I have the following system:

Code: 
X(k) = alpha*trueVal(k) + Noise            //Volume measurement
Y(k) = beta*X(k) + Noise                    //Pressure measurement
k = day1, day2, day3, etc
In my system I measure the volume about 2 hours before the pressure measurement. So, basically I am trying to predict the pressure 2 hours after volume has been measured.

Of course I do not know what trueValue(k) is. Also X(k) is iid. So, even though it is a time series in terms of day1, day2, etc., X(k) does not depend on X(k-1), or X(k-2), etc.

What kind of regression, machine learning or state-space model can I use for finding alpha and beta?

I do not think I can use Kalman filter because it requires Markov assumption on X(k).

Thanks in advance