In 1961, James and Stein discovered a remarkable estimator which dominates the maximum-likelihood estimate of the mean of a p-variate normal distribution, provided the dimension p is greater than two. This paper, by applying "James-Stein estimation theory", derives the James-Stein state filter (JSSF), which is a robust version of the Kalman filter. The JSSF is designed for situations where the parameters of the state-space evolution model are not known with any certainty.