Hello,

I'm currently trying to implement a Kalman Filter for the state estimation for an LSTM, the only thing is how can I be sure the state is observable? I managed to separate the state update equation and the measurement equation, retrieving the network written in state-space form:

x(k+1) = f(x(k), u(k))

y(k) = g(x(k))

I already implemented an Unscented Kalman Filter, it yields good results, but I have no proof about if the filter is safely working or not, I have no guaranties about the state observability. I'm worried about the fact that currently is working well because is not exploring unobservable states, hiding the possible instability of the observer.

Does anyone know how to proceed?

Thank you all.

Simone Pozzoli