(Part of) the idea seems to be synthesizing missing data from later observations of the known data, i. e. "to arrive at this state (A_t,C_t,E_t), the initial state must have been...(A_t-1,B_t-1,C_t-1,E_t-1)..."

I have my doubts that this can just overcome the fundamental problem of chaos, but it doesn't sound impossible.