Sequential processing of uncorrelated measurements in Kalman Filter 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 $x$.
I think it is evident in both cases. It follows directly from
$$ P(A|B,C,D) = P(((A|B)|C)|D)$$
.i.e.
$$P(x[k]\!=\!\hat{x}[k]|\!\hat{z}_1[k]\!=\!z_1[k],\!\hat{z}_2\![k]\!=\!z_2[k])\!=\! P\Bigg(
  \Big(
      x[k]\!=\!\hat{x}[k]|\!\hat{z}_1[k]\!=\!z_1[k]
  \Big)|\!\hat{z}_2[k]\!=\!z_2[k]
\Bigg)$$
As long as you don't do a prediction update it should be fine.
For nonlinear system, you won't get the same exact estimate, because you will end up with a new dynamics, input, measurement and feedback matrices on every "single-measurement" update