Suppose that we have the regular system used in Kalman-Bucy filtering as $$dX(t)=F(t)X(t)dt+G(t)dB^1_t $$ $$ dZ(t)=H(t)X(t)dt+V(t)dB^2_t $$
The only difference is that $(H(t),V(t)) $ are randomly picked from an independently distribution of pairs $(H^\tau (t),V^\tau(t))_\tau $ where $\tau$ follows a exponential distribution.
Is there any paper/book/etc. working with these sort of filtering? Is it at all implementable?