I have been using linear Kalman Filters for several different applications. I wrote the implementation from scratch and it follows Welch & Bishop verbatim in the simplest way.
I have also heard of implementations that employ matrix decompositions, such as SVD. I do a simple matrix inversion in the computation of the K matrix.
My question is what is the advantage of using a less naive approach? Is it for computation speed, robustness or both (or something else)? I haven't had any issues with my implementation, although my data is reasonably well behaved, at least for the moment.