Propagation and fusion of uncertain geometric information

Propagation and fusion of geometric information is of great significance in multisensorial systems, mainly in robotics applications, where multiple sensors or mobile sensor systems that change their perspective of the environment capture uncertain sparse, and sometimes partial, geometric data. In a sensor data fusion problem a set of constraints that describe the relationships between problem inputs and desired solutions can be defined. Constraints and geometric features can be organized in a graph in which nodes stand for geometric primitives – whose uncertainty in their location is represented by regions in their parameter spaces – and arcs for constraints. This paper deals with the problem of propagating uncertainty sets over graphs of geometric constraints. When a new measurement is acquired, a new uncertainty set is introduced for the corresponding geometric feature. This set is propagated all over the graph of geometric constraints and fused at each node with previous information, updated sets are thus obtained as well as final uncertainty regions for each feature.