Optimal FSL smoothing for delayed descriptor systems

In the brief, the optimal FSL (fixed-small-lag) smoother for descriptor systems is considered, where there are instantaneous and single delayed measurement, and the above two series of measurements have been corrupted by multiplicative noises. Singular value decomposition and projection theorem are used to deal with such a difficult problem, the fixed-small-lag smoother is presented for the case of the fixed-lag m being smaller than the delay d.