Kalman smoother and weighted fusion algorithm for fractional systems

For the linear discrete fractional state-space systems, a fractional Kalman smoother is presented in this paper. The detail derivation is given. For the multisensor linear discrete fractional state-space systems, a weighted measurement fusion algorithm is presented based on the linear minimum variance optimal fusion rules. It is rigorously proved that the weighted measurement fusion fractional Kalman smoother is numerically identical to the centralized fusion fractional Kalman smoother, so that it has the global optimality. Its effectiveness is shown by a simulation example.