Hello Peter
For some reasons your last post has not appeared in my news browser, so I cannot reply it directly. But I've read this in google's archives.
I'd rather not introduce additional variables in my state vector. I assume that the system has a consant velocity and I am using accelerations as noise just to predict what Q should look like and see whether I can trust the results I get from the data.
If by innovation you mean z-H*x(k/k-1), its covariance is mainly diagonal. Its 2 x 2, because measurement z contains only positions, not velocities. If you are asking about corelation of w1 = x(k/k)-x(k/k-1), then position and velocity along one coordinate (e.g position x and vx) are corelated, but not in the same way as: w2 = xtrue - x(k/k-1) (here I know the true values because I check this method for a generated sequence). the latter, cov(w2) is more or less similar to:
Q= |0.25C, 0.5C| |0.5C , C |
but the former, cov(w1), is sth like:
[3
*C1 2*C1] [2*C1 C1 ]
with C1 being sth like:
[ a 0] [ 0 b]
where a is generally greater than b. (More or less agrees with standard deviations I introduced on ax and ay to generate the process noise) So the correlation tendency seems to be inverted in some way. If I use the result as my initial Q, it does not converge, but oscilates with these proportions maintained.
Concerning gestures, I am aware, that various gestures produce different covariance. My intention is to work on sign language gestures, so I think it is possible to determine a covariance matrix which will embrace most signs. But as I mentioned, let Q determined from the predictions be large, its ok until it agrees with the process noise covariance found using true position values.
Regards
Piotr