We describe a proposed architecture for the Large Synoptic Survey Telescope (LSST) moving object processing pipeline based on a similar system under development for the Pan-STARRS project. This pipeline is responsible for identifying and discovering fast moving objects such as asteroids, updating information about them, generating appropriate alerts, and supporting queries about moving objects. Of particular interest are potentially hazardous asteroids (PHA's). We consider the system as being composed of two interacting components. First, candidate linkages corresponding to moving objects are found by tracking detections ("tracklets"). To achieve this in reasonable time we have developed specialized data structures and algorithms that efficiently evaluate the possibilities using quadratic fits of the detections on a modest time scale. For the second component we take a Bayesian approach to validating, refining, and merging linkages over time. Thus new detections increase our belief that an orbit is correct and contribute to better orbital parameters. Conversely, missed expected detections reduce the probability that the orbit exists. Finally, new candidate linkages are confirmed or refuted based on previous images. In order to assign new detections to existing orbits we propose bipartite graph matching to find a maximum likelihood assignment subject to the constraint that detections match at most one orbit and vice versa. We describe how to construct this matching process to properly deal with false detections and missed detections.