To get orientation as a from of euler angles (e.g., pitch, roll, azimuth) in Android, it is required to execute followings:
In the first one, I realize that it uses a kind of TRIAD algorithms; Rotation matrix (R[]) is composed of gravity, geomagnetic X gravity, gravity X (geomagnetic X gravity) --- X is cross product.
See codes below:
float Ax = gravity[0];
float Ay = gravity[1];
float Az = gravity[2];
final float Ex = geomagnetic[0];
final float Ey = geomagnetic[1];
final float Ez = geomagnetic[2];
float Hx = Ey*Az - Ez*Ay;
float Hy = Ez*Ax - Ex*Az;
float Hz = Ex*Ay - Ey*Ax;
final float normH = (float)Math.sqrt(Hx*Hx + Hy*Hy + Hz*Hz);
if (normH < 0.1f) {
// device is close to free fall (or in space?), or close to
// magnetic north pole. Typical values are > 100.
return false;
}
final float invH = 1.0f / normH;
Hx *= invH;
Hy *= invH;
Hz *= invH;
final float invA = 1.0f / (float)Math.sqrt(Ax*Ax + Ay*Ay + Az*Az);
Ax *= invA;
Ay *= invA;
Az *= invA;
final float Mx = Ay*Hz - Az*Hy;
final float My = Az*Hx - Ax*Hz;
final float Mz = Ax*Hy - Ay*Hx;
if (R != null) {
if (R.length == 9) {
R[0] = Hx; R[1] = Hy; R[2] = Hz;
R[3] = Mx; R[4] = My; R[5] = Mz;
R[6] = Ax; R[7] = Ay; R[8] = Az;
} else if (R.length == 16) {
R[0] = Hx; R[1] = Hy; R[2] = Hz; R[3] = 0;
R[4] = Mx; R[5] = My; R[6] = Mz; R[7] = 0;
R[8] = Ax; R[9] = Ay; R[10] = Az; R[11] = 0;
R[12] = 0; R[13] = 0; R[14] = 0; R[15] = 1;
}
}
However, I cannot understand SensorManager.getOrientation().
azimuth = (float)Math.atan2(R[1], R[4]);
pitch = (float)Math.asin(-R[7]);
roll = (float)Math.atan2(-R[6], R[8]);
What is the exact algorithms to get euler angles?
Let me try to explain: getRotationMatrix compose rotation matrix on the basis of gravity and megnetic vector.
Our main goal here is to construct NED frame
We assume that gravity points toward the center of the Earth and magnet to the north Pole. But in real cases these vectors are non-perpendicular, that's why we firstly calculate vector H that is orthogonal to E and A and belong to tangential plane. H is a cross-product (E x A) and is orthogonal to E and A.
float Hx = Ey*Az - Ez*Ay;
float Hy = Ez*Ax - Ex*Az;
float Hz = Ex*Ay - Ey*Ax;
final float normH = (float)Math.sqrt(Hx*Hx + Hy*Hy + Hz*Hz);
normalize acceleration and H vector (because these vectors will compose a basis of ENU coordinate system)
final float invH = 1.0f / normH;
Hx *= invH;
Hy *= invH;
Hz *= invH;
final float invA = 1.0f / (float)Math.sqrt(Ax*Ax + Ay*Ay + Az*Az);
Ax *= invA;
Ay *= invA;
Az *= invA;
Find last basis vector (M) as cross-product of H and A:
double Mx = Ay * Hz - Az * Hy;
double My = Az * Hx - Ax * Hz;
double Mz = Ax * Hy - Ay * Hx;
Coordinates of the arbitrary vector (a) in body frame expresses through NED coordinates as a = Ra' R - Transformation matrix matrix, whose columns are the coordinates of the new basis vectors in the old basis
But coordinates in NED frame are calculated as a' = T^(-1) * a. For orthogonal transformation matrix inverse is equal to transposed matrix. Thus we have:
R[0] = Hx; R[1] = Hy; R[2] = Hz;
R[3] = Mx; R[4] = My; R[5] = Mz;
R[6] = Ax; R[7] = Ay; R[8] = Az;
Once we have rotation matrix we can convert it to Euler angles representation. Formulas of convertion depend from convention that you use. Your formulas
azimuth = (float)Math.atan2(R[1], R[4]);
pitch = (float)Math.asin(-R[7]);
roll = (float)Math.atan2(-R[6], R[8]);
are correct for Tiat Bryan angles with convention Y-X-Z. In order to better understand conversion from rotation matrix to Euler angles I would suggest to study an article of Gregory G. Slabaugh - "Computing Euler angles from a rotation matrix"