[R] Kalman Filter in Control situation.

[Leeds, Mark (IED)]

you have to be really careful because
There are two versions of the kalman filter in terms of notation ( even
where you don't have exogenous )

Y_t = F_tprime*theta_t-1 + epsilon_t
G_t = G_t*theta_t-1 + omega_t
-----------------------------------------

Y_t = F_tprime*theta_t + epsilon_t
G_t = G_t*theta_t-1 + omega_t

I haven't looked at any of the kalman filter routines ( there something
in the base KalmanLike, dlm package
Has one and I guess dsel and probabyl others ) but I think hey usually
explain which notation they are using.

The two variations above derive different recursions but you get the
same answer at each step
as long as you estimate the variances consistently depending on the
framework.




-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Todd Remund
Sent: Wednesday, December 20, 2006 12:19 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Kalman Filter in Control situation.

I am looking for a Kalman filter that can handle a control input.  I
thought that l.SS was suitable however, I can't get it to work, and
wonder if I am not using the right function.  What I want is a Kalman
filter that accepts exogenous inputs where the input is found using the
algebraic Ricatti equation solution to a penalty function.  If K is the
gain matrix then the exogenous input would be u_t = -Kx_n,  where x_n is
the Kalman filter state estimate.  These inputs would be entered as such
x_t = Ax_t-1 + Bu_t-1 + Ge_t.  Is l.SS in the dse1 package the correct
parametrization of the Kalman filter?

Thank you very much,
Todd Remund

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