Innovation calculation

[NPounder]

Is there a reason why fwd_modelled is calculated as bellow and isn't just H0? I expect the innovations to be y-H0 where y is the observation vector and H0 the forward modelled observations but it is currently as below. There is another variable, y (as opposed to y_orig) which is calculated as
y = y_orig + H_matrix.x0 - H0 so perhaps this used to use y instead of y_orig (although the different x is unexplained). Perhaps this is a different measure of the innovation?
The uncertainty correction is currently using the innovations but needs y-H0 so it would be good to understand the intention here?
fwd_modelled = H_matrix_.dot(x_analysis-x_forecast) + H0
innovations = y_orig - fwd_modelled
https://github.com/multiply-org/KaFKA-InferenceEngine/blob/de745bb2478e8b29354a604ac5e612044267f0f7/kafka/inference/solvers.py#L72-73

[NPounder]

I have modified the innovations to be y-H0 for now as these are needed for the correction (in branch timePropagation). If alternative versions of innovation are required we can discuss the best solution.