This paper presents a maximum likelihood approach to 3-D complex-object position estimation. To this end a simple 3-D modeling scheme for complex objects is proposed. The surface of an object is modeled as a collection of patches of primitive quadrics, i.e., planar, cylindrical, and spherical patches, possibly augmented by boundaries. The primitive surface-patch models are specified by geometric parameters, reflecting location, orientation, and dimension information of the 3-D primitives. The object-position estimation is based on sets of range data points, each set associated with a model primitive. The range data may be obtained by laser range finders or by passive or active stereo vision. Probability density functions are introduced that model the generation of range measurement of points on the 3-D primitives. This entails the formulation of a noise mechanism in three-space accounting for inaccuracies in the 3-D measurements and possibly for inaccuracies in the 3-D modeling. A formal probabilistic mechanism is derived to combine the various pieces of 3-D information obtained from the different data patches. In this way special attention is directed at appropriately weighting the estimated local geometric parameters of the object primitives to arrive at an optimal overall object-position estimation. In this paper the problem of matching object features to measurement features is not addressed. The work reported here appears to be the first to treat object positioning within a formal statistical estimation framework. The techniques used are based on asymptotic analysis, and are not restricted to range data but can be applied to any type of data. They permit controlled decomposition of a large problem into small problems where maximum likelihood estimation or Bayesian estimation or recognition can be realized locally, and these results can be combined to arrive at globally optimum estimation or recognition.