The invention is a method and apparatus for determining the shape and location of objects by trilateration based on the output of a plurality of range sensors. The range measurements from a plurality of sensors are correlated with each other to identify one or more potential objects. With respect to each potential object, it is assumed that the object can be one of a finite number of possible predefined shapes. For each potential object, a metric is calculated for each of the predefined shapes using the set of range measurements upon which the potential object is based defining the likelihood that the set of readings correspond to an actual object of that predefined shape. Each potential object is then assumed to have the predefined shape that yielded the lowest metric (i.e., that yielded the metric that indicates the highest likelihood that the object has the corresponding shape). The list of potential objects is then ordered according by their calculated metrics from lowest to highest. The ordered list is then pared down to a smaller list of actual objects by selecting the potential object highest on the ordered list and assuming that it is an actual object and then removing from the list all other lower-ordered potential objects that are based on any of the individual measurements upon which the selected object is based and repeating this process until all potential objects on the list have either been selected as an actual object or removed from the list.