System Basis

Fundamentals

The Head Track System presented in these lines is based on the measurement of the earth magnetic field (from now EMGF).

EMGF can be represented as a vector what we will call M.

We have represented a coordinates system xyz with the vector M inside.

The xy plane is parallel to the earth surface, and the z axis is perpendicular to the earth surface.

- Mx, My, Mz represent the components of M over xyz; 

- α and δ represent the angles formed by M to the coordinates system.

M, leaves the earth with a certain angle from its surface, and the component of M parallel to the earth surface (formed by Mx and My, the green one), always points to the magnetic north.

Looking the xy plane from above 

NOTE: to simplify comprehension, we have represented the xy plane "reflected"

If we knew the M projection over xy plane (the green vector) , we could determine Mx & My and vice versa: if we knew Mx & My we could determine the magnitude of the M projection over the xy plane. Moreover, knowing all these data, we could determine α through the basic trigonometry.

=> In other words, if we were able to measure Mx & My, we could determine the angle that forms our reference system in respect to the magnetic north. And is in this way how the Head Tracking System determines the horizontal angle

Let's continue with the explanation

If the reference system xyz is tilted respect to the earth surface, this is equivalent to tilt the vector M respect to the reference system, which is the same to change the angle δ.

Changing the angle δ, the green vector (an therefore Mx & My) changes too but not the angle α which remains constant.

Seen from above:

So if we were able to measure the maximum magnitude (in absolute terms) of the M vector  we could determine what are its Mx & My components and therefore what's the value of the angle δ, given that the projection of M over xy is proportional to M and to the cos(δ).

=> In other words: if we were able to measure Mx and My and the maximum value of M, we could determine the α angle  (between our system coordinates and the magnetic north) and the  δ angle.

And is in this way how the Head Tracking System determines the horizontal and vertical movements.

The Head Tracking System presented here, uses 2 magnetic sensors (magnetoresistive sensors) each one perpendicular to the other. Both measure simultaneously the projection of the EMGF (Mx & My) above them.

The system needs to be calibrated in order to work properly. Through calibration process, maximum values of Mx & My are determined, which should match with the maximum value of  M

Once Calibrated, the system is ready to work.

As a magnetic sensor, the head track system may not work properly in the proximity of big metallic things.

Practical Approach :

The system has 2 magnetic sensors which must be calibrated before  processing sampled data.

After calibration, magnetic sensors will be measured through a sampling process.

Once sampled, some process will be necesary to determine α and  δ angles.

CALIBRATION

=> Determine max value of Mx and My (through calibration process).

Once calibrated, these values remain constant.  

=> Sampled values of Mx and My (Msx and Msy) must be normalized, and the normalized sampled values of Mx and My, will be Mnx & Mny:

=> α, δ angles are calculated as follows:

Where Mn is the normalized value of M which is equal to 1.