Quaternion kinematics for the error-state Kalman filter
نویسنده
چکیده
This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the rotation group and its Lie structure, with formulations using both quaternions and rotation matrices. It makes special attention in the definition of rotation perturbations, derivatives and integrals. It provides numerous intuitions and geometrical interpretations to help the reader grasp the inner mechanisms of 3D rotation. The whole material is used to devise precise formulations for error-state Kalman filters suited for real applications using integration of signals from an inertial measurement unit (IMU). 1 Quaternion definition and properties 1.1 Definition of quaternion One introduction to the quaternion that I find particularly attractive is given by the CayleyDickson construction: If we have two complex numbers A = a + bi and C = c + di, then constructing Q = A+ Cj and defining k , ij yields a number in the space of quaternions H, Q = a+ bi+ cj + dk ∈ H , (1) where {a, b, c, d} ∈ R, and {i, j, k} are three imaginary unit numbers defined so that i = j = k = ijk = −1 , (2a) from which we can derive ij = −ji = k , jk = −kj = i , ki = −ik = j . (2b)
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ورودعنوان ژورنال:
- CoRR
دوره abs/1711.02508 شماره
صفحات -
تاریخ انتشار 2017