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

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.

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  • $\begingroup$ Can one assume $\boldsymbol{R}$ and $\boldsymbol{Q}$ are constant for your case? $\endgroup$
    – Royi
    Commented 14 hours ago
  • $\begingroup$ @Royi Not 100% but once they change, they are usually constant for a long period of time. So for all practical purposes, yes we can assume they are contant. $\endgroup$ Commented 13 hours ago

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