Algorithm 1 Computation of ideal Kalman filter gains on Poisson-distributed sequence. The gains do not depend on the actual measurements, so there is no need to include them in the calculations.

$k_{1,1}^p=1$ for j from 1 to n   $k_{j,0}=c_j^p/(h^2{c}_j^p+{\sigma }_R^2)$   $c_j=(1-k_{j}h)c_j^p$   $k_{j,l}=(1-k_{j}h)k_{j,l}^p,l\in 1,\dots ,j$   $c_{n+1}^p=c_n+\Delta T_n{\sigma }_Q^2$   $k_{j+1,l}^p=k_{j,l+1},l\in 0,\dots ,j$ end