A parallel supervision system is built in this paper in order to accurately estimate vehicle $\rm CO_2$ emissions. Only on-board diagnostics (OBD)-independent information is used, making the model capable of making predictions based on future road gradients and planned speed trajectories. Based on the parallel theory, the actual traffic environment is considered the physical world, while the combined $\rm CO_2$ model (which consists of physical and data-driven models) is the core part of the artificial world. The physical model uses a cascaded structure with engine speeds and torques as intermediate variables, and the data-driven model relies on a modified long short-term memory (LSTM) neural network. When the historical data is sufficient in size and diversity, the data-driven model is appropriate and achieves more accurate estimations; otherwise, the physical model is preferable because of its greater robustness. Based on this combined model, the supervision system can leverage both the learning ability and physics-based knowledge. Two real-world experimental case studies have been performed to validate this system. According to the research analysis, both the physical and data-driven models achieve sufficient accuracy. The physical model indicates more robustness even when some primary parameters (gear ratios) are unknown, which can be used as a supplement to the data-driven model. Moreover, the deterioration factor (DF) of vehicle $\rm CO_2$ emissions is considered to simulate aged vehicles. This parallel supervision system can effectively address the gap between regulatory test cycles and real-world carbon emissions.