# Finding North direction from magnetometer and accelerometer fusion

I was understanding accelerometer and gyro sensor fusion from this video. At time 3:56, Brian says:

To get north, we need to do some cross products. We can start with our measured mag (magnetometer) and accel vectors in the body frame.

1. Down is the opposite direction of the acceleration vector and then
2. East is the cross-product of down and the magnetic field and finally
3. north is the cross-product of East and down.

So the orientation of the body is simply the rotation between the body frame and the Northeast down frame and I can build the direction cosine matrix directly from the north east and down vectors that I just calculated.

I understand that "down is the opposite direction of the acceleration vector". But I dont get how "East is the cross-product of down and magnetic field". Q1. Can someone help me understand this (in the context of facts that I know as noted below)?

I know:

• By the right hand rule for cross product, cross product of two 3D vectors is a new 3D vector is perpendicular to both vectors and thus normal to the plane containing them
• In NED frame, all axes are perpendicular to each other. So we can get any axes vector by taking cross product of rest two (correct me if am wrong). So, in case of NED, cross product of North and Down will give East (again, correct me if am wrong). But magnetometer direction is earth's magnetic North pole, a bit different from geographic North. Q2. So does the points 2 and 3 in quotes trying to find geographic North from magnetic North pole?

Q3. If yes to Q2, wont cross product of East and down will give back magnetic North (that is, measured magnetic field), instead of geographic North?

PS: robotics noob here!