# Using kalman filter when samples don't have time index

Assume $X$ and $N$ are two sets of observations from two different normal distribution, where $X$ represents clean data and $N$ represents noise; and $A$ a projection matrix of a filter and the relation between $X$ and $Y$ defines as:

$Y=A \times X + N$

considering that $X_i$ are not sequential samples and are just different observations from a normal distribution (there is no time involved), are we allowed to use a Kalman filter to estimate $A$ and parameters of $N$?

My example in your last post, which solves this problem using a Kalman Filter, shows you can use non-time dependent observations, in any order, to estimate $A$ and $N$. It's called using Kalman Filters for parameter estimation.