  We have developed a general Bayesian algorithm for determining the
coordinates of points in a three-dimensional space. The algorithm takes as
input a set of probabilistic constraints on the coordinates of the points, and
an a priori distribution for each point location. The output is a
maximum-likelihood estimate of the location of each point. We use the extended,
iterated Kalman filter, and add a search heuristic for optimizing its solution
under nonlinear conditions. This heuristic is based on the same principle as
the simulated annealing heuristic for other optimization problems. Our method
uses any probabilistic constraints that can be expressed as a function of the
point coordinates (for example, distance, angles, dihedral angles, and
planarity). It assumes that all constraints have Gaussian noise. In this paper,
we describe the algorithm and show its performance on a set of synthetic data
to illustrate its convergence properties, and its applicability to domains such
ng molecular structure determination.
