The limiting variance of the estimation error is obtained for the optimal H-2 filter for discrete time systems when the intensity of the measurement noise tends to zero. In particular, an explicit expression is obtained for the lowest achievable mean-square error when the measurement noise is slowly varying and has intensity which tends to zero. This limitation can be characterized completely by the system order, the dimension of the process noise, the number of the system's transmission zeros, and the location of the system's unstable transmission zeros. (C) 2003 Elsevier Science Ltd. All rights reserved.