DeviceMotion relative to world - multiplyByInverseOfAttitude

Question

What is the correct way to use CMAttitude:multiplyByInverseOfAttitude?

Assuming an iOS5 device laying flat on a table, after starting CMMotionManager with:

CMMotionManager *motionManager = [[CMMotionManager alloc]init];
[motionManager startDeviceMotionUpdatesUsingReferenceFrame:
    CMAttitudeReferenceFrameXTrueNorthZVertical];

Later, CMDeviceMotion objects are obtained:

CMDeviceMotion *deviceMotion = [motionManager deviceMotion];

I expect that [deviceMotion attitude] reflects the rotation of the device from True North.

By observation, [deviceMotion userAcceleration] reports acceleration in the device reference frame. That is, moving the device side to side (keeping it flat on the table) registers acceleration in the x-axis. Turning the device 90° (still flat) and moving the device side to side still reports x acceleration.

What is the correct way to transform [deviceMotion userAcceleration] to obtain North-South/East-West acceleration rather than left-right/forward-backward?

CMAttitude multiplyByInverseOfAttitude seems unnecessary since a reference frame has already been specified and it is unclear from the documentation how to apply the attitude to CMAcceleration.

Answer 1

The question would not have arisen if CMDeviceMotion had an accessor for the userAcceleration in coordinates of the reference frame. So, I used a category to add the required method:

In CMDeviceMotion+TransformToReferenceFrame.h:

#import <CoreMotion/CoreMotion.h>

@interface CMDeviceMotion (TransformToReferenceFrame)
-(CMAcceleration)userAccelerationInReferenceFrame;
@end

and in CMDeviceMotion+TransformToReferenceFrame.m:

#import "CMDeviceMotion+TransformToReferenceFrame.h"

@implementation CMDeviceMotion (TransformToReferenceFrame)

-(CMAcceleration)userAccelerationInReferenceFrame
{
    CMAcceleration acc = [self userAcceleration];
    CMRotationMatrix rot = [self attitude].rotationMatrix;

    CMAcceleration accRef;
    accRef.x = acc.x*rot.m11 + acc.y*rot.m12 + acc.z*rot.m13;
    accRef.y = acc.x*rot.m21 + acc.y*rot.m22 + acc.z*rot.m23;
    accRef.z = acc.x*rot.m31 + acc.y*rot.m32 + acc.z*rot.m33;

    return accRef;
}

@end

and in Swift 3

extension CMDeviceMotion {

    var userAccelerationInReferenceFrame: CMAcceleration {
        let acc = self.userAcceleration
        let rot = self.attitude.rotationMatrix

        var accRef = CMAcceleration()
        accRef.x = acc.x*rot.m11 + acc.y*rot.m12 + acc.z*rot.m13;
        accRef.y = acc.x*rot.m21 + acc.y*rot.m22 + acc.z*rot.m23;
        accRef.z = acc.x*rot.m31 + acc.y*rot.m32 + acc.z*rot.m33;

        return accRef;
    }
}

Now, code that previously used [deviceMotion userAcceleration] can use [deviceMotion userAccelerationInReferenceFrame] instead.