I am trying to use DLM package in R to estimate a state space repersentation of the term structure model, where observation and state equation are as follows

y_t= F\beta_t+\epsilon_t

\beta_{t+1}= \bar{\beta}+\eta_t

where \epsilon_t and \eta_t are Gaussian. Only modification with standard DLM representation in the R is the term \bar{\beta}

(random coefficient) (which is also unknown and has to be estimated via maximum likelihood with dlmmle) in the state equation. I am not sure how to use DLM package to estimate such models.

I would be extremely grateful for the any help in this regard.