2.5.3. Global the Second-Stage Pose Estimation

The factor graph structure of the global two-stage optimization is similar to that of the single platform, the difference is that in the global optimization process only the GNSS positioning information (if any) is needed to be taken into consideration. This is due to the GNSS positioning information from different agents will also generate new position constraints on the global map making the track change significantly and intersect, even if there is no visual re-location at that position. In this case, we would lower the threshold in line with the RANSAC algorithm. If it can pass the detection after reducing the number of inner points, a new closed-loop will be established here. The subsequent processing is consistent with the closed-loop process described above.

#### **3. Simulation and Experimental Result**

#### *3.1. Virtual Simulation Experiment Platform*

The overall architecture of the multi-unmanned platform simulation system based on Unity3D and ROS architecture is shown in Figure 5. The UAV flight control and visual simulation is based on Flightmare [22]. The ROS Gazebo [23] simulation environment was run on Computer A to constrain the movements of UAVs and UGVs through dynamic models, and to generate the true values of the position and motion velocity. Position and velocity errors were superimposed to generate virtual IMU and GNSS data. Among them, GPS positioning information in GPGGA format was chosen as GNSS satellite positioning. The location and timestamp of an agent sent to the visual simulation module was passed through ROS-Unity3D interface. The visual simulation module moves the agent's model to the corresponding coordinates, renders the photo, and finally sends the most up-todate image and timestamp to the algorithm verification program on Computer B. The configuration of the two computers in the figure is shown in the Table 1.
