I'm starting to brush up on the Kalman Filtering I learned a couple decades ago. From what I remember, if you have a measurement vector
$$ z=H x + v $$ and the $n$ components of the measurement noise $v$ are uncorrelated with each other, then you can process the measurements sequentially in the KF equations. Is there a good reference somewhere (preferably online) that discusses why this is so? Intuitively it is understandable if each measurement $z$ depends on only one state element in $x$, but it isn't obvious if each measurement of $z$ depends on several elements of $x$.