I’m obviously not @junpenglao , but my interpretation of this model is a type of statespace model, with a GRW hidden state and non-guassian emissions. This is perfectly kosher. I think the marketing guys used to do something similar to this for time-varying parameters, but they now recommend using an HSGP instead; maybe @cetagostini can confirm?
On that note, you might be interested in this post by @bwengals where he shows equivalence between a GP with a certain kernel and a GRW.