Getting magnetic field values in global coordinate

问题:

For an Android application, I need to get magnetic field measurements across the axis of global (world's) coordinate system. Here is how I'm going (guessing) to implement this. Please, correct me if necessary. Also, please, note that the question is about algorithmic part of the task, and not about Android APIs for sensors - I have an experience with the latter.

First step is to obtain TYPE_MAGNETIC_FIELD sensor data (M) and TYPE_ACCELEROMETER sensor data (G). The second is supposed to be used according to Android's documentation, but I'm not sure if it shouldn't be TYPE_GRAVITY instead (again as G), because accelerometer seems providing not the pure gravity.

Next step is to get rotation matrices via getRotationMatrix(R, I, G, M), where R and I are rotation and inclination matrix correspondingly.

And now goes the most questionnable part: in order to convert M vector into the world's coordinate system, I suppose to multiply [R * I] * M.

I'm not sure this is a correct way for transforming magnetic field reading into another basis. Also, I don't know if remapCoordinateSystem should be used in addition or as replacement for something above.

If there exists some source code which does this thing already, I'd appreciate posting a link, but I don't want to use big general purposes libraries (for example, for augmented reality support) for this specific task, because I'd like to keep it as simple as possible.

P.S.

I came to the idea to add some information to the original post for clarity.

Let us suppose a device rests on a table and continuously reads data from its magnetic sensor. Each measurement contains 3 values, presenting magnetic field in axis X, Y, Z, which are device's local coordinate system. I take it that I can neglect environmental field fluctuations (smoothed by lowpass filter), so this 3 values should remain almost the same all the time the device remains in place. If we rotate device around any axis, the values change, because we change the local coordinate system. But the field itself is not actually changed. So I want to translate local X, Y, Z field measurements into such X', Y', Z', that they keep their respective values regardless to device rotation, provided that device is not moved from its location (only rotated).

I've implemented the algorithm described above and got regular and noticable changes in values X', Y', Z', obtained through suggested transformations, so there is something wrong in it.

P.P.S.

Occasionally I've found an exact duplicate of my question here on SO - How can I get the magnetic field vector, independent of the device rotation? - but unfortunately the answer contains my suggestions, and OP of that question confirms that they do not work.

回答1:

The coordinates of M with respect to the word coordinate is just the multiplication R*M.

The rotation matrix R is mathematically the change of basis matrix from the device coordinate to the word coordinate. Let X, Y, Z be the device coordinate basis and W_1, W_2, W_3 be the word coordinate basis then
M = m_1 X + m_2 Y + m_3
and also
M = c_1 W_1 + c_2 W_2 + c_3 W_3
where R * (m_1, m_2, m_3) = (c_1, c_2, c_3) transpose.

Low pass filter is only used to filter out accelerations in the X, Y directions. RemapCoordinateSystem is used to change the order of the basis, ie changing from W_1, W_2, W_3 to W_1, W_3, W_2.

回答2:

The magnetometer sensor on your device returns a 3-vector in device coordinates. You can use getRotationMatrix() to get a matrix that could be used to convert that device-coordinates vector to world coordinates. You could also learn about Quaternions and use TYPE_ROTATION_VECTOR directly. However, there's no Quaternion library in Android (that I know of) and that's a discussion beyond the scope of this question.

However, none of this will do you any good because the device orientation information is based in part on the value from the magnetometers. In other words, the device will always tell you that the magnetic vector is facing exactly North.

Now, what you can do is get magnetic dip. This is one of the outputs from getRotationMatrix(), although you'll have to convert a matrix to an angle for it to be useful. That too, is beyond the scope of this question.

Finally, your last option is to build a table which is level and which has an arrow on it pointing true north. (You'll have to align it by the stars at night or something.) Then, place your device flat on the table with the top of the device facing north. In this case, device coordinates will be the same as world coordinates and the magnetometer sensor will produce the values you want.

Your comments indicate that you're interested in local variations. There's simply no way to get true north with your Android device alone. Theoretically, you could build a table as I described, and then walk around holding the device in strictly the same orientation as before, keeping an eye on the table for reference. I doubt you could pull it off, though.

You could try using gyros in your app to help you keep the device oriented exactly the same way at all times, but the gyros in any Android device you use are likely to drift too much for this to work.

Or perhaps we still don't understand what you're trying to do. Bottom line, though, is that you simply cannot get a global coordinate system with an Android device alone -- whatever you get will always be aligned with the local magnetic field at that exact spot.