  We consider the problem of estimating a random state vector when there is
information about the maximum distances between its subvectors. The estimation
problem is posed in a Bayesian framework in which the minimum mean square error
(MMSE) estimate of the state is given by the conditional mean. Since finding
the conditional mean requires multidimensional integration, an approximate MMSE
estimator is proposed. The performance of the proposed estimator is evaluated
in a positioning problem. Finally, the application of the estimator in
inequality constrained recursive filtering is illustrated by applying the
estimator to a dead-reckoning problem. The MSE of the estimator is compared
with two related posterior Cram\'er-Rao bounds.
