Systems and methods for operating a robotic system. The methods comprise: inferring, by a computing device, a first heading distribution for the object from a 3D point cloud; obtaining, by the computing device, a second heading distribution from a vector map; obtaining, by the computing device, a posterior distribution of a heading using the first and second heading distributions; defining, by the computing device, a cuboid on a 3D graph using the posterior distribution; and using the cuboid to facilitate driving-related operations of a robotic system.