The authors consider the following linear mean-square stable system
where is the system state vector, is the measurement, is the state combination to be estimated, and are Wiener processes, is the disturbance signal satisfying
and all the matrices are constants and of the appropriate dimensions. They consider the following filter for the estimation of :
and invstigate the stochastic filtering problem: given , find an asymptotically stable linear filter of the above form that leads to an estimation such that
is negative for all nonzero .