Can someone help me with a Kalman Filter problem?

I'm tying to implement a Kalman filter for a system of 6 dependent variables. The purpose is to define 6 stock prices (i) as the sum of a common factor between all the stocks and an individual factor, both of which are unobserved of course.

The measurement equation should be:

Price(i,t) = lambda1 * common(t) + lambda2 * individual(i,t) + error where lambda1 and lambda2 should be time dependent.

Both the common and the individual factor follow an AR(1) process in the transition equation:

common(t) = a* common(t-1) + error (a is the autocorrelation coefficient)

individual(i,t) = b* individual (t-1) + error (b is the autocorrelation coefficient)

I'm stuck on how to define two transition equations in the system and how to write them as an AR(1) process.

Can someone help me with this?

thanks