I'm currently working on state-dependent parameter modeling based on the methodology described in a paper provided by my professor. I have little prior experience in this field, and I’m struggling to fully grasp the formulas and underlying concepts.
The task given to me is to fit a model to a rainfall dataset using several features: Wind Speed over 2 minutes (WSF2), Wind Direction over 2 minutes (WDF2), Maximum Temperature, and Minimum Temperature, with the goal of predicting rainfall. From my understanding of the paper, 𝑢𝑑(𝑘)
represents the discrete-time sampled input signals. The final model described in the paper uses a quasi-ARMAX structure, with parameters approximated using RNNs. The predicted output is modeled as the difference between the current and previous measured outputs, where the measured outputs are obtained by adding noise to the ideal (noise-free) output.
What I need help with is confirming whether I’ve correctly understood this framework. Specifically, I’m unsure if using WSF2 and WDF2 as disturbance noise (as my professor instructed) is appropriate. Based on my interpretation, these should be part of the input vector 𝑢𝑑(𝑘), not treated as external noise. Shouldn't the dataset be modeled first to determine how these variables relate to the output, and only then apply the method described in the paper?
I'd really appreciate if someone could review my understanding and clarify if my concern is valid.
P/s: images of equations of delta_y_m (difference measured outputs) and related variables included


