Mix Frequency Without Explicit Growth Trend

Dear Prof. Pfeifer,

I have a question about your book, A Guide to Specifying Observation Equations for the Estimation of DSGE Models.
book link
In section 7.3, Mixed frequency without explicit growth trend, listing 15, we are converting a quarterly model into monthly frequency. we can only observe quarterly data for y. so we create y_tilde_quarterly, and relate it to monthly y, y_tilde.
from my understanding, the observations should be y_tilde_quarterly. However, in your listing 15, the varobs includes y_tilde.

Could you help me understand why it is y_tilde here rather than y_tilde_quarterly?

Thank you so much for your help in advance!


Really appreciate any inputs at this point.