Filtering in discrete-time systems with state and observation noises correlated on a finite time interval

The aim of this note is to give recurrence equations for the state estimate and the error covariance of a linear discrete-time system whose state and observation noises arc correlated on a finite time interval. More precisely, we give the recurrence state estimation equations for the system (1) , (2) under the assumptions that noises w(k) and w(l) are uncorrelated for , while and are uncorrelated for or , where are known nonnegative integers.