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I have a linear state space model (SSM) that looks like this

\begin{align} {\dot {x}} & = {\rm \textbf{A}}{x} + {\rm \textbf{B}}{u} \\ {y} & = {\rm \textbf{c}}{x} \end{align}

I was able to roughly estimate the value of the matrix \$A\$ & \$B\$. While \$C\$ is known! I would like to fine tune the value of the elements of these matrices.

\$\textbf{A}\$ is 4x4, \$\textbf{B}\$ is 3x4, and \$\textbf{C}\$ is 1x4. There are made up from a combination of ten parameters. Can I use the Kalman filter to somehow estimate the value of these parameters? If so, can you please explain to my how I can do it and if I need to redfine my system.

Thinking along the line of Online-parameter estimation. If Kalman Filter cannot be used, can you explain why and what alternatives are there?

Thank you for taking the time to read my question

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    \$\begingroup\$ The KF estimates the state, and not the A, B, C, D matrices. You need parameter estimation - Matlab has a toolbox to do this, including least squares, instrumental variable \$\endgroup\$ – Chu Sep 29 '16 at 13:36
  • \$\begingroup\$ that is true, however the I have seen some works do the so called -joint state-parameter estimation- with the Kalman filter. \$\endgroup\$ – TheCake90 Sep 29 '16 at 13:52

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