Active noise cancellation using kalman filter
I guess you use the LMS and RLS filters because they are adaptive, and you can do the same thing with the Kalman filter, if you augment the state-vector with the parameters of the model. You then get a non-linear system, and you can solve that using any number of non-linear Kalman-filter implementations, the most common being the extended Kalman filter (EKF), then second most common the unscented Kalman filter (UKF), and then there are a fair few more exotic variants, such as the second order Kalman filter. The convergence properties of any of these filters have not been proved, but they seem to work really well in practice. The UKF is typically regarded as better than the older EKF, since it does not require the inversion of the Jacobian, and it behaves as a higher order approximation -- 3rd order for Gaussian noise I seem to remember (compared to first order for the EKF).

The EKF is perhaps a bit more straight forward to get started with. You use the EKF for parameter adaptation by modeling unknown parameters as Wiener processes. Consider the linear system
\begin{align*}
 \dot{x} &amp;= A(\theta) x + B(\theta) u + w \\
 y &amp;= C(\theta) x + v
\end{align*}
with unknown parameters $\theta \in \mathcal{R}^{p}$. By augmenting the state vector to include the unknown parameters, $\chi^{\text{T}} = [x^{\text{T}}, \theta^{\text{T}}]$, we obtain the non-linear system $\dot{\chi} = f(\chi,u) + w$, $y = h(\chi) + v$, where
\begin{align*}
 f(\chi,u) &amp;=
 \left[ \begin{array}{c} 
  A(\theta) x + B(\theta) u \\
  0
 \end{array} \right] \\
 h(\chi) &amp;= C(\theta) x .
\end{align*}
The Jacobians $F$ and $H$ for this system are found as
\begin{align*}
 F &amp;=
 \left[ \begin{array}{cc} 
  A(\theta) &amp; \frac{\partial}{\partial \theta}[A(\theta) x + B(\theta) u] \\
  0 &amp; 0
 \end{array} \right]_{\hat{x}, \hat{\theta}} , \\
 H &amp;= 
 \left[ \begin{array}{cc} 
  C(\theta) &amp; \frac{\partial}{\partial \theta}[C(\theta) x]
 \end{array} \right]_{\hat{x}, \hat{\theta}} .
\end{align*}

The general implementation of the EKF and UKF, as well as for parameter adaption, can be found in several publication. I personally like "Optimal State Estimation: Kalman, H$_{\infty}$, and Nonlinear Approaches" by Dan Simon, 2006 (ISBN: 978-0-471-70858-2).