How to calculate Heading using Gyro and magnetometer

I have raw data of Gyroscope and magnetometer. on basis of this data, i have to calculate Heading information with an accuracy of 1Deg.

I would like to know, is there any algorithm which can help me to get heading info using available information with mentioned accuracy?

Any article or any link also will be helpful.

Thanks

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– ankhzet
Jan 28 '16 at 12:31

The question is too broad in its current form. What algorithm(s) did you try, and where exactly did you get stuck? Note that requests for off-site resources are considered off-topic here.

– njuffa
Jan 28 '16 at 20:38

Check out yaw returned by Phone's motion API

– nbsrujan
Jan 29 '16 at 9:03

1 Answer
1

I am assuming you are using phone to collect gyroscope+magnetometer data.

gyroscope+magnetometer

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' oryaw` component from Motion sensor API of Android/IOS device.

Gyro+Magnetometer

Accelerometer+Magnetometer

rotation-matrix' or

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.

accelerometer

magnetometer

accelerometer

magnetometer

Accelerometer

Magnetometer

accelerometer+magnetometer

Android sensor coordinate system

Tilt compensation algorithm

Let accelerometer and magnetometer give you

accelerometer

magnetometer

$beginbmatrix G_x\ G_y\ G_z endbmatrix and beginbmatrix H_x\ H_y\ H_z endbmatrix$

readings respectively. They are in device frame, and device is rotated through

$\begin{bmatrix} \theta (roll) & \phi (pitch) & \psi (yaw) \end{bmatrix}$ .

Where $\psi (yaw)$ is heading you are looking for. So rotation matrix of device will be

$R = R_y(\theta)*R_x(\phi)*R_z(\psi)$

$beginbmatrix G_x\ G_y\ G_z endbmatrix = R_y(theta)*R_x(phi)*R_z(psi)*beginbmatrix 0\ 0\ g endbmatrix$

$beginbmatrix H_x\ H_y\ H_z endbmatrix = R_y(theta)*R_x(phi)*R_z(psi)*beginbmatrix Bcosdelta\ 0\ Bsindelta endbmatrix$

We have to solve for $\psi$ . So step by step solving for $\psi$ .

$R_x(-phi)*R_y(-theta)*beginbmatrix G_x\ G_y\ G_z endbmatrix = R_z(psi)*beginbmatrix 0\ 0\ g endbmatrix$

From above, equating to zero we get

$tantheta = (-G_x/G_z)\ tanphi = G_y/(-G_x*sintheta + G_z*costheta)$

Having $\theta, \phi$ from above

$resB = R_x(-phi)*R_y(-theta)*beginbmatrix B_x\ B_y\ B_z endbmatrix$

$tan\psi = ResB_x/ResB_y$

This is basic method of obtaining Heading value from accelerometer+magentomete. Yaw/Heading value is provided by Motion sensor APIs present in mobile phones.

accelerometer+magentomete

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.

sensor-fusion

Accelerometers

Magnetometer

gyroscope

There are numerous algorithms to estimate accurate heading values. Some of them are

thank you for your detailed answer. I forgot to mention about my application in my question. My application is related to aviation field. My magnetometer will be located on aircraft vertical fin. I will try this approach also

– Pratik
Jan 29 '16 at 11:26

@Pratik If magnetometer is located on aircraft fin, check out Magnetometer readings once. You have to calibrate keeping magnetometer before you use it, if sensor doesn't calibrate by itself.

– nbsrujan
Feb 1 '16 at 15:33

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