I have a data set consisting of noisy position values of a trajectory of a human hand. I want to estimate a generative model of these trajectories, and the obvious choice is a Kalman Filter/linear dynamical system.
Since the relationship of position/velocity/acceleration is well known, I chose a LDS with 3 latent variables (for each dimension) and hard coded the transition and emission matrices. I tuned the variances as diagonal covariances via "occular inspection".
(I maybe should have learned all the parameters via EM, with possibly more stats, with a prior on the model parameters somewhat, I know.)
Having done that, I realized that the LDS struggled with sudden changes of direction. Thus I wondered whether the assumption that acceleration is actually Gaussian distributed is correct.
Now I have several questions.
- How would I check whether the Gaussian assumption is a good one? One problem is, that I cannot get a reliable sample from the accelerations, since even the position signals have outliers, and so the outliers of the second derivative will be even more severe.)
- What state space models are there that do not assume Gaussianity all over the place? Which of those have inference fast enough to be usable in a real time system with ~20 predictions a second?
- Does anyone have any experiences with similar settings and might have any advice on which models to use?