# Uniform prior + Kalman Filter

the context of my questions is the following:

assuming a uniformly distributed random variable ( defined by physics in [a; b]) as a prior I want to identify the correct value of it via the Kalman Filter. As far as I read the KF is only applicable to normally distributed RVs. So my approach would be to transform the uniform RV to a normal RV, do the update and retransform it to a uniform distribution.

First of all, it this approach correct?

Second, if the approach is correct, how do I perform the transformation? All I found was the Box-Muller method, but this method needs two initial uniform RVs. I guess I can somehow just assume a certain 2nd RV to satisfy this condition. However I am not sure how this 2nd dummy RV needs to be defined so that it doesn't break the physical conditions the 1st RV (needs to) satisfies.