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cmatlabvectoraccelerometerquaternions

Kalman filter - quaternions - angle sensor

Kalman filters and quaternions are something new for me.

I have a sensor which output voltage on its pins changes in function of its inclination on x,y and/or z-axis, i.e. an angle sensor.

My questions:

  • Is it possible to apply a Kalman filter to smooth the results and avoid any noise on the measurements?

  • I will then only have 1 single 3D vector. What kind of operations with quaternions could I use with this 3d vector to learn more about quaternions?

Solution

  • You can apply a Kalman filter to accelerometer data, it's a powerful technique though and there are lots of ways to do it wrong. If your goal is to learn about the filter then go for it - the discussion here might be helpful.

    If you just want to smooth the data and get on with the next problem then you might want to start with a moving average filter, or traditional lowpass/bandpass filters.

    After applying a Kalman filter you will still have a sequence of data - it won't reduce it to a single vector. If this is your goal you might as well take the mean of each coordinate sequence.

    As for quaternions, you could probably come up with a way of performing quaternion operations on your accelerometer data but the challenge would be to make it meaningful. For the purposes of learning about the concept you really need it to make some sense, so that you can visualise the results and interpret them.

    I would be tempted to write some functions to implement quaternion operations instead - multiplication is the strange one. This will be a good introduction to the way they work, and then when you find an application that calls for them you can use your functions and you'll already know how the mechanics work.

    If you want to read the most famous use of quaternions have a look at Maxwell's equations in their original quaternion form, before Heaviside dramatically simplified them and put them in the vector notation we use today.

    Also a lot of work is done using tensors these days and if you're interested in the more complex mathematical datatypes that would be a worthwhile one to look into.