Miller orientation algorithm are obtained. For this, an analytical reference model of the angular motion of a rigid body was applied in the form of a four-frequency representation of the orientation quaternion.The numerical implementation of the reference model for a given set of frequencies is presented in the form of constructed trajectories in the configuration space of orientation parameters. A software-numerical implementation of Miller's algorithm is carried out for different values of the coefficients and the values of the coefficients are obtained, which optimize the error of the accumulated drift. It is shown that for the presented reference model of angular motion, Miller's algorithm with a new set of coefficients provides a lower computational drift error compared to with the classic Miller algorithm and the Ignagni modification, which are optimized for conical motion.
Two new three-frequency reference models of solid motion taking into account the vibrational environment are proposed. They are based on a four-frequency reference model of rotation [1], which implements rotations according to Krylov angles. For the developed models the analytical dependences for quasi-coordinates, projections of the angular velocity vector and components of the quaternion of orientation corresponding to such rotational motion are obtained.
The urgency of taking into account the influence of vibration in traffic modeling on the basis of domestic and foreign literature in the field of navigation, including for the last 10 years. The main sources of vibration are described in detail and what types of oscillations they correspond to - harmonic oscillations occur in moving elements of onboard systems, such as the engine rotor, and in the engine unit and its units there are oscillations that have the character of random broadband noise. Methods of correction of such influence for increase of accuracy of definition of orientation of object are analyzed. The location of the components of the platformless inertial navigation system relative to the vibration sources is considered to be related to the strength of the influence of the vibration environment on the accuracy of the obtained data.
Numerical implementations of the models are obtained and the drift error for the third-order orientation algorithm is estimated for several sets of specified parameters in a certain way. The parameters are chosen arbitrarily, but taking into account the existing restrictions on angular motion. The corresponding figures show the result for one of these sets of numerical values (which shows the result of the research in the most detail). The obtained results are compared with the corresponding results for the four-frequency rotation model [1]. The expediency of using new three-frequency models under certain conditions is shown.
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