Generally speaking, we use a linear model to estimate parameters. Of course, we can use nonlinear model to estimate parameters too but it could be much more complicated [The first particle filter routines was released in Dynare 4.3. But it was not that clean and efficient at that time. Now It should be stable and efficient.]
In the linear model, variables are usually log-linearized[LaTex] \hat{x}_{t}\equiv\log x_{t}-\log x[/LaTex] So in order to take data to model, we could define a growth variable as [LaTex]\text{d}x\equiv\log x_{t}-\log x_{t-1}=\hat{x}_{t}-\hat{x}_{t-1}[/LaTex]then we define dx as varobs in Dynare model file. Then the growth data could be constructed from statistical level data and taken to model by loading the data into the model.
So the data are not necessarily be de-trended using HP filter when one estimate the parameters in the model though sometimes it is used. To my understanding, in this case, the cycle part of the HP filter is taken to model variable [LaTex]\hat{x}_{t}[/LaTex]directly without defining a new observable variable. By definition, the cycle part of HP filter is the periodic variation around its trend. And the log-deviation form [LaTex]\hat{x}_{t}[/LaTex] refers to the deviation from its steady state value. In this sense, the cycle part of HP filter matches [LaTex]\hat{x}_{t}[/LaTex] in implication to some extent.