Abstract
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.
Highlights
Accurate representations of the rigid body orientation is important in design and analysis of strapdown inertial navigation systems (SINS), which are widely used in aerospace engineering
A key step in developing the orientation algorithm is the estimation of error in determining the orientation, when the orientation quaternions are computed within a time cycle [tn−1, tn]
We find that according to Eq (22), this quaternion corresponds to the following angular velocity vector components ωi (t) = [2kβ, 2kα cos(2kβ t), −2kα sin(2kβ t)]
Summary
Tn−1 where ω(t) is the angular velocity vector and θ n is the apparent rotation vector. In [7], a series of algorithms for the determination of the rotation quaternion is developed, which have different orders up to the fourth inclusive Another approach is based on the Taylor time series decomposition of sine and cosine functions of half true rotation angle in the representation of the orientation quaternion components and the use the rotation vector as an intermediate parameter [22]. Optimization is based on obtaining an analytical expression for the algorithm error in the form of a stepped series with further determination of unknown coefficients, based on the condition of cutting off the highest order terms of the series Another method, which implements essentially the same approach, was presented in [13]. Conclusions are drawn with respect to the value of the accumulated drift error based on the derived two-frequency models if compared to the conventional case of regular precession, discussed in the literature
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