Are matrix decomposition based Kalman filter algorithms faster or more robust?

Question

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.

Answer 1

The naive implementation is not numerically stable. The truncation error (because of finite word length) could destroy the result.

For real life application, it is necessary to use more robust (with respect to numerical error) implementation. For example, U-D factor implementation is one of the most robust implementation.

Many industry products include special designed numerical error capture part to reset the Kalman filtering.