Sensor fusion with compass and gyroscope: between 0 and 360 degrees

Question

I'm developing a small indoor navigation app in which I use the gyro and the compass for the device orientation. I use the gyro to smooth the compass data. My sensor fusion looks like the following. This is my motionHandler where everything happens.

// Listen to events from the motionManager
motionHandler = ^ (CMDeviceMotion *motion, NSError *error) {

        __block float heading;
        heading = mHeading;

        CMAttitude *currentAttitude = motion.attitude;

        //Initial heading setting
        if (lastHeading == 0 && heading != 0) {
            updatedHeading = heading;
        }
        lastHeading = heading;

        if (oldQuaternion.w != 0 || oldQuaternion.x != 0 || oldQuaternion.y != 0 || oldQuaternion.z != 0){
            diffQuaternion = [self multiplyQuaternions:[self inverseQuaternion:oldQuaternion] :currentAttitude.quaternion];
            diffQuaternion = [self normalizeQuaternion:diffQuaternion];
        }            
        oldQuaternion = currentAttitude.quaternion;

        diffYaw = RADIANS_TO_DEGREES([self yawFromQuaternion:diffQuaternion]);         

        quaternion = currentAttitude.quaternion;

        //Get Pitch
        rpy.pitch = -[self pitchFromQuaternion:quaternion];
        rpy.pitch += M_PI/2;                        

        //Use Yaw-Difference for Heading
        updatedHeading = updatedHeading - diffYaw;

        //Heading has to be between 0 and 360 degrees
        if (updatedHeading < 0) {
            updatedHeading = 360 + updatedHeading;
        }
        else if (updatedHeading > 360) {
            updatedHeading -= 360;
        }

        //fusionate gyro estimated heading with new magneticHeading
        updatedHeading = (19.0*updatedHeading + 1.0*heading)/20.0;

        //generate queternion
        rotation = [self createFromAxisAngle:0 :rpy.pitch :DEGREES_TO_RADIANS(updatedHeading)];
    };

The actual sensor fusion formula is this line: updatedHeading = (19.0*updatedHeading + 1.0*heading)/20.0;. And this is my didUpdateHeading-function which receives the newest heading-information:

- (void)locationManager:(CLLocationManager *)manager didUpdateHeading:(CLHeading *)newHeading
{
    // Get new heading
    mHeading = newHeading.magneticHeading;    

    mHeading += 90;

    if (mHeading > 360) {
        mHeading -= 360;
    }
}

diffYaw is the change of the heading computed by the gyroscope. rotation ist the final quaternion. This works perfect, except one particular case: at the transition between 0 und 360 degrees.

If updatedHeading is near to but smaller than 360 and mHeading is just above 0 the result moves in a circle. For example if updatedHeading = 355 and mHeading = 5, the correct result should be between 360 and 5. But my formula computes 337,5 degrees, which is clearly completly wrong!

There have to be any common workarounds for this problem, I think…

Answer 1

I usually do something like the following in these types of angle computations:

updatedHeading -= angleDiff(updatedHeading, mHeading) * 0.05;

where angleDiff() is:

double angleDiff( double angle1, double angle2 )
{
    double angle = angle1 - angle2;
    if( angle > 180 ) {
        angle -= 360;
    } else if( angle <= -180 ) {
        angle += 360;
    }
    return angle;
}

You may want to get updatedHeading back in the 0-360 range after this by:

updatedHeading = fmod( updatedHeading + 360, 360 );

Your example gives 355.5 with this computation.