If I have $m$ measurements to estimate an $n$ dimensional state vector, and I am using Kalman filter to do the filtering, then: Should I put all the $m$ measurements together in the measurement matrix (measurement transformation matrix ) and perform the filtering or, should I filter each measurement sequentially? Please provide some supporting explanation for your choice.

For e.g: Let $m=2$ and $n=3$. The state vector is 3 dimensional and we need to use the two measurements to get the posterior estimate the state vector. Now I can use one of these two methods:

1. Use all these measurements together to form a gain matrix of size $3\times 2$.

2. Use one measurement at one time and perform the filtering two times. The gain matrix will be $3\times 1$ in this case.

Which of the two methods is a better choice?

For e.g: Let $m=2$ and $n=3$. The state vector is 3 dimensional and we need to use the two measurements to get the posterior estimate the state vector. Now I can use one of these two methods:

1. Use all these measurements together to form a gain matrix of size $3\times 2$.

2. Use one measurement at one time and perform the filtering two times. The gain matrix will be $3\times 1$ in this case.

Which of the two methods is a better choice?