My recent pastime interest deals with the nonlinear sensor fusion of GNSS, barometer, magnetometer, accelerometer and gyroscope data. I had a look at the EKF, UKF and Particle Filters but gave up as it would have taken me far too much time to understand these filters sufficiently well since I am a structural engineer by training.
I have therefore decided to do things my way. What I came up with was a space-time finite element where the Hermitian shape functions represent the position coordinates, the local magnetic north vector as well as a rotation angle. The latter two can be indirectly transformed into the orientation quaternion. Each finite element represents a certain timespan and contains the corresponding sensor data. The error of the sensor data interpolation within an element is minimized with the help of a Newton based approach. Due to computational constraints it is obviously not possible to connect an increasing number of finite elements as time progresses. I have therefore used static condensation to get the gain from previous elements so that only one element is considered at any time.
My problem now is that this works remarkably well. Far better than I thought that it would. I therefore believe that something like this must already exist. However, I have very little insight into this field so that I would be grateful if some experts could put this approach into the right perspective and give me some feedback.
I have uploaded the preprint of this approach that contains all the details and an example to arXiv
Many thanks in advance.