Comment by ajb

In most cases the data a kalman filter is working on has some precision which is much lower than the available precision in the floating format you are using. The problem is inherently a statistical one, since the expected precision depends on the statistics of your data source.

So you would probably adopt some conservative approach in which you showed that the worst case floating point rounding error is << some quantile of error due to the data.

But, I think specialised tools are more commonly used than general process. Eg, see https://github.com/arpra-project/arpra