Android phone orientation overview including compass

Question

You might want to check out the One Screen Turn Deserves Another article. It explains why you need the rotation matrix.

In a nutshell, the phone's sensors always use the same coordinate system, even when the device is rotated.

In applications that are not locked to a single orientation, the screen coordinate system changes when you rotate the device. Thus, when the device is rotated from its default view mode, the sensor coordinate system is no longer the same as the screen coordinate system. The rotation matrix in this case is used to transform A to C (B always remains fixed).

Here's a code snippet to show you how it can be used.

SensorManager sm = (SensorManager) getSystemService(SENSOR_SERVICE);

// Register this class as a listener for the accelerometer sensor
sm.registerListener(this, sm.getDefaultSensor(Sensor.TYPE_ACCELEROMETER),
                    SensorManager.SENSOR_DELAY_NORMAL);
// ...and the orientation sensor
sm.registerListener(this, sm.getDefaultSensor(Sensor.TYPE_MAGNETIC_FIELD),
                    SensorManager.SENSOR_DELAY_NORMAL);

//...
// The following code inside a class implementing a SensorEventListener
// ...

float[] inR = new float[16];
float[] I = new float[16];
float[] gravity = new float[3];
float[] geomag = new float[3];
float[] orientVals = new float[3];

double azimuth = 0;
double pitch = 0;
double roll = 0;

public void onSensorChanged(SensorEvent sensorEvent) {
    // If the sensor data is unreliable return
    if (sensorEvent.accuracy == SensorManager.SENSOR_STATUS_UNRELIABLE)
        return;

    // Gets the value of the sensor that has been changed
    switch (sensorEvent.sensor.getType()) {  
        case Sensor.TYPE_ACCELEROMETER:
            gravity = sensorEvent.values.clone();
            break;
        case Sensor.TYPE_MAGNETIC_FIELD:
            geomag = sensorEvent.values.clone();
            break;
    }

    // If gravity and geomag have values then find rotation matrix
    if (gravity != null && geomag != null) {

        // checks that the rotation matrix is found
        boolean success = SensorManager.getRotationMatrix(inR, I,
                                                          gravity, geomag);
        if (success) {
            SensorManager.getOrientation(inR, orientVals);
            azimuth = Math.toDegrees(orientVals[0]);
            pitch = Math.toDegrees(orientVals[1]);
            roll = Math.toDegrees(orientVals[2]);
        }
    }
}

Roll is a function of gravity, a 90 degree roll puts all of gravity into the x register.

Pitch is the same, a 90 degree pitch up puts all of the component of gravity into the y register.

Yaw / Heading / azimuth has no effect on gravity, it is ALWAYS at right angles to gravity, hence no matter which way you are facing gravity will be imeasurable.

This is why you need a compass to assess, maybe that makes sense?