What's the most computationally efficient implementation of Kalman Filter

Question

I know there are many formulations of the Kalman Filter. A few I can name are:

• Classical Covariance Form
• Informational Filter Form
• Square-Root Form or Factor Form

But somehow it's hard for me to find a summary of their pros and cons from the computational standpoint. I want to find the computationally cheapest solution.

In my use case, my state transition matrix is the identity (the $F$ matrix in wikipedia) and the state transition noise covariance $Q$ matrix has a nice principal component structural (I can just take the first dozens of eigenvalues to compress the covariance matrix). My observation vector size is usually at least 1/3, sometimes more than the state vector. My $R$ (observation noise) is diagonal. We can assume $R,Q$ are constant for all practical purposes

But I'd like to hear more about this computation complexity topic in general.