Vins theory and code explanation 0 -- theoretical basis in vernacular

VINS One of the more difficult problems in is the calculation of quaternion rotation , Derivation, etc . Therefore, this part should be explained separately .
1. It involves the basic properties of rotating quaternions
stay SLAM All quaternion rotations involved in are unit quaternions , This is important , So say it alone , This sum SLAM The rotation matrix in is consistent , Because the rotation matrix is orthogonal , Neither of them will change the size of the state quantity , It's just a change in direction . The representation of quaternions and the basic operations book are very clear , Not much .
2. Quaternion derivation
This part is in VINS Is very important , Because it usually involves IMU This part of the theoretical knowledge is needed to solve quaternion rotation by integration .

VINS In the calculation IMU The second derivative is used when pre integrating and rotating quaternions , Later, the first derived formula is used to solve the Jacobi and covariance moment array state error propagation equation .

3. Quaternion and 3D Derivation of point product
set up Pc=q*Pw, among Pc Is the point in the camera coordinate system ,Pw Is a point in the world coordinate system . From the above formula, we can see , The increment of the moving quaternion can be determined by δθ Express , So ask Pc Increment quaternion δθ The reciprocal of a quaternion can be expressed as the reciprocal of a quaternion .

This part is very useful in finding the visual Jacobian matrix , In fact, the derivation process is similar to SLAM The left multiplicative perturbation models of Lie Algebras in Lecture 14 are similar .