3

The quaternion part [q_x, q_y, q_z, q_w] has four numbers but is a representation of 3D orientation, which has 3 degrees of freedom. Another common representation for orientation is the matrix Lie group $\mathrm{SO}(3)$, which is the group of $3\times 3$ rotation matrices (9 numbers, but only 3 degrees of freedom). Neither the quaternion nor the rotation ...


3

I don't know if this is mathematically sound or not, but it's given me good results in practice. What I've done in this situation personally, when I expect/know that there is a bias, is to include the bias as a state in my state space representation of the system. For example, if I have a system to track position, I might write the state space models like: $$...


1

Adding to Parker's answer, the quaternion is avoided many cases due to its complexity in getting a closed-form Jacobian. Also, it unnecessarily increases the number of optimization states. Due to these problems rotation vector (3x1) is usually preferred and that's why you see it as 3x1. Note that the rotation vector is different from Euler angles and does ...


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