I have a Kalman filter problem please.

xt=u+z(1,t-1)+x(t-1)+d·[y(t-1)-x(t-1)]+e(x,t)

yt=u+z(2,t-1)+y(t-1)-d·[y(t-1)-x(t-1)]+e(y,t)

z1 and z2 are AR(1) processes

z(1,t)=p1z(1,t-1)+e(1,t)

z(2,t)=p2z(2,t-1)+e(2,t)

The observations are xt and yt

The state variables are z1 and z2

The errors have mean zero and are Gaussian.

The variance-covariance matrix for the vector ex,ey,e1,e2 is :

sx^2

sxy sy^2

sx1 sy1 s1^2

sx2 sy2 s12 s2^2

There is contemporaneous correlation between the errors, however there are no intertemporal correlation, ie, no correlation of any sort for the error across the periods.

Please note the state variable exists as lagged one period behind in the observational variable.

Can someone please work out the complete Kalman filter law of iteration for the estimated state variable z1 and z2, filter gain, and steady state value for filter variance P0, in this forum or send me pdf?

I am from biology background and this level of maths is beyond me. Thank you.