  This paper develops an analytical method of truncating inequality constrained
Gaussian distributed variables where the constraints are themselves described
by Gaussian distributions. Existing truncation methods either assume hard
constraints, or use numerical methods to handle uncertain constraints. The
proposed approach introduces moment-based Gaussian approximations of the
truncated distribution. This method can be applied to numerous problems, with
the motivating problem being Kalman filtering with uncertain constraints. In a
simulation example, the developed method is shown to outperform unconstrained
Kalman filtering by over 40% and hard-constrained Kalman filtering by over 17%.
