In the Kalman filter toolbox at http://becs.aalto.fi/en/research/bayes/ekfukf/cwpa_demo.html the example code shows that a function lti_disc is called, which is essentially a matrix exponential function. What is the purpose of such matrix exponentiation? Given a really simple transition model such as, e.g.
F = [ 1 0 ; 0 1 ] ;
and doing the matrix exponentiation with lti_disc will always give a different transition matrix A, depending on the values of the Q process noise covariance, which is also an input to the lti_disc function.