How to implement Kalman to merge the data obtained by two Leap Motion devices?

Question

Only position data is obtained from Leap Motion devices. This data was already processed to be on the same coordinate axis by means of a homogeneous transformation.

I'm reviewing WTF is Sensor Fusion? The good old Kalman filter, but it considers speed and acceleration, data that I don't need and my doubt arises if they are all necessary to implement the Kalman filter, as I just need to get the correct estimate of the position between the Leap devices.

I would appreciate a response that clarifies the implementation of these matrices for this case.

Answer 1

You don't need speed and acceleration in your Kalman filter. A Kalman works on any state vector, the components of that vector could be anything, and not necessarily positions. They could be water densities, magnetic field strengths, you name it.

In your case the state vector is just the components of the position.

Of course how you implement the predict phase of the Kalman is up to you. Typically one predicts the new positions by multiplying the velocties by the timestep to get a position delta and then adding that on to the original position. Your velocity is not in the state but that's irrelevant. You can estimate a velocity based on the previous positions, you can make it as simple or as sophisticated as you want. Ultimately you are going to have to predict the new positions based on the previous ones if that's all you've got.

The update phase ought to be straightforward as your expected measurements are simply the predicted positions.