  A generalized state space representation of dynamical systems with random
modes switching according to a white random process is presented. The new
formulation includes a term, in the dynamics equation, that depends on the most
recent linear minimum mean squared error (LMMSE) estimate of the state. This
can model the behavior of a feedback control system featuring a state
estimator. The measurement equation is allowed to depend on the previous LMMSE
estimate of the state, which can represent the fact that measurements are
obtained from a validation window centered about the predicted measurement and
not from the entire surveillance region. The LMMSE filter is derived for the
considered problem. The approach is demonstrated in the context of target
tracking in clutter and is shown to be competitive with several popular
nonlinear methods.
