I would like to estimate this system with state space modeling in order to perform some initial tests as an empirical analysis.
$ \begin{cases} x_t = \mu_t + \beta_1x_t + \varepsilon \\ \mu_t = c_{t-1} + \gamma \mu_{t-1} + \epsilon_{1,t}\\ c_{t} = \rho c_{t-1} + \epsilon_{2,t} \end{cases} $
Do you know if there is a standard toolbox (R or Matlab) that allows me to express the two states equation with the autoregressive component? I've already checked some toolboxes but I wasn't able to express the states equation in this way.