An augmented optimal filter for multi-channel stochastic singular systems with multiplicative noise

An augmented optimal filtering algorithm is proposed for multi-channel stochastic singular systems with multiplicative noise in this paper. First, the state estimation problem of the systems is transformed into the problem for reduced-order subsystems by restricted equivalent transformation. Then, based on the subsystems the problem is transformed into the normal form by state augmentation. So the standard results for nonsingular systems with multiplicative noise can be used. The filtering algorithm on the basis of the linear minimum variance criterion is given and optimal estimation of dynamic noise is also obtained by the algorithm. The effectiveness of the proposed algorithm is shown by a simulation example.