I have a filter to detect when a slow moving signal (oven temperature) reaches steady state. I am using a linear regression of a moving window and looking at the slope. Based on the equations for linear regression including $\sum xy$, $\sum x^2$ and $(\sum x)^2$ I am thinking this is a non linear filter, is this true? Is it still true to say this is a FIR filter though?
Also if I am trying to get an estimate for reaching steady state is there a better filter, or can similar quality be achieved with a linear filter given Gaussian noise? Basically I am looking for a good theoretical analysis of this type of filter to way its pros and cons?