But i have some problems…
My device need to calculate velocity and traveled path of the car. As you said in comment 79 :”Accelerometer measures combined gravity Rg and device acceleration Ra: Rag = Rg + Ra”. Then you calculated Ra using magnitometer data. So i have 2 questions:

1) If we use magnitometer+accelerometer, gyro isn’t needed? Can gyro improve results?
2) Can we calculate Ra from Rag using only gyro+accelerometer, without magnitometer.

Would it be possible to accept data from two seperate serial ports and plot the received data on one chart?
Also could we have a feature to add a scale(s) for X & Y axis?

Thanks

Barry

I am trying to measure roll and pitch degree of moving object (sort of a cylinder).
I am bit of confuse, is that your algorithm can measure roll pitch degree of moving object?

Thank You

I’m an engineering student doing work with an autonomous UAV for my
senior project. Your website has been a tremendous help and I’d like
to say thanks for all your hard work.

I have a question about your filter algorithm and I’d like to know if
there’s a flaw in my logic. The question begins with understanding
that orientation, or the pitch and roll, of the UAV can be found
relatively accurately using the accelerometer as a reference and the
gyroscope as a temporary heavily-weighted input that will be corrected
over-time due to the fact that once movement stops, the accelerometer
will gain more weight. This fights the gyroscopic drift.

However, once external forces are applied, this accelerometer
reference is no longer valid as gravity is not the only force. There
are linear forces at work. BUT, and here’s my question, would it be
possible to record pitch and roll of the UAV the SPLIT second before
those external linear forces were applied (assuming no rotation is
going to occur during linear translation) and use the current roll and
pitch to calculate the the g’s caused by gravity alone? What you would
be left with are the linear accelerations picked up by the
accelerometer.

Could this gravity vector be put back into your normal algorithm? At
the present moment, I don’t see why not. No rotations are occurring
and even if they were, the gyroscope would register them and adjust
the pitch and roll angles.

So for example, the UAV tilts 30 degrees and takes off in the X
direction. Eventually more than 1g is registered and the current
orientation is used to calculate where exactly the gravity vector is.
This gravity vector fuels the REstimated vector in your original
algorithm. Changes in pitch or roll are registered by the gyroscope.

Is there something wrong with this logic? This seems like a good way
to isolate linear accelerations. I feel like although there’s some
circular logic in there, so I wanted to contact you and make sure. As
long as the roll and pitch can be obtained accurately, I feel as
though this algorithm is self-sustaining.

Please let me know your thoughts!

W = Z x M ( where “x” is the vector cross product), note order is important, use right-hand coordinate system rule.

Then obtain North (N) , as a vector perpendicular to bot Z and W simply get:

N = W x Z

Or in one formula

N = (Z x M) x Z , using triple product formula

N = (Z.Z) M – (M.Z)Z , where “.” is the scalar dot product , since Z is a unit vector this becomes

N = M – (M.Z) Z
The scalar -(M.Z) = -cos(M,Z)|M||Z| = -cos(M,Z) ( since M,Z unit vectors) is the correction term , you can visualize this as if it pulls the uncorrected vector M away from Z depending on the angle between M and Z.
Note that in particular if M is perpendicular to Z , then M.Z = 0 , so N = M as expected.

Finally you may want to normalize N to make sure it is a unit vector:

N’ = Normalize(N)

This is a very nice article. It explains the concepts of a DCM very well.
I wonder about one thing though. The North vector the magnetometer is pointing at is not perpendicular to the Zenith vector. It is pointing into the ground in a northerly direction. The angle with the XY plane, or surface of the earth, is the inclination of the earth magnetic field.

I myself am in the middle of incorperating the magnetometer into a 6DOF IMU so I am not really sure about how to cope with this. But I think you have to transform the compass vector to the world frame, then you can correct for the inclination to make the Vector perpendicular to the Zenith vector. The result is transformed back to the body frame. After that it can be used like you describe.