Attitude reconstruction from strap-down rate gyros using power series

This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

Performance Evaluation of Direction Cosine Matrix and Madgwick’s as 3D Orientation Estimation Algorithm for Estimating Ground Contour

Contour interval is elevation difference between two contour lines that are adjacent and parallel. Ground Contour interval is an important information that must be provided in a construction. Ground contour interval estimation problem could be viewed as a 3D trajectory estimation problem. One framework, called dead reckoning, is often used for motion (position and orientation) tracking of a mobile systems over time. Dead reckoning requires a precise 3D orientation estimation algorithm. Two competing algorithms are Direction Cosine Matrix and Madgwick’s. To ensure the 3D trajectory estimation gives an accurate result, these two algorithms must be carefully and thoroughly evaluated. This research is part of a complete research on the development of a ground contour estimation and only focuses on comparison between two 3D orientation estimation algorithm.