and are not neccessarily Gaussian

In this case, the Linear-Gaussian model is still useful. By assuming the system to be of the above form (that is, Linear, Gaussian, and Markov) we gain a great deal of computational simplicity. For many systems, over suitable time-intervals, this sub-optimal model may be quite suffiecient. Of course, for moderately non-linear systems this may be completely useless. Just as we approximate Dynamical Systems with Linear Approximations, we may consider this model the ``linearized'', ``first-order'' approximation.

We begin by finding an orthogonal basis for . We may implement standard Gramm-Schmidt orthogonalization in as follows: