An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest problem settings, however, it is not possible to compute the standard Bayesian conditional mean estimate due to the associated computationally infeasible high-dimensional integrals. Thus we present an estimator that is closely related to the conditional mean (based on asymptotic theory and empirical experience) but is computationally feasible in all settings of practical interest. We demonstrate the procedure on a problem in missile accuracy analysis. The article also includes some comments on the potential application of several other Bayesian techniques—namely the Laplace and Gibbs sampling integration methods—in the CEP estimation problem, as well as some comments on how our technique could apply in certain other (i.e., non-CEP) high-dimensional estimation problems.