In this paper, we consider the problem of state estimation using the standard Kalman filter recursions which takes account of the available sensor health information. Given a stochastic description of the sensor health, we are able to show that the expected error covariance converges to a unique value for all initial values, while the available previous work only showed the upper bound of the expected error covariance converges. Our approach provides both theoretical value to the analysis as well as the potential to get tighter upper bound. Our results provide a criterion of evaluating the sensor measurement. In the multisensor fusion problem, depending on the system error tolerance levels, it can then be determined whether to fuse a particular sensor measurement or not. Examples and simulations are provided to assist the theory.