I am assuming you are using phone to collect gyroscope+magnetometer
data.
You cannot calculate Heading with Gyro+Magnetometer
unless you know initial state of device. You have to try Accelerometer+Magnetometer
. You can get heading values from rotation-matrix' or
yaw` component from Motion sensor API of Android/IOS device.
If you want to implement of your own try tilt-compensation algorithm. All you have to do is implement tilt- compensated ecompass using accelerometer
and magnetometer
. You get accelerometer
and magnetometer
readings in device frame. Accelerometer
and Magnetometer
gives readings as a function of rotation of device. This rotation contains information of Roll, Pitch and Heading of device. Following is explanation and derivation of heading estimation using accelerometer+magnetometer
.

Tilt compensation algorithm
Let accelerometer
and magnetometer
give you

readings respectively. They are in device frame, and device is rotated through
.
Where
is heading you are looking for. So rotation matrix of device will be



We have to solve for
. So step by step solving for
.

From above, equating to zero we get

Having
from above


This is basic method of obtaining Heading value from accelerometer+magentomete
. Yaw/Heading value is provided by Motion sensor APIs present in mobile phones.
You have to look at few things while implementing sensor-fusion
algorithms. Accelerometers
doesn't always gravity direction, it gives direction of ovarall acceleration experienced by the sensor eg, devices under linear accelerations. Magnetometer
readings are subjected distortion due to ferromagnetic substances in vicinity. Accuracy depends on systematic bias component in gyroscope
sensor too.
There are numerous algorithms to estimate accurate heading values. Some of them are