Using the Kalman filter to determine beta in a regression Is the Kalman filter applicable to determine beta coefficients of a multiple regression?( 1 dependent & 3 independent variables in a time series type regression analysis)
 A: As user cardinal pointed out in the comment below, the Kalman filter is applicable for updating  you can flip the problem around and consider updates to the present parameter vector, $\beta_n$.
We have the re-interpreted prediction/observation equations for one additional data point:
$\beta_{n+1} = \beta_n$
$y_n=\beta_n'X_n+v_n$
Begin with estimates $\beta_{\text{init}}$ and $P_{\text{init}}$ and perform updates as:
$r = y_n - \beta_{\text{prev}}'X_n$
$s = X_n' P_{\text{prev}} X_n+\sigma_n^2$
$G = P_{\text{prev}}X_n/s$
$\beta_{\text{next}}=\beta_{\text{prev}}+Gr$
$P_{\text{next}}=(1-X_n'G)P_{\text{prev}}$
$\beta_{\text{init}}$ and $P_{\text{init}}$ come from a full multiple regression on previous data. $\sigma_n^2=\text{Var}(v_n)$ is a modeling choice that lets you control how much you allow the new data point to influence your new estimates.
The Kalman filter is not directly applicable as it has a different purpose. It in fact uses a given $\beta$ and other parameters to make accurate predictions about states $X_n$ given observations $y_n$.
While the observation formulae are equivalent in both cases, in the case of the Kalman filter, $A$,$B$,$C$,$cov(w)$ and $cov(v)$ are provided along with $y_n$ up to some time.
The difference between the techniques is one of parameter estimation (multiple regression) vs state estimation (Kalman filter).
