Miss distance is an important parameter of assessing highly maneuvering targets interception. Due to the noise-corrupted measurement and the fact that not all the state variables can be directly measured, the miss distance becomes a random variable with a priori unknown distribution. Currently, such a distribution is mainly evaluated by the method of Monte Carlo simulation. In this paper, an analytic approach is obtained in discrete-time controlled system with noise-corrupted state information. The system is subject to a bang-bang control strategy. The analytic distribution is validated through the comparison with Monte Carlo simulation.